JP7003261B2 - 変調重複変換のための分析／合成ウインドウ関数 - Google Patents

変調重複変換のための分析／合成ウインドウ関数 Download PDF

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JP7003261B2
JP7003261B2 JP2020526081A JP2020526081A JP7003261B2 JP 7003261 B2 JP7003261 B2 JP 7003261B2 JP 2020526081 A JP2020526081 A JP 2020526081A JP 2020526081 A JP2020526081 A JP 2020526081A JP 7003261 B2 JP7003261 B2 JP 7003261B2
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ルツキー・マンフレッド
チェカリンスキー・アレクサンダー
ガイガー・ラルフ
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Description
１．背景
重複変換が、いくつかのオーディオコーディングの用途に関して開発されている。これらの変換は、通常は、オーディオ信号に関して、より大きなデータセット（例えば、２つの連続したフレーム）の連続したブロックについて実行される。後続のブロックが重複してよい。したがって、或るブロックの最後の部分が、後続のブロックの最初の部分と一致する。ウインドウ関数を使用することができる。
変調重複変換を具現化する非対称修正離散コサイン変換（ＭＤＣＴ）ウインドウ、非対称修正離散サイン変換（ＭＤＳＴ）、および時間－周波数変換が開発されている。
非対称修正離散コサイン変換（ＭＤＣＴ）ウインドウ、非対称修正離散サイン変換（ＭＤＳＴ）ウインドウ、および他の種類のウインドウが、とりわけオーディオコーディングの用途などの低遅延の信号の用途に関して、対称形状と比べて良好な周波数応答をもたらすがゆえに、過去数年において開発されてきた。
例えばＧ．７１８またはＭＰＥＧ－４ ＡＡＣ－ＥＬＤウインドウなど、第１世代のウインドウ形状は、周波数応答の設計に注目していたにすぎない。最近の開発においては、例えば３ＧＰＰ ＥＶＳコーデックにおいて使用されるＡＬＤＯウインドウなど、量子化誤差の時間変調に関与するウインドウの時間的形状も考慮されている。
しかしながら、そこで提示されている設計手法には、ウインドウ形状が不連続な微分を示し、周波数応答が最適にならないという問題が伴う。この文書において説明される発明は、この問題を克服するための解決策を提示する。
２．発明の概要
一態様によれば、複数のフレームを含んでいる情報信号をエンコードするための装置であって、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している分析ウインドウ関数を使用して変調重複変換分析を実行するように構成され、情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を、周波数ドメイン（ＦＤ）表現へと変換する変調重複変換ツールと、
情報信号またはその処理されたバージョンのＦＤ表現に基づいて、ビットストリームを作成するように構成されたビットストリームライタと
を備えており、
分析ウインドウ関数は、非対称であるように定義され、
分析ウインドウ関数は、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義され、
分析ウインドウ関数は、絶対的な最大値が第１および第３の区間の一方にあるように定義され、
線形関数は、定数値１による定数関数である、装置が提供される。
分析ウインドウ関数を、分析ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義することができる。
情報信号をエンコードするための装置は、複数のフレームを含むことができ、装置は、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している分析ウインドウ関数を使用して変調重複変換分析を実行するように構成され、情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を、周波数ドメイン（ＦＤ）表現へと変換する変調重複変換ツールと、
情報信号またはその処理されたバージョンのＦＤ表現に基づいて、ビットストリームを作成するように構成されたビットストリームライタと
を備えることができ、
分析ウインドウ関数は、非対称であるように定義され、
分析ウインドウ関数は、分析ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義され、
線形関数は、定数関数である。
情報信号をエンコードするための装置は、複数のフレームを含むことができ、装置は、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している分析ウインドウ関数を使用して変調重複変換分析を実行するように構成され、情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を、周波数ドメイン（ＦＤ）表現へと変換する変調重複変換ツールと、
情報信号またはその処理されたバージョンのＦＤ表現に基づいて、ビットストリームを作成するように構成されたビットストリームライタと
を備えることができる。
装置は、
時間入力バッファならびに／あるいはコサインまたはサイン値を分析ウインドウ関数の値でスケーリングする
ように構成された変調重複変換ツールを備えることができる。
装置は、
Figure 0007003261000001
、および
Figure 0007003261000002
の形態の入力バッファを使用するように構成された変調重複変換ツールを備えることができ、
ここで
Figure 0007003261000003
は、時間的瞬間
Figure 0007003261000004
における情報信号または情報信号の処理されたバージョンのＴＤサンプルであり、
Figure 0007003261000005
は、１フレームにおいて処理されるサンプルの数であり、
Figure 0007003261000006
は、変調重複変換ウインドウにおける先頭のゼロの数である。
装置は、
Figure 0007003261000007
を実行するように構成された変調重複変換ツールを備えることができ、
ここでは、
Figure 0007003261000008
は、周波数インデックス
Figure 0007003261000009
における変調重複変換周波数値であり、
Figure 0007003261000010
は、時間的瞬間であり、
Figure 0007003261000011
は、分析ウインドウ関数であり、
Figure 0007003261000012
は、時間入力バッファであり、
Figure 0007003261000013
は、１フレームにおいて処理されるサンプルの数である。
周波数ドメイン（ＦＤ）において定義された情報信号またはその処理されたバージョンをデコードするための装置は、
情報信号をエンコードしているビットストリームを読み取るように構成されたビットストリームリーダと、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンについて逆変調重複変換合成を実行するように構成された逆変調重複変換ツールと
を備えることができ、
合成ウインドウ関数は、非対称であるように定義され、
合成ウインドウ関数は、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義され、
合成ウインドウ関数は、絶対的な最大値が第１および第３の区間の一方にあるように定義され、
線形関数は、定数値１による定数関数である。
装置は、
合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義された合成ウインドウ関数
を備えることができる。
周波数ドメイン（ＦＤ）において定義された情報信号またはその処理されたバージョンをデコードするための装置は、
情報信号をエンコードしているビットストリームを読み取るように構成されたビットストリームリーダと、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンについて逆変調重複変換合成を実行するように構成された逆変調重複変換ツールと
を備えることができ、
合成ウインドウ関数は、非対称であるように定義され、
合成ウインドウ関数は、合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義され、
線形関数は、定数関数である。
周波数ドメイン（ＦＤ）において定義された情報信号またはその処理されたバージョンをデコードするための装置が、
情報信号をエンコードしているビットストリームを読み取るように構成されたビットストリームリーダと、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンについて逆変調重複変換合成を実行するように構成された逆変調重複変換ツールと
を備えることができる。
装置において、逆変調重複変換ツールは、
時間ドメインエイリアシングバッファにおける値を合成ウインドウ関数の値でスケーリングする
ように構成されてよい。
装置において、逆変調重複変換ツールは、
Figure 0007003261000014
の形態の時間ドメイン（ＴＤ）信号表現を生成するように構成されてよく、
ここで
Figure 0007003261000015
は、エイリアシングバッファであり、
Figure 0007003261000016
は、情報信号またはその処理されたバージョンであり、
Figure 0007003261000017
は、ＴＤフレームのサンプルの数である。
装置において、逆変調重複変換ツールは、
時間エイリアシングされたバッファのウインドウ処理を実行する
ように構成されてよい。
装置において、逆変調重複変換ツールは、
Figure 0007003261000018
を実行することによってウインドウ処理を実行するように構成されてよい。
装置において、逆変調重複変換ツールは、重畳加算演算を実行するように構成されてよい。
装置において、逆変調重複変換ツールは、重畳加算演算を
Figure 0007003261000019
Figure 0007003261000020
Figure 0007003261000021
として実行するように構成されてよく、
ここで
Figure 0007003261000022
は、出力値であり、
Figure 0007003261000023
は、ウインドウ処理された時間エイリアシングバッファであり、
Figure 0007003261000024
は、１フレーム内のサンプルの数である。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、絶対的な最大値が第１または第３の区間にあるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、蛇行部分において、相対的な最大値が第１または第３の区間にあり、相対的な最小値が第２の区間にあるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、蛇行部分において、第１および第３の区間の少なくとも一方に対応する蛇行ウインドウ関数の値が０．９よりも大きくなるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、蛇行部分において、２つのフレームの３０％および５０％からなる区間において線形関数よりも大きい値を呈するように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、分析ウインドウ関数および／または合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、分析ウインドウ関数および／または合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること５％未満であるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、－３＊１０－４～＋３＊１０－４の間の第２の数値微分を呈するように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、－２＊１０－５～＋２＊１０－５の間の第３の数値微分を呈するように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、－０．０１～＋０．０１の間の第１の数値微分を呈するように定義される
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、－１０－４～＋１０－４の間の第２の数値微分を呈するように定義される
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、－１０－５～＋１０－５の間の第２の数値微分を呈するように定義される
ような装置であってよい。
装置は、
線形関数が、非増加関数であるように定義されてよい
ような装置であってよい。
装置は、
線形関数が、狭義減少関数であるように定義されてよい
ような装置であってよい。
装置は、
線形関数が、非減少関数であるように定義されてよい
ような装置であってよい。
装置は、
線形関数が、狭義増加関数であるように定義されてよい
ような装置であってよい。
装置は、
線形関数が、一定の値あるいは最大＋２％または－２％で変化する値を有するように定義されてよい
ような装置であってよい。
装置は、
線形関数が、－０．０５～－０．２０の間の増分を有するように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、非対称であるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および合成ウインドウ関数が、互いの時間反転バージョンであるように定義されてよい
ような装置であってよい。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数の値を記憶するための記憶スペース
を備えることができる。
装置において、修正重複変換は、修正離散コサイン変換（ＭＤＣＴ）または修正離散サイン変換（ＭＤＳＴ）であってよく、逆修正重複変換は、逆修正離散コサイン変換（ＩＭＤＣＴ）または逆修正離散サイン変換（ＩＭＤＳＴ）である。
装置は、
分析ウインドウ関数および／または合成ウインドウ関数が、定数値１による定数関数であってよい
ような装置であってよい。
システムが、
としてのエンコーダと、
前記装置としてのデコーダと
を備えることができる。
システムにおいて、エンコーダは、ビットストリームを送信するように構成された通信ユニットを備えることができ、かつ／またはデコーダは、ビットストリームを受信するように構成された通信ユニットを備える。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している分析ウインドウ関数を使用して情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を周波数ドメイン（ＦＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）分析を実行すること、を含む方法が提供される。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している分析ウインドウ関数を使用して情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を周波数ドメイン（ＦＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）分析を実行することを含んでおり、
分析ウインドウ関数は、非対称であるように定義され、
分析ウインドウ関数は、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義され、
分析ウインドウ関数は、絶対的な最大値が第１および第３の区間の一方にあるように定義され、
線形関数は、定数値１による定数関数である、方法が提供される。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している分析ウインドウ関数を使用して情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を周波数ドメイン（ＦＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）分析を実行することを含んでおり、
分析ウインドウ関数は、非対称であるように定義され、
分析ウインドウ関数は、分析ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義され、
線形関数は、定数関数である、方法が提供される。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンの周波数ドメイン（ＦＤ）表現を時間ドメイン（ＴＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）合成を実行すること、を含む方法が提供される。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンの周波数ドメイン（ＦＤ）表現を時間ドメイン（ＴＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）合成を実行することを含んでおり、
合成ウインドウ関数は、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義され、
合成ウインドウ関数は、絶対的な最大値が第１および第３の区間の一方にあるように定義され
線形関数は、定数値１による定数関数である、方法が提供される。
一態様によれば、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンの周波数ドメイン（ＦＤ）表現を時間ドメイン（ＴＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）合成を実行することを含んでおり、
合成ウインドウ関数は、非対称であるように定義され、
合成ウインドウ関数は、合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％未満であるように定義され、
線形関数は、定数関数である、方法が提供される。
プロセッサ上で実行されたときに一方法を前記プロセッサに実行させることができる命令を格納した非一時的な記憶ユニット。
複数のフレームを含む情報信号をエンコードするための装置であって、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している分析ウインドウ関数を使用して修正離散コサイン変換（ＭＤＣＴ）分析を実行するように構成され、情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を、周波数ドメイン（ＦＤ）表現へと変換するＭＤＣＴツールと、
情報信号またはその処理されたバージョンのＦＤ表現に基づいて、ビットストリームを作成するように構成されたビットストリームライタと
を備える装置が提供される。
例において、ＭＤＣＴツールは、時間入力バッファおよび／またはコサイン値を分析ウインドウ関数の値でスケーリングするように構成される。
例において、ＭＤＣＴツールは、
Figure 0007003261000025
の形態の入力バッファを使用するように構成され、
ここで
Figure 0007003261000026
は、時間的瞬間
Figure 0007003261000027
における情報信号または情報信号の処理されたバージョンのＴＤサンプルであり、
Figure 0007003261000028
は、１フレームにおいて処理されるサンプルの数であり、
Figure 0007003261000029
は、ＭＤＣＴウインドウにおける先頭のゼロの数である。
例において、初期化を、
Figure 0007003261000030
として実行することができる。
例において、ＭＤＣＴ（または、ＭＤＳＴ）ツールは、
Figure 0007003261000031
を実行するように構成され、
ここで
Figure 0007003261000032
は、周波数インデックス
Figure 0007003261000033
におけるＭＤＣＴ（または、ＭＤＳＴ）周波数値であり、
Figure 0007003261000034
は、時間的瞬間であり、
Figure 0007003261000035
は、分析ウインドウ関数であり、
Figure 0007003261000036
は、時間入力バッファであり、
Figure 0007003261000037
は、１フレームにおいて処理されるサンプルの数である。
例において、
情報信号をエンコードしているビットストリームを読み取るように構成されたビットストリームリーダと、
少なくとも４つの地点に対応して線形関数と交差する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンについて逆修正コサイン変換（ＩＭＤＣＴ）（または、ＩＭＤＳＴ）合成を実行するように構成されたＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールと
を備える装置が提供される。
例において、ＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールは、時間ドメインエイリアシングバッファにおける値を合成ウインドウ関数の値でスケーリングするように構成される。
例において、ＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールは、
Figure 0007003261000038
の形態の時間ドメイン（ＴＤ）信号表現を生成するように構成され、
ここで
Figure 0007003261000039
は、エイリアシングバッファであり、
Figure 0007003261000040
は、情報信号またはその処理されたバージョンであり、
Figure 0007003261000041
は、ＴＤフレームのサンプルの数である。
例において、ＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールは、時間エイリアシングされたバッファのウインドウ処理を実行するように構成される。
例において、ＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールは、
Figure 0007003261000042
を実行することによってウインドウ処理を実行するように構成される。
例において、ＩＭＤＣＴ（または、ＩＭＤＳＴ）ツールは、例えば
Figure 0007003261000043
Figure 0007003261000044
Figure 0007003261000045
としてであってよい重畳加算演算を実行するように構成され、
ここで
Figure 0007003261000046
は、出力値であり、
Figure 0007003261000047
は、ウインドウ処理された時間エイリアシングバッファであり、
Figure 0007003261000048
は、１フレーム内のサンプルの数である。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、蛇行部分において、
第１の交差点と第２の交差点との間の第１の区間において線形関数よりも大きくなり、
第２の交差点と第３の交差点との間の第２の区間において線形関数よりも低くなり、
第３の交差点と第４の交差点との間の第３の区間において線形関数よりも大きくなる
ように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、絶対的な最大値が第１または第３の区間にあるように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、蛇行部分において、相対的な最大値が第１または第３の区間にあり、相対的な最小値が第２の区間にあるように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、蛇行部分において、第１および第３の区間の少なくとも一方に対応する蛇行ウインドウ関数の値が０．９よりも大きくなるように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、蛇行部分において、２つのフレームの３０％および５０％からなる区間において線形関数よりも大きい値を呈するように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、分析ウインドウ関数および／または合成ウインドウ関数の最大値が同じ時間的瞬間における線形関数の値を上回ること２５％（特に、５％）未満であるように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、－３＊１０－４～＋３＊１０－４の間の第２の数値微分および／または－２＊１０－５～＋２＊１０－５の間の第３の数値微分を呈するように定義される。
例において、線形関数は、一定の値あるいは最大＋２％または－２％で変化する値を有するように定義される。
例において、線形関数は、－０．０５～－０．２０の間の増分を有するように定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数は、非対称であるように定義される。
例において、分析ウインドウ関数および合成ウインドウ関数は、互いに対称に定義される。
例において、分析ウインドウ関数および／または合成ウインドウ関数の値を記憶するための記憶スペース。
例において、
上述および／または後述のとおりの装置としてのエンコーダと、
上述および／または後述のとおりの装置としてのデコーダと
を備えるシステムが提供される。
例において、エンコーダは、ビットストリームを送信するように構成された通信ユニットを備え、かつ／またはデコーダは、ビットストリームを受信するように構成された通信ユニットを備える。
例において、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している分析ウインドウ関数を使用して情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を周波数ドメイン（ＦＤ）表現へと変換するためのＭＤＣＴ（ＭＤＳＴ）分析を実行すること、を含む方法も提供される。
例において、少なくとも４つの地点に対応して線形関数を通過する蛇行部分を有している合成ウインドウ関数を使用して情報信号またはその処理されたバージョンの周波数ドメイン（ＦＤ）表現を時間ドメイン（ＴＤ）表現へと変換するためのＭＤＣＴ（または、ＭＤＳＴ）合成を実行すること、を含む方法も提供される。
本発明に使用される分析および／または合成ウインドウ関数は、ＭＤＣＴ（または、ＭＤＳＴ）合成および分析の実行に特に適することが注目されている。
変調重複変換のための分析／合成ウインドウ関数の例、ならびにそれらを使用する方法および装置が、以下に開示される。
３．図面の説明
先行技術による仕組みを示している。 先行技術による仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例によるエンコーダを示している。 例によるエンコーダを示している。 例によるデコーダを示している。 例によるデコーダを示している。 例による方法を示している。 例による方法を示している。 例による装置を示している。 例による装置を示している。 例による仕組みを示している。 先行技術による仕組みを示している。 例による仕組みを示している。 例による仕組みを示している。 例による仕組みを示している。 例による仕組みを示している。 例による仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。 例による関数の仕組みを示している。
４．例
情報信号を、時間ドメインＴＤにおいて、サンプルの連続として記述することができる（例えば、ブロックｂおよび例えば時刻などのインデックスｎについてのｘｂ（ｎ））。ＴＤ表現は、それぞれが複数のサンプルに関連付けられた複数のフレームで構成され得る。周波数ドメインＦＤにおいて、フレームを、それぞれが特定の周波数に関連付けられた一連のビン（例えば、Ｘ（ｋ））（各々の周波数はインデックスｋに関連付けられている）として表すことができる。
変調重複変換技術（例えば、修正離散コサイン変換（ＭＤＣＴ）技術、または修正離散サイン変換（ＭＤＳＴ）技術、など）を使用して、ＴＤ表現をＦＤ表現に変換することができる。そのような技術を、例えばエンコーダ側に実装し、サンプリングされた値を周波数値に変換することができる。
逆変調重複変換技術（逆修正離散コサイン変換（ＩＭＤＣＴ）技術、または逆修正離散サイン（ＩＭＤＳＴ）技術、など）を使用して、ＦＤ表現をＴＤ表現に変換することができる。そのような技術を、例えばデコーダ側に実装し、（例えば、再生を実行するために）周波数値をＴＤ値に変換することができる。
下記の表が、以下の箇所で用いられる記号を示している
Figure 0007003261000049
 図１３および図１３Ａが、それぞれエンコーダ装置１３０および１３０Ａを示している。エンコーダ装置１３０または１３０Ａのそれぞれは、信号処理技術を実行することができる機能ブロックなどの複数のツールを備えることができる。これらのブロックのそれぞれは、スタンドアロンのデバイスであってよく、あるいはハードウェア構造をエンコーダ装置１３０および１３０Ａの他のツールと分け合う機能ブロックであってよい。
エンコーダ装置１３０または１３０Ａは、情報信号（例えば、オーディオ信号）を時間ドメイン（ＴＤ）表現から周波数ドメイン（ＦＤ）表現へと変換することができる変調重複変換ツール１３１（低遅延修正離散コサイン変換（ＭＤＣＴ）ツール、または低遅延修正離散サイン変換（ＭＤＳＴ）ツール、または別の種類の変調重複変換ツール、など）を備えることができる。変調重複変換ツール１３１（例えば、ＭＤＣＴまたはＭＤＳＴツール）は、変調重複変換分析（例えば、ＭＤＣＴ分析、ＭＤＳＴ分析）を実行する。
例えば変調重複変換ツール１３１の下流に位置し、あるいはＴＤにおいて動作する他のツールが、設けられてよい。それらのいくつかが、ここで言及される。
エンコーダ装置１３０は、ＦＤにおいて線形予測符号化（ＬＰＣ）分析を実行するためのＬＰＣツール１３２を備えることができる。エンコーダ装置１３０Ａは、ＦＤにおいてＬＰＣ分析を実行するためのスペクトルノイズシェーピング（ＳＮＳ）ツール１３２Ａを備えることができる。
ＳＮＳを、ＬＰＣの一般化と見なすことができ、したがって、いくつかの例においては、ＬＰＣブロック１３２を、ＳＮＳツール１３２Ａの特定の例と見なすことができる（したがって、エンコーダ装置１３０を、エンコーダ装置１３０Ａの特定の例と見なすことができる）。
エンコーダ装置１３０および１３０Ａのそれぞれは、ＦＤにおいて（例えば、変調重複変換ツールによって出力された）情報信号の各々のウインドウ内のノイズの時間形状を制御するための時間ノイズシェーピング（ＴＮＳ）ツール１３３を備えることができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、ＦＤにおいて信号を処理するスペクトル量子化器１３４を備えることができる。ＴＮＳツール１３３によって出力された信号を、例えばデッドゾーンプラス一様しきい値スカラ量子化（ｄｅａｄ－ｚｏｎｅ ｐｌｕｓ ｕｎｉｆｏｒｍ ｔｈｒｅｓｈｏｌｄｓ ｓｃａｌａｒ ｑｕａｎｔｉｚａｔｉｏｎ）を使用して、量子化することができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、例えばスペクトル量子化器１３４の下流のノイズレベル推定器１３６を備えることができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、例えばエントロピーコーディングを実行し、例えばビットストリームを圧縮するために、ＦＤにおいて信号を処理するコーダ１３５を備えることができる。コーダ１３５は、例えばエントロピーコーディングを実行することができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、例えばデコーダにおける帯域幅コントローラを制御することができる帯域幅検出器１３７ａを備えることができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、時間ドメインＴＤにおいて信号を処理するツールを備えることができる。例えば、エンコーダ装置１３０または１３０Ａは、デコーダ側のＴＤにおいてアクティブなロングタームポストフィルタリング（ＬＴＰＦ）を制御するためのリサンプリングツール１３８ａ（例えば、ダウンサンプラ）および／またはＬＴＰＦツール１３８ｂを備えることができる。
エンコーダ装置１３０および１３０Ａのそれぞれは、上流に配置されたＴＤおよび／またはＦＤツールから得られたデータでビットストリームを準備するためのビットストリームマルチプレクサツール（ビットストリームライタ）１３７を備えることができる。ビットストリームは、情報信号のデジタル表現を、デコーダ側で使用される制御データと共に含むことができる。ビットストリームは、圧縮されてよく、あるいは圧縮された部分を含むことができる。
図１４および図１４Ａが、それぞれデコーダ装置１４０および１４０Ａを示している。デコーダ装置１４０および１４０Ａのそれぞれは、例えば、例えばエンコーダ１３０または１３０Ａによってエンコードされた情報信号のデジタル表現をデコードすることができる。
デコーダ装置１４０および１４０Ａのそれぞれは、信号表現をＦＤからＴＤへと変換するために、逆変調重複変換ツール１４７（例えば、低遅延逆ＭＤＣＴツールまたは低遅延逆ＤＭＳＴツール）を備えることができる。変調重複変換ツール１４７は、変調重複変換合成（例えば、ＭＤＣＴ合成および／またはＭＤＳＴ合成、など）を実行する。
例えば逆変調重複変換ツール１４７の上流に位置し、あるいはＴＤにおいて動作する他のツールが、設けられてよい。それらのいくつかが、ここで言及される。
デコーダ装置１４０および１４０Ａのそれぞれは、エンコーダ装置（例えば、装置１３０または１３０Ａ）から（例えば、伝送によって）ビットストリームを取得するためのビットストリーム多重化ツール１４１を備えることができる。例えば、エンコーダ装置１３０または１３０Ａからの出力が、デコーダ装置１４０または１４０Ａへの入力信号としてもたらされてよい。
デコーダ装置１４０および１４０Ａのそれぞれは、例えばビットストリーム内のデータを解凍することができるデコーダ１４２を備えることができる。算術デコーディングが実行されてよい。残差デコーディングが実行されてもよい。
デコーダ装置１４０および１４０Ａのそれぞれは、ＦＤにおいて信号を処理するノイズフィリングツール１４３を備えることができる。
デコーダ装置１４０および１４０Ａのそれぞれは、ＦＤにおいて信号を処理するグローバルゲインツール１４４を備えることができる。
デコーダ装置１４０および１４０Ａのそれぞれは、ＦＤにおいて信号を処理するＴＮＳデコーダツール１４５を備えることができる。
デコーダ装置１４０は、ＭＤＣＴ（または、ＭＤＳＴ）シェーピングツール１４６を備えることができる（他の重複変換ツールも可能である）。ＭＤＣＴ（または、ＭＤＳＴ）シェーピングツール１４６は、ＦＤスペクトル（例えば、ＭＤＣＴまたはＭＤＳＴスペクトル、など）へと変換されたデコードされたＬＰフィルタ係数（例えば、ＬＰＣデコーディングツール１４６ａから得られる）から計算された利得係数を適用することによって信号を処理することができる。
デコーダ装置１４０Ａは、例えばＳＮＳツール１３２ＡからＬＰＣ係数を取得するＳＮＳデコーダツール１４６Ａ’を備えることができる。
デコーダ装置１４０および１４０Ａのそれぞれは、ＴＤにおいてポストフィルタを実行するためのＬＴＰＦツール１４８を備えることができる。
デコーダ装置１４０Ａは、例えば、帯域幅検出器１３７ａから帯域幅情報を取得することができるデコーダ帯域幅コントローラ１４９を備えることができる。
エンコーダ装置１３０（または、１３０Ａ）およびデコーダ装置１４０（または、１４０Ａ）は、システムを形成するように互いに合わせて構成されてよい。
基本的に、エンコーダ装置１３０または１３０Ａにおける変調重複変換ツール１３１の下流のツールおよびデコーダ装置１４０または１４０Ａにおける逆変調重複変換ツール１４７の上流のツールは、ＦＤにおいて信号処理を実行でき、したがってＦＤツールである。
ここで、例えばツール１３１および１４７における変換技術に関する技術が論じられる。
一般的に、ＭＤＣＴ、ＭＤＳＴ、などは、重複変換であるという追加の特性を有する離散変換である。これらの変換のうちの１つが、より大きなデータセット（例えば、２つの連続するフレーム）の連続するブロックについて実行される。後続のブロックが重複してよい。したがって、或るブロックの最後の部分が、後続のブロックの最初の部分に一致し得る。ウインドウ関数ｗｎ（ｎ＝０，…，２Ｎ－１）を使用することができる。特に、ウインドウ関数を、重みとして使用することができる。利点は、ブロックの境界における不連続を回避または低減できることである。
図１５が、例えば変調重複変換ツール１３１（ＭＤＣＴツールであってよい）において変調重複変換分析を実行するための方法１５０を示している。現在のフレーム
Figure 0007003261000050
の入力信号
Figure 0007003261000051
は、
Figure 0007003261000052
個のオーディオサンプルで構成されてよく、最新のオーディオサンプルは
Figure 0007003261000053
に位置する。
ステップＳ１５１において、入力バッファを更新することができる。変調重複変換
Figure 0007003261000054
のための時間入力バッファを、以下のように更新することができる。
Figure 0007003261000055
Figure 0007003261000056
Figure 0007003261000057
後者は、一貫性のためだけに必要な初期化である。
ステップＳ１５２において、
Figure 0007003261000058
個の時間サンプルのブロックを、以下の式
Figure 0007003261000059
を使用して周波数係数
Figure 0007003261000060
に変換することができ、ここで
Figure 0007003261000061
は、使用されるフレームサイズに応じた非対称変調重複変換ウインドウ（例えば、ＭＤＣＴウインドウ）である。
図１６が、例えば変調重複変換ツール１４７（ＩＭＤＣＴツールであってよい）において変調重複変換合成（例えば、ＭＤＣＴ合成）を実行するための方法１６０を示している。ここで、スペクトル
Figure 0007003261000062
（すなわち、ＦＤにおける表現）を、以下のステップによってＴＤへと変換することができる。
ステップＳ１６１において、フレーム
Figure 0007003261000063
の時間ドメインエイリアシングバッファ
Figure 0007003261000064
の生成を実行することができる。例えば、
Figure 0007003261000065
である。
ステップＳ１６２において、時間ドメインエイリアシングバッファのウインドウ処理を実行することができる。例えば、
Figure 0007003261000066
である。
ステップＳ１６３において、フレーム
Figure 0007003261000067
の再構成された時間サンプル
Figure 0007003261000068
を得るための重畳加算（ｏｖｅｒｌａｐ－ａｄｄ）演算を実行することができる。例えば、
Figure 0007003261000069
Figure 0007003261000070
である。
特に、分析におけるウインドウ関数
Figure 0007003261000071
（分析ウインドウ関数）および合成におけるウインドウ関数
Figure 0007003261000072
（合成ウインドウ関数）を、互いに時間反転となるように定義することができる。分析および合成ウインドウのウインドウ係数は、互いの時間反転バージョンである。
特に有効なウインドウ関数（例えば、合成ウインドウ関数）が、４つの地点に対応して線形関数と交差する蛇行部分を有する分析ウインドウ関数であってよいことが、注目されている。
図４が、分析ウインドウ関数４０を示している。分析ウインドウ関数４０を、０～２Ｎの間で定義することができ、あるいは０と２Ｎの８０％～８５％または９０％の間の中間値（例えば、８１．２５％）との間で定義することができる。いくつかの例において、分析ウインドウ関数４０は、異なる（例えば、より広い）範囲において定義されてもよい。
分析ウインドウ関数４０は、少なくとも一部分について、線形関数４０’を参照して定義されてもよい。図４において、線形関数４０’は、値が１の定数関数である。しかしながら、線形関数４０’は、一般に、例えば
Figure 0007003261000073
に関して定義される線形関数であってよく、ここで
Figure 0007003261000074
は、０～２Ｎの間（または、その非ゼロ部分）のインデックスであり、
Figure 0007003261000075
および
Figure 0007003261000076
は定数である。
分析ウインドウ関数４０は、蛇行部分４４を含むことができる。蛇行部分４４は、分析ウインドウ関数４０が４つの地点＃１、＃２、＃３、＃４において線形関数４０’に出会い、さらには／あるいは交差するような蛇行部分であってよい。
蛇行部分４４は、分析ウインドウ関数４０が、例えばインデックスのうちの９９％超など、インデックスの大部分において線形関数４０’とは異なるような蛇行部分であってよい。
蛇行部分４４は、少なくとも地点（交差点＃１、＃２、＃３、＃４）に関するインデックスのうちの１つの直前の１つのインデックスにおいて、分析ウインドウ関数４０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数の値（例えば、１）よりも大きく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、分析ウインドウ関数４０の値が交差点における線形関数の値よりも小さくなるような蛇行部分であってよい。
蛇行部分４４は、少なくとも交差点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、分析ウインドウ関数４０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数の値（例えば、１）よりも小さく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、分析ウインドウ関数４０の値が交差点における線形関数の値よりも大きくなるような蛇行部分であってよい。
蛇行部分４４は、交差点＃１、＃２、＃３、＃４のそれぞれが、先行および後続の交差点にすぐには連続しないような蛇行部分であってよい。例えば、２つの交差点＃１、＃２、＃３、および＃４の間で、分析ウインドウ関数４０の少なくとも１つのインデックスが、同じインデックスにおける分析ウインドウ関数４０の値と一致しない値を有する。
分析ウインドウ関数４０を、蛇行部分４４に対応して、
・第１の交差点＃１と第２の交差点＃２との間の第１の区間４１において線形関数４０’よりも大きくなり、
・第２の交差点＃２と第３の交差点＃３との間の第２の区間４２において線形関数４０’よりも低くなり、
・第３の交差点＃３と第４の交差点＃４との間の第３の区間４３において線形関数４０’よりも大きくなる
ように定義することができる。
第１の交差点＃１は、第２の交差点＃２に先行でき、第２の交差点＃２は、第３の交差点＃３に先行でき、第３の交差点＃３は、第４の交差点＃４に先行できる。
蛇行部分４４は、最初の交差点と最後の（例えば、第４の）交差点との間を延びることができる。いくつかの例において、交差点は、４つだけであってよい。
さらに、分析ウインドウ関数４０は、負の最小値に到達し得る初期減少部分４５を含むことができる。負の最小値は、２Ｎの６．２５％と２Ｎの１８．７５％との間に位置することができる。さらに、分析ウインドウ関数４０は、負の最小値から蛇行部分４４に向かって（例えば、第１の交差点＃１に向かって）急速に増加する急増部分４６を含むことができる。さらに、分析ウインドウ関数４０は、蛇行部分４４から０へと急速に減少する急減部分４７を含むことができる。さらに、分析ウインドウ関数４０は、２Ｎ（２つのフレームのサイズ）の８０％～８５％または９０％の間で始まり、２Ｎの終わりまで続くことができる常時ゼロ部分４８を含むことができる。
絶対的な最大値４１’は、第１の区間４１（または、第３の区間）に位置する。
分析ウインドウ関数４０は、蛇行部分４４において、第３の区間４３（または、第１の区間）に位置する相対的な最大値４３’を有することができ、相対的な最小値４２’が、第２の区間４２に位置する。
分析ウインドウ関数４０は、蛇行部分４４において、０．９よりも大きい第２の区間４２に対応する蛇行ウインドウ関数４０の値を有することができる。第２の区間４２は、０．９よりも上であってよい。
分析ウインドウ関数４０は、蛇行部分４４において、２つのフレーム（２Ｎ）の３０％および５０％からなる区間において線形関数４０’よりも低い値を呈することができる。例において、２つのフレーム（２Ｎ）の５０％の後で、ウインドウ関数４０は線形関数４０’よりも大きくてよい。したがって、地点＃３は、第１のフレームの最後のインデックスに対応でき、あるいは第２のフレームの最初のインデックスに対応できる。２つのフレームの３０％～５０％の区間において、蛇行ウインドウ部分４４は、線形関数を下回ってよい。
蛇行ウインドウ関数４４の最大値４１’は、同じインデックスｎにおける線形関数４０’の値を上回ること２５％未満（好ましくは、５％または３％未満）であってよい。
分析ウインドウ関数４０は、０．０２～－０．０２の間の第１の数値微分を呈することができる。第２の数値微分は、－５＊１０－４～＋５＊１０－４の間であってよく、好ましくは－３＊１０－４と＋３＊１０－４の間であってよい。第３の数値微分は、－２＊１０－５から＋２＊１０－５の間であってよい。
線形関数４０’は、非増加関数であってよい。それらの例において、線形関数４０’は、非減少関数であってよい。線形関数４０’は、一定の値あるいは最大＋２％または－２％で変化する値を有することができる。
分析ウインドウ関数を、非対称になるように定義することができる。
いくつかの例において、分析ウインドウ関数は、蛇行部分４４の区間（サブセクション）のいくつかが上述の説明に対して逆の順序であるような分析ウインドウ関数であってよい。
図２６および図２７が、分析ウインドウ関数４０を示している（図２７は、図２６の一部分の拡大図である）。分析ウインドウ関数２４０を、０～２Ｎの間で定義することができ、あるいは０と２Ｎの８０％～８５％または９０％の間の中間値（例えば、８１．２５％）との間で定義することができる。いくつかの例において、分析ウインドウ関数４０は、異なる（例えば、より広い）範囲において定義されてもよい。
分析ウインドウ関数４０は、少なくとも一部分について、線形関数２４０’を参照して定義されてもよい。図２７において、線形関数２４０’は、値が１の定数関数である。しかしながら、線形関数４０’は、一般に、例えば
Figure 0007003261000077
に関して定義される線形関数であってよく、ここで
Figure 0007003261000078
は、０～２Ｎの間（または、その非ゼロ部分）のインデックスであり、
Figure 0007003261000079
および
Figure 0007003261000080
は定数である（例えば、ａ＝０、ｂ＝１）。
分析ウインドウ関数２４０は、蛇行部分２４４を含むことができる。蛇行部分２４４は、分析ウインドウ関数２４０が４つの地点＃１、＃２、＃３、＃４において線形関数２４０’に出会い、さらには／あるいは交差するような蛇行部分であってよい。
蛇行部分２４４は、分析ウインドウ関数２４０が、例えばインデックスのうちの９９％超など、インデックスの大部分において、線形関数２４０’とは異なるような蛇行部分であってよい。
蛇行部分２４４は、少なくとも地点（交差点）＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、分析ウインドウ関数２４０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数２４０’の値よりも大きく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、分析ウインドウ関数２４０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数２４０’の値よりも小さくなるような蛇行部分であってよい。
蛇行部分２４４は、少なくとも交差点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、分析ウインドウ関数４０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数２４０’の値よりも小さく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、分析ウインドウ関数４０の値が交差点における線形関数２４０’の値よりも大きくなるような蛇行部分であってよい。
蛇行部分２４４は、交差点＃１、＃２、＃３、＃４のそれぞれが、先行および後続の交差点にすぐには連続しないような蛇行部分であってよい。例えば、２つの交差点＃１、＃２、＃３、および＃４の間で、分析ウインドウ関数２４０の少なくとも１つのインデックスが、同じインデックスにおける分析ウインドウ関数２４０の値と一致しない値を有する。
分析ウインドウ関数２４０を、蛇行部分２４４に対応して、
・第１の交差点＃１と第２の交差点＃２との間の第１の区間２４１において線形関数２４０’よりも大きくなり、
・第２の交差点＃２と第３の交差点＃３との間の第２の区間２４２において線形関数２４０’よりも低くなり、
・第３の交差点＃３と第４の交差点＃４との間の第３の区間２４３において線形関数２４０’よりも大きくなる
ように定義することができる。
第１の交差点＃１は、第２の交差点＃２に先行でき、第２の交差点＃２は、第３の交差点＃３に先行でき、第３の交差点＃３は、第４の交差点＃４に先行できる。
蛇行部分２４４は、最初の交差点と最後の（例えば、第４の）交差点との間を延びることができる。いくつかの例において、交差点は、４つだけであってよい。
分析ウインドウ関数２４０は、すべて正の値を有することができる。最小値は、０という値であってよく、分析ウインドウ関数２４０の最初のインデックスおよび／または分析ウインドウ関数２４０の最後のインデックスに位置することができる。分析ウインドウ関数２４０は、蛇行部分２４４（例えば、第１の交差点＃１）に向かって急速に増加する急増部分２４６を含むことができる。さらに、分析ウインドウ関数２４０は、蛇行部分２４４から０へと急速に減少する急減部分２４７を含むことができる。分析ウインドウ関数２４０は、２Ｎ（２つのフレームのサイズ）の８４％～９０％の間で始まり、２Ｎの終わりまで続くことができる常時ゼロ部分２４８を含むことができる。
絶対的な最大値２４１’は、第１の区間４１（または、第３の区間）に位置する。
分析ウインドウ関数２４０は、蛇行部分２４４において、第３の区間２４３（または、第１の区間）に位置する相対的な最大値２４３’を有することができ、さらには／あるいは相対的な最小値２４２’が、第２の区間２４２に位置する。
分析ウインドウ関数２４０は、蛇行部分２４４において、０．９５よりも大きい第２の区間２４２に対応する蛇行ウインドウ関数２４０の値を有することができる。第２の区間２４２は、０．９５よりも上であってよい。第１および／または第３の区間２４１および／または２４３は、１．０５未満であってよい。
分析ウインドウ関数２４０は、蛇行部分２４４において、２つのフレーム（２Ｎ）の３０％および５０％からなる区間において線形関数２４０’よりも低い値を呈することができる。例において、２つのフレーム（２Ｎ）の５０％の後で、ウインドウ関数２４０は線形関数２４０’よりも大きくてよい。したがって、地点＃３は、第１のフレームの最後のインデックスに対応でき、あるいは第２のフレームの最初のインデックスに対応できる。２つのフレームの３０％～５０％の区間において、蛇行ウインドウ部分２４４は、線形関数を下回ってよい。
蛇行ウインドウ関数２４４の最大値２４１’は、同じインデックスｎにおける線形関数２４０’の値を上回ること２５％未満（好ましくは、５％または３％未満）であってよい。
分析ウインドウ関数２４０は、－０．０１～＋０．０１の間の第１の数値微分を呈することができる。第２の数値微分は、－１０－４～＋１０－４の間であってよい。第３の数値微分は、－１０－５～＋１０－５の間であってよい。
線形関数４０’は、非増加関数であってよい。それらの例において、線形関数４０’は、非減少関数であってよい。線形関数４０’は、一定の値あるいは最大＋２％または－２％で変化する値を有することができる。
分析ウインドウ関数を、非対称になるように定義することができる。
いくつかの例において、分析ウインドウ関数２４０は、蛇行部分２４４の区間（サブセクション）のいくつかが上述の説明に対して逆の順序であるような分析ウインドウ関数であってよい。
図２８および図２９が、分析ウインドウ関数４０および２４０を比較している。
図６が、分析ウインドウ関数６０の別の例を示している。図７が、蛇行部分６４に対応する分析ウインドウ関数６０の拡大図を示している。
この場合、分析ウインドウ関数６０は、少なくとも一部分について、線形関数６０’を参照して定義されてもよい。図７において、線形関数６０’は、線形減少関数（「斜めの線」）である。
蛇行部分６４は、分析ウインドウ関数６０が４つの地点において線形関数６０’に出会い、さらには／あるいは交差するような蛇行部分であってよい。
分析ウインドウ関数４０を、蛇行部分６４に対応して、
・第１の交差点＃１’と第２の交差点＃２’との間の第１の区間６１’において線形関数６０’よりも大きくなり、
・第２の交差点＃２’と第３の交差点＃３’との間の第２の区間６２’において線形関数６０’よりも低くなり、
・第３の交差点＃３’と第４の交差点＃４’との間の第３の区間６３’において線形関数６０’よりも大きくなり、
・第４の交差点＃４’と第５の交差点＃５’との間の第４の区間６４’において線形関数６０’よりも低くなり、
・第５の交差点＃５’と第６の交差点＃６’との間の第５の区間６５’において線形関数６０’よりも大きくなる
ように定義することができる。
絶対的な最大値は、第１の区間６１’に位置してよい（例えば線形関数が増加関数である他の例では、第５の区間に位置してよい）。
分析ウインドウ関数６０は、蛇行部分６４において、第３の区間６３’および／または第５の区間６５’における相対的な最大値を有することができ、相対的な最小値が、第２の区間６２’および／または第４の区間６４’に位置する。
分析ウインドウ関数６０は、蛇行部分６４において、０．９よりも大きく、特に０．９５よりも大きい第１および第３の区間の少なくとも一方に対応するウインドウ関数の値を有することができる（例えば線形関数が増加関数である他の例では、第３および第５の区間にあってよい）。
分析ウインドウ関数６０は、蛇行部分６４において、２つのフレーム（２Ｎ）の３０％および５０％からなる区間において線形関数６０’よりも大きい値を呈することができる。
ウインドウ関数６０の最大値は、同じインデックスｎにおける線形関数６０の値を上回ること２５％未満（好ましくは、５％未満）であってよい。
線形関数６０’は、非増加関数であってよく、特に狭義減少関数（ｓｔｒｉｃｔｌｙ ｄｅｃｒｅａｓｉｎｇ ｆｕｎｃｔｉｏｎ）であってよい。
分析ウインドウ関数を、非対称になるように定義することができる。
例において、分析ウインドウ関数は、図６とは逆の区間を有してもよい。
例において、合成ウインドウ関数は、分析ウインドウ関数に対して対称になると解釈できる。例えば、対称軸は、２Ｎ範囲の中央（例えば、４７９または４８０）にあってよい。
合成ウインドウ関数９０の例が、図９に示されている（例えば、図４の分析ウインドウ関数４０に関連する合成ウインドウ関数）。合成ウインドウ関数９０を、０～２Ｎの間で定義することができ、あるいは２Ｎの１０％または１５％～２０％の間の中間値と２Ｎとの間で定義することができる。
合成ウインドウ関数９０は、少なくとも一部分について、線形関数（この場合には図示されていないが、一定の値１である）を参照して定義されてもよい。図９において、線形関数は、値が１の定数関数であってよい。しかしながら、線形関数は、一般に、例えばｙ＝ａｎ＋ｂに関して定義される線形関数であってよい。
合成ウインドウ関数９０は、蛇行部分９４を含むことができる。蛇行部分９４は、合成ウインドウ関数９０が４つの交差点＃１、＃２、＃３、＃４（＃２だけが図示されている）において線形関数９０’（分かりやすくするために一部分だけが示されているが、定数１）に遭遇および／または交差するような蛇行部分であってよい。合成ウインドウ関数は、ウインドウの中央（地点＃２）、すなわちサンプルつまりサンプルＮ－１とＮとの間で、値１と交差することができる。
蛇行部分９４は、合成ウインドウ関数９０が、例えばインデックスのうちの９９％超など、インデックスの大部分において、線形関数９０’とは異なるような蛇行部分であってよい。
蛇行部分９４は、少なくとも地点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、合成ウインドウ関数９０の値が地点（＃１、＃２、＃３、＃４の）における線形関数の値（例えば、１）よりも大きく、少なくとも（地点に関する）同じインデックスの直後のインデックスにおいて、合成ウインドウ関数９０の値が交差点における線形関数の値よりも小さくなるような蛇行部分であってよい。蛇行部分９４は、少なくとも地点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、合成ウインドウ関数９０の値が地点（＃１、＃２、＃３、＃４の）における線形関数の値よりも小さく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、合成ウインドウ関数９０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数の値よりも大きくなるような蛇行部分であってよい。
蛇行部分９４は、地点＃１、＃２、＃３、＃４のそれぞれが別の地点＃１、＃２、＃３、＃４にすぐには連続しないような蛇行部分であってよい。例えば、＃１、＃２、＃３、および＃４のうちの２つの地点の間で、合成ウインドウ関数９０の少なくとも１つのインデックスが、同じインデックスにおける合成ウインドウ関数９０の値と一致しない値を有してよい。
合成ウインドウ関数９０を、蛇行部分９４に対応して、
・第１の交差点＃１（図９には示されていないが、図４の地点＃４に対称であるとして表すことができる）と第２の交差点＃２（この場合には、例えば２Ｎ範囲の中央の４８０番目のサンプルに位置する）との間の第１の区間９１において線形関数９０’よりも大きくなり、
・第２の交差点＃２と第３の交差点＃３（図９には示されていないが、図４の地点＃３に対称であるとして表すことができる）との間の第２の区間９２において線形関数９０’よりも低くなり、
・第３の交差点＃３と第４の交差点＃４（図９には示されていないが、図４の地点＃１に対称であるとして表すことができる）との間の第３の区間９３において線形関数９０’よりも大きくなる
ように定義することができる。
さらに、合成ウインドウ関数９０は、２Ｎの１０％～１５％の間に位置してよい常時ゼロ部分９８を含むことができる。さらに、合成ウインドウ関数９０は、蛇行部分９４に向かって０から急速に増加する急増部分９７を含むことができる。さらに、合成ウインドウ関数９０は、蛇行部分９４から負の最小値に向かって急速に減少する急減部分９６を含むことができる。負の最小値は、２Ｎの８１．２５％と２Ｎの９３．７％との間に位置することができる。さらに、合成ウインドウ関数９０は、負の最小値から０に達する最終増加部分９５を含むことができる。
絶対的な最大値は、第３の区間９３（または、第１の区間）に位置できる。
合成ウインドウ関数９０は、蛇行部分９４において、第１の区間９１（または、第３の区間）に相対的な最大値を有することができ、相対的な最小値が、第２の区間に位置する。
合成ウインドウ関数９０は、蛇行部分９４において、０．９よりも大きい第１および第３の区間（９１、９３）の少なくとも一方に対応する蛇行ウインドウ関数の値を有することができる。第３の区間は、０．９を上回ることができる。
合成ウインドウ関数９０は、蛇行部分９４において、２つのフレーム（２Ｎ）の３０％および５０％からなる区間において線形関数よりも大きい値を呈することができる。
合成ウインドウ関数９０の最大値は、同じインデックスｎにおける線形関数の値を上回ること２５％未満（好ましくは、５％未満）であってよい。
合成ウインドウ関数９０は、０．０２～－０．０２の間の数値微分を呈することができる。第２の数値微分は、－５＊１０－４～＋５＊１０－４の間であってよく、好ましくは－３＊１０－４と＋３＊１０－４の間であってよい。第３の数値微分は、－２＊１０－５から＋２＊１０－５の間であってよい。
合成線形関数９０は、非増加関数であってよい。他の例において、合成線形関数９０は、非減少関数であってよい。合成線形関数９０は、一定の値あるいは最大＋２％または－２％で変化する値を有することができる。
合成ウインドウ関数９０を、非対称になるように定義することができる。
いくつかの例において、合成ウインドウ関数９０は、図９に示される形状に関して対称な関数であってよい。例えば、０における値は、図９の９６０における値になり、１における値は、図９の９５９における値になり、以下同様である。
合成ウインドウ関数２９０の例が、図３０に示される（例えば、図２６～図２９の分析ウインドウ関数２４０に関連する合成ウインドウ関数）。合成ウインドウ関数２９０を、０～２Ｎの間で定義することができ、あるいは２Ｎの１０％または１５％～２０％の間の中間値と２Ｎとの間で定義することができる。
合成ウインドウ関数２９０は、少なくとも一部分について、線形関数２９０’（この場合には図示されていないが、一定の値１である）を参照して定義されてもよい。
図３０において、線形関数２９０’は、値が１の定数関数であってよい。しかしながら、線形関数は、一般に、例えばｙ＝ａｎ＋ｂに関して定義される線形関数であってよい。
合成ウインドウ関数２９０は、蛇行部分２９４を含むことができる。蛇行部分２９４は、合成ウインドウ関数２９０が４つの交差点＃１、＃２、＃３、＃４（＃２だけが図示されている）において線形関数２９０’（分かりやすくするために一部分だけが示されているが、定数１）に遭遇および／または交差するような蛇行部分であってよい。合成ウインドウ関数は、ウインドウの中央（地点＃２）、すなわちサンプルつまりサンプルＮ－１とＮとの間で、値１と交差することができる。
蛇行部分２９４は、合成ウインドウ関数２９０が、例えばインデックスのうちの９９％超など、インデックスの大部分において、線形関数２９０’とは異なるような蛇行部分であってよい。
蛇行部分２９４は、少なくとも地点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、合成ウインドウ関数９０の値が地点（＃１、＃２、＃３、＃４の）における線形関数の値（例えば、１）よりも大きく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、合成ウインドウ関数９０の値が交差点における線形関数の値よりも小さくなるような蛇行部分であってよい。
蛇行部分２９４は、少なくとも地点＃１、＃２、＃３、＃４に関するインデックスのうちの１つの直前の１つのインデックスにおいて、合成ウインドウ関数２９０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数の値よりも小さく、少なくとも（交差点に関する）同じインデックスの直後のインデックスにおいて、合成ウインドウ関数２９０の値が交差点（＃１、＃２、＃３、＃４の）における線形関数の値よりも大きくなるような蛇行部分であってよい。
蛇行部分２９４は、交差点＃１、＃２、＃３、＃４のそれぞれが別の地点＃１、＃２、＃３、＃４にすぐには連続しないような蛇行部分であってよい。例えば、＃１、＃２、＃３、および＃４のうちの２つの交差点の間で、合成ウインドウ関数２９０の少なくとも１つのインデックスが、同じインデックスにおける合成ウインドウ関数２９０の値と一致しない値を有してよい。
合成ウインドウ関数２９０を、蛇行部分２９４に対応して、
・第１の交差点＃１と第２の交差点＃２（この場合には、例えば２Ｎ範囲の中央の４８０番目のサンプルに位置する）との間の第１の区間２９１において線形関数２９０’よりも大きく（例えば、１よりも大きく）なり、
・第２の交差点＃２と第３の交差点＃３との間の第２の区間２９２において線形関数２９０’よりも低くなり、
・第３の交差点＃３と第４の交差点＃４との間の第３の区間２９３において線形関数２９０’よりも大きくなる
ように定義することができる。
合成ウインドウ関数２９０は、ウインドウ（２Ｎ個のサンプル）の１つの境界に位置してよく、サンプルのうちの１０％～１５％の間を含んでよい常時ゼロ部分２９８を含むことができる。さらに、合成ウインドウ関数２９０は、蛇行部分２９４に向かって０から急速に増加する急増部分２９７を含むことができる。さらに、合成ウインドウ関数２９０は、蛇行部分２９４から０に向かって急速に減少する急減部分２９６を含むことができる。
絶対的な最大値は、第３の区間２９３（または、第１の区間）に位置できる。
合成ウインドウ関数２９０は、蛇行部分２９４において、第１の区間２９１（または、第３の区間）に相対的な最大値を有することができ、相対的な最小値が、第２の区間に位置する。
合成ウインドウ関数２９０は、蛇行部分２９４において、０．９または０．９５よりも大きい第１および第３の区間（２９１、２９３）の少なくとも一方に対応する蛇行ウインドウ関数の値を有することができる。第３の区間は、０．９５を上回ることができる。
合成ウインドウ関数２９０は、蛇行部分２９４において、２つのフレーム（２Ｎ）の３０％および５０％からなる区間において線形関数よりも大きい値を呈することができる。
合成ウインドウ関数２９０の最大値は、同じインデックスｎにおける線形関数の値を上回ること２５％未満（好ましくは、５％または３％未満）であってよい。
合成ウインドウ関数２９０は、－０．０１～＋０．０１の間の数値微分を呈することができる。第２の数値微分は、－１０－４～＋１０－４の間であってよい。第３の数値微分は、－１０－５～＋１０－５の間であってよい。
合成線形関数９０は、非増加関数であってよい。他の例において、合成線形関数９０は、非減少関数であってよい。合成線形関数９０は、一定の値あるいは最大＋２％または－２％で変化する値を有することができる。
合成ウインドウ関数９０を、非対称になるように定義することができる。
いくつかの例において、合成ウインドウ関数９０は、図９に示される形状に関して対称な関数であってよい。例えば、０における値は、図９の９６０における値になり、１における値は、図９の９５９における値になり、以下同様である。
５．検討
この関数が、特にオーディオコーディングのためのＭＤＣＴ（または、ＭＤＳＴなど）およびＩＭＤＣＴ（または、ＩＭＤＳＴなど）の技術にきわめて適した非常に興味深い特徴を有することが、注目されている。
ＭＤＣＴウインドウ形状の滑らかさの指標として、下記のような数値微分を使用する。
Figure 0007003261000081
ＭＤＣＴウインドウの品質を評価するための別の指標は、
Figure 0007003261000082
によって表される量子化誤差の時間形状である。
量子化誤差は、オーディオコーディングプロセスの一部としてスペクトルドメインに導入される可能性がある。
ここで、ＡＬＤＯウインドウについて説明する。ＡＬＤＯは、優れた時間形状を提供する非対称ウインドウの設計手法である。ＥＶＳコーデックにおいて使用されるＡＬＤＯウインドウの設計プロセスは、（３ＧＰＰ）および［２］で説明されている。図１が、ＡＬＤＯウインドウの仕組みについて、概略のウインドウ形状を示している。
ＡＬＤＯウインドウは、４つの部分、すなわち立ち上がり関数、厳密に１の部分、減衰関数、およびゼロで構成される。ｗ４におけるゼロの数が、ｗ２における１の数も決定し、ｗ２＝２＊ｗ４である。ｗ１およびｗ３を求める方法は、［１］および［２］で説明されている。
図２が、パラメータＬｚ＝１８０（ＭＤＣＴウインドウにおける先頭のゼロの数、図１のＷ４（ｎ））に関して、［１］および［２］に従って設計されたＡＬＤＯウインドウを示しており、総ウインドウ長は９６０サンプルである。
図２の４番目の線図（「時間変調量子化誤差」）において見て取ることができるように、ＡＬＤＯは、２つの連続する重複合成ウインドウのエネルギー和が１に近いことを意味する量子化誤差の良好な時間形状を示す。最適な結果は、対称なウインドウ形状によって達成される１だけを必要とすると考えられる。
この設計手法の欠点を、主として、数値微分を大まかに示している図２の２番目の線図（「数値微分」）において見て取ることができる。ウインドウ形状が連続的に微分可能な数学関数ではないため、周波数応答に関して最適ではないことを見て取ることができる。ウインドウ形状における静的な１ゆえに、立ち上がり関数からの滑らかな遷移および減衰関数への滑らかな遷移が、不可能である。
本発明は、時間形状を最適化するために厳密に１の部分を維持するという設計上の制約から離れる。代わりに、それらの１を、線形関数（例えば、「１」などの定数値）の周囲を蛇行する一連の値で置き換える。この解決策は、時間形状を最適な状態の近くに保ちつつ、滑らかで連続的なウインドウ形状を可能にする。
図３が、本発明による蛇行セクション（部分）を備えて設計された典型的なウインドウを示している。図３の４番目の線図（「時間変調量子化誤差」）において見て取ることができるとおり、量子化誤差の時間形状に関するウインドウの特性は、ＡＬＤＯウインドウに類似している。しかしながら、図３の第２の線図（「数値微分」）を図２（ＡＬＤＯウインドウ）の第２の線図と比較すると、本発明により、連続的に微分可能なウインドウ形状を生成できることを、理解できるであろう。これにより、例えば、ＡＬＤＯウインドウに使用される設計プロセスでは不可能であった阻止帯域の減衰がより大きいウインドウ形状の設計が可能になる。
図４が、典型的なウインドウ形状４０をさらに詳細に概説している。この例において、蛇行セクションは、４つの地点に対応する線形関数（この場合は、定数値「１」）との交差に基づく。さらに多くの交差も可能であるが、４つが最も少ない数と考えられる。
このようなウインドウは、周波数応答についての１つの誤差関数を量子化ノイズの最適な時間形状からの偏差を表す誤差関数と組み合わせる数学的最適化プロセスの結果であってよい。
一部の実装は、例えば固定小数点の実装など、特定のデータ形式を必要とした。そのような実装に関して、ウインドウ係数の値の範囲は、１を超える値が異なるスケーリングを必要とするため、スケーリングされ得る。このような場合、蛇行セクションは１の周囲ではない可能性がある。スケーリングを元に戻した後にのみ、値は明白な範囲に入る。
図５が、ＭＤＣＴウインドウ係数５０が固定小数点の実装の内部においてどのように表されるかについての例を示している。これは、固定小数点アーキテクチャゆえに一部の値が２ｘでスケーリングされ、他の値が２ｘ－１でスケーリングされる典型的な表現である。
一般的な場合を考えると、ウインドウは必ずしも１の周囲を蛇行しなくてもよく、仮想の斜め線の周囲を交差することなく蛇行することができる。図６が、３つの異なるウインドウ、すなわち
・ｗ１：１の周囲の新たな最適化された蛇行（ウインドウ関数７０）；
・ｗ２：Ｇ．７１８ウインドウ（まったく蛇行していない）（ウインドウ関数７０’）；
・ｗ３：特別な場合についての新たな最適化されウインドウ：斜め線の周囲を蛇行（ウインドウ関数６０）
を示している。
説明されるＭＤＣＴウインドウは、完全な再構成の特性を満たす。そのため、例えば［３］で説明されているように、ＭＤＣＴがウインドウ操作、時間ドメインエイリアスキャンセル（ＴＤＡＣ）ステップ、および離散コサイン変換（ＤＣＴ）タイプＩＶカーネルとして分解されると考える。
したがって、ウインドウ処理およびＴＤＡＣを、分析における折り畳みステップおよび合成側における展開ステップと見なすことができる。後者において、２つのブロックの展開されたシーケンスが、重畳加算演算にて結合される。ブロック１（８１）およびブロック２（８２）の仕組みを参照する図８を参照されたい。
分析側の重複領域について、ブロック１のウインドウ処理およびＴＤＡＣを、
Ｐ１（ｎ）＝ｗａ（Ｎ＋ｎ）－ｗａ（２Ｎ－１－ｎ）（ここで、ｎ＝０…Ｎ－１）
と表すことができ、ブロック２は
Ｐ２（ｎ）＝ｗａ（Ｎ＋ｎ）＋ｗａ（Ｎ－１－ｎ）（ここで、ｎ＝０…Ｎ－１）
である。
合成側については、Ｐ１およびＰ２が展開され、ウインドウ処理され、重畳加算が実行される。
Ｏ（ｎ）＝ｗｓ（Ｎ＋ｎ）Ｐ１（ｎ）＋ｗｓ（ｎ）Ｐ２（ｎ）（ここで、ｎ＝０…Ｎ－１）
これを、
Ｏ（ｎ）＝ｗａ（Ｎ＋ｎ）ｗｓ（Ｎ＋ｎ）－ｗａ（２Ｎ－１－ｎ）ｗｓ（Ｎ＋ｎ）＋ｗａ（ｎ）ｗｓ（ｎ）＋ｗａ（Ｎ－１－ｎ）ｗｓ（ｎ）（ここで、ｎ＝０…Ｎ－１）
と記述することができ、これを２つの成分に分けることができる。
ＰＲ１：完全な再構成成分
ｗａ（Ｎ＋ｎ）ｗｓ（Ｎ＋ｎ）＋ｗａ（ｎ）ｗｓ（ｎ）＝１（ここで、ｎ＝０…Ｎ－１）
ＰＲ２：エイリアスキャンセル成分
ｗａ（Ｎ－１－ｎ）ｗｓ（ｎ）－ｗａ（２Ｎ－１－ｎ）ｗｓ（Ｎ＋ｎ）＝０（ここで、ｎ＝０…Ｎ－１）
図９～図１２が、分析および合成のシーケンスを示している。
ここで、現在の分析および合成ウインドウ関数の数値微分に関して、図１９および図２０が参照される。
第２および第３の数値微分も考慮することにより、現在の例の特性（例えば、図４の例に関する図１９、および図２６の例に関する図３１）を、先行技術（ＡＬＤＯ、図２０）の特性と明瞭に区別することが可能である。
変調重複変換ウインドウ形状（例えば、ＭＤＣＴまたはＭＤＳＴウインドウ形状）の滑らかさの指標として、次のような数値微分を使用することができる。
Figure 0007003261000083
各々の係数の重要性に重みを付け、すなわち振幅が大きいほど重みも大きくなるように、以下が重み付けを表す。
Figure 0007003261000084
これにより、ウインドウ形状の連続性の分析において低レベルのウインドウ係数を無視することができる。
図１９、図２０、および図３１において、第１の数値微分は、正規の重み付けされたバージョン（破線）でプロットされている。１９０２および３１０２が、本発明のウインドウ関数の第１の数値微分を示しており、１９０４および３１０４（破線）が、本発明のウインドウ関数の第１の数値微分の重み付けされたバージョンを示している。２００２が、ＡＬＤＯウインドウ関数の第１の数値微分を示しており、２００４（破線）が、ＡＬＤＯウインドウ関数の第１の数値微分の重み付けされたバージョンを示している。
第２および第３の数値微分（ＮＤ）について、第１の数値微分の重み付けされたバージョンが使用される。１９１０および３１１０が、本発明のウインドウ関数の第２の数値微分の重み付けされたバージョンを示している。２０１０が、ＡＬＤＯウインドウ関数の第２の数値微分の重み付けされたバージョンを示している。１９２０が、本発明のウインドウ関数の第３の数値微分の重み付けされたバージョンを示している。２０２０および３１２０が、ＡＬＤＯウインドウ関数の第３の数値微分の重み付けされたバージョンを示している。
見て取ることができるとおり、第２のＮＤバージョンが、ＡＬＤＯウインドウについていくつかの明確なピーク２０２１を示しているが、本発明のウインドウは、穏やかな変化しか示していない。第３のＮＤについて、両方のウインドウの振幅レベルも明確に相違し、表現可能である。
ここで、ＡＬＤＯのウインドウ設計および本発明のウインドウ関数の自由度の分析を示す。
ＡＬＤＯの設計手法［２］は、自由度として、パラメータＣ１、Ｃ２およびゼロの数Ｌｚのみを提供する。この提案の方法では、設計プロセスにおいて与えられた自由度がきわめて限定されているため、近接場または非近接場の減衰に注目することが不可能である。
ＡＬＤＯアルゴリズムを拡張してより高い自由度を可能にするために、［２］の設計手法を断念し、数値最適化法と交換する必要がある。第１のステップにおいて、ウインドウの中央の厳密な１の部分を維持しつつ、自由なウインドウ係数（または、設計パラメータ）が最適化される。
分析および合成ウインドウが常に互いの時間反転バージョンであると仮定すると、完全な再構成の制約を、
ｗａ（Ｎ＋ｎ）ｗｓ（Ｎ＋ｎ）＋ｗａ（ｎ）ｗｓ（ｎ）＝１（ここで、ｎ＝０…Ｎ－１）
→ｗ（Ｎ＋ｎ）ｗ（２Ｎ－ｎ）＋ｗ（ｎ）ｗ（Ｎ＋ｎ）＝１（ここで、ｎ＝０…Ｎ－１）
によって表すことができる。
これを、例えば
ｗ（２Ｎ－ｎ）＝（１－ｗ（ｎ）ｗ（Ｎ＋ｎ））／ｗ（Ｎ＋ｎ）（ここで、ｎ＝０…Ｎ－１）
によって自由係数の数を１．５Ｎに制限することで、常に満たすことができる。
ゼロ部分は、ｗ（２Ｎ－ｎ）内に位置する。中央の厳密な１の制約について、ウインドウ係数の２＊Ｌｚが非自由係数と見なされる。変換長がＮ＝４８０であり、ウインドウサイズが２Ｎであり、Ｌｚ＝１８０である場合、自由度は１．５Ｎ－２＊Ｌｚ＝３６０個の自由係数となる。このウインドウは、中間ウインドウと呼ばれる。
新たな発明は、厳密に１の部分を、１の周囲または任意の他の直線状の（例えば、斜めの）線（例えば、４０’、６０’、９０’）の周囲の蛇行セクション（例えば、４４、６４、９４）で取り替えることによって、自由度を最大値まで増加させる。したがって、中央部分の半分だけを自由係数から除外すればよい。結果として、利用可能な係数の数は、１．５＊４８０－１８０＝５４０個の自由係数へと増加する。これにより、任意のインデントされた焦点に向けて周波数応答を最大限に最適化することができる。
図２１および図２２が、設計手法の比較を示している。特に、図２１は、ＡＬＤＯ（２１１）対中間（２１２）対新たな発明（２１３）の比較ウインドウ形状を示している。図２２は、ＡＬＤＯ（２１１）、中間（２１２）、および新たな発明（２１３）のウインドウ形状のズーム（拡大図）を示している。
中間ウインドウおよび新たな発明のウインドウは、同じ焦点に向けて最適化されている。
図２３が、ＡＬＤＯ（２３１）、中間（２３２）、および新たな発明（２３３）による周波数応答のプロットを示している。中間（２３１）および新たな発明のウインドウ（２３３）は、異なる領域に焦点を当てることができ、この場合には、非近接場のより良好な改善を達成する。これは、例えば、帯域制限された信号によって引き起こされるエイリアシング歪みを回避するために必要であり、あるいは信号がフィルタバンクを介してリサンプリングされるときに常に必要である。この焦点は、ＡＬＤＯウインドウでは、形状の制御に使用できるパラメータが２つしかないため、不可能である。中間および新たな発明のウインドウを比較すると、新たな発明においては、時間ドメインにおけるきわめて連続的な形状ゆえに、応答の変動がはるかに少ないことが明らかである。
図２４が、中間（２４２）および新たな発明（２４３）を比較する周波数応答のズーム（拡大図）を示している。見て取ることができるとおり、新たな発明のウインドウ（２４３）は、すべてのサイドロープについて有意に大きい減衰を常に示している。これは、蛇行部分（４４、６４、９４）が厳密な１の部分よりもウインドウの設計に有益であることを裏付けている。
ウインドウの時間変調に関して、ＡＬＤＯウインドウの主な動機が、量子化誤差の大きな時間変動を回避するために、非対称形状を最大振幅１と組み合わせることであることに、注意すべきである。量子化誤差は周波数ドメインにおいて追加され、その時間的形状は、合成ウインドウの形状によって制御される。
実際に、ここでもやはり、蛇行シーケンスは、このウインドウの特性も改善する。図２５が、ＡＬＤＯウインドウ（２５３）および提案される発明（２５１）によって引き起こされる量子化誤差の時間変調の直接比較を示している。見て取ることができるとおり、最大の時間歪みは、新たな発明においてより低く、したがって歪みがあまり目立たない。
上述の例において、蛇行部分は、例えばＤＣＴカーネルと（少なくとも部分的に）対応する。例において、少なくとも１つの第１の交差点（例えば、＃１）が最初のフレームにあり、少なくとも別の交差点（例えば、＃３）が後続のフレームにある。例において、１つの交差点（例えば、＃２）が最初のフレームと後続のフレームとの間の境界にある。
例において、「蛇行」とは、線形関数との交差が少なくとも４つ存在することを意味する（蛇行部分が少なくとも２つの地点、場合によっては少なくとも４つの地点で線形関数と交差する）。例えば、蛇行部分は、増加部分、それに続く減少部分、それに続く増加部分、などを有することができ、あるいは減少部分、それに続く増加部分、それに続く減少部分、などを有することができる。
６．他の例
図１７が、エンコーダ装置１３０（または、１３０Ａ）および／またはＭＤＣＴツール１３１を実装でき、さらには／あるいは方法１５０の少なくともいくつかのステップを実行することができる装置１１０を示している。装置１１０は、プロセッサ１１１と、プロセッサ１１１によって実行されたときにプロセッサ１１１にＭＤＣＴ合成を実行させることができる命令を記憶するブロック１１４を有する非一時的メモリユニット１１２とを備えることができる。さらに、非一時的メモリユニット１１２は、ブロック１１３で、例えば上述のとおりの分析ウインドウ関数を格納することができる。装置１１０は、入力情報信号（例えば、オーディオ信号）を取得することができる入力ユニット１１６を備えることができる。一時的記憶スペース１１８を、更新されるデータを保存するために予約することができる（例えば、入力バッファ）。
図１８は、デコーダ装置１４０（または、１４０Ａ）および／またはＩＭＤＣＴ１４７を実装でき、さらには／あるいは方法１６０を実行することができる装置１２０を示している。装置１２０は、プロセッサ１２１と、プロセッサ１２１によって実行されたときにプロセッサ１２１にとりわけＭＤＣＴ合成プロセスを実行させることができる命令を記憶するブロック１２４を有する非一時的メモリユニット１２２とを備えることができる。装置１２０は、ＦＤにおける情報信号（例えば、オーディオ信号）のデコードされた表現を取得することができる入力ユニット１２６を備えることができる。したがって、プロセッサ１２１は、情報信号のＴＤ表現を得るためのプロセスを実行することができる。このデコードされた表現を、出力ユニット１２７を使用して外部のユニットへと提供することができる。出力ユニット１２７は、例えば、（例えば、Ｂｌｕｅｔｏｏｔｈなどの無線通信を使用して）外部のデバイスおよび／または外部の記憶スペースと通信するための通信ユニットを備えることができる。プロセッサ１２１は、オーディオ信号のデコードされた表現をローカル記憶スペース１２８に保存することができる。
例において、装置１１０および１２０は、同じデバイスであってよい。例において、装置１１０および１２０は、例えば無線で、例えばプロトコルＢｌｕｅｔｏｏｔｈを使用して、情報信号および／または制御データを交換する。
特定の実装の要件に応じて、例をハードウェアにて実装することができる。実装を、例えばフロッピーディスク、デジタル多用途ディスク（ＤＶＤ）、ブルーレイディスク、コンパクトディスク（ＣＤ）、読み出し専用メモリ（ＲＯＭ）、プログラマブル読み出し専用メモリ（ＰＲＯＭ）、消去可能なプログラマブル読み出し専用メモリ（ＥＰＲＯＭ）、電子的に消去可能なプログラマブル読み出し専用メモリ（ＥＥＰＲＯＭ）、またはフラッシュメモリなど、それぞれの方法が実行されるようにプログラマブルなコンピュータシステムと協働する（あるいは、協働できる）電子的に読み取り可能な制御信号を格納したデジタル記憶媒体を使用して実行することができる。したがって、デジタル記憶媒体は、コンピュータにとって読み取り可能であってよい。
一般に、例を、プログラム命令を有するコンピュータプログラム製品として実装することができ、プログラム命令は、コンピュータプログラム製品がコンピュータ上で実行されるときに上記方法のうちの１つを実行するように動作することができる。プログラム命令は、例えば、機械で読み取ることができる媒体に格納されてよい。
他の例は、機械で読み取ることができる担体に格納された本明細書に記載の方法のうちの１つを実行するためのコンピュータプログラムを含む。したがって、換言すると、方法の例は、コンピュータプログラムであり、このコンピュータプログラムは、このコンピュータプログラムがコンピュータ上で実行されたときに本明細書に記載の方法のうちの１つを実行するためのプログラム命令を有する。
したがって、本方法のさらなる例は、本明細書に記載の方法のうちの１つを実行するためのコンピュータプログラムを含み、該コンピュータプログラムが記録されたデータ担体媒体（あるいは、デジタル記憶媒体またはコンピュータにとって読み取り可能な媒体）である。データ担体媒体、デジタル記憶媒体、または記録されたメディアは、無形で一時的な信号ではなく、有形かつ／または非一時的である。
さらなる例は、本明細書に記載の方法のうちの１つを実行する処理ユニット、例えばコンピュータ、またはプログラマブル論理デバイスを含む。
さらなる例は、本明細書に記載の方法のうちの１つを実行するためのコンピュータプログラムがインストールされたコンピュータを含む。
さらなる例は、本明細書に記載の方法のうちの１つを実行するためのコンピュータプログラムをレシーバへと（例えば、電子的または光学的に）伝送する装置またはシステムを含む。レシーバは、例えば、コンピュータ、モバイルデバイス、メモリデバイス、などであってよい。装置またはシステムは、例えば、コンピュータプログラムをレシーバへと伝送するためのファイルサーバを備えることができる。
いくつかの例においては、プログラマブル論理デバイス（例えば、フィールドプログラマブルゲートアレイ）を使用して、本明細書に記載の方法の機能の一部またはすべてを実行することができる。いくつかの例においては、フィールドプログラマブルゲートアレイがマイクロプロセッサと協働して、本明細書に記載の方法のうちの１つを実行することができる。一般に、本方法は、任意の適切なハードウェア装置によって実行され得る。
上述の例は、上述の原理の例示にすぎない。本明細書に記載の構成および詳細について、修正および変更が明らかであることを理解されたい。したがって、本発明は、本明細書における例の説明および解説として提示された特定の詳細によってではなく、添付の特許請求の技術的範囲によってのみ限定される。
７．ウインドウ関数のいくつかの例
ここに数値例を示す。関数を得るための閉じた形式の数式が見つからなかったため、例を以下に示す。以下での値は、いくつかの例においては最初の値が時刻ｎ＝０に関連付けられ、最後の値が最後の時刻ｎ＝２Ｎ－１に関連付けられる（順方向）のに対し、いくつかの例においては最初の値が時刻ｎ＝２Ｎ－１に関連付けられ、最後の値が最初の時刻ｎ＝０に関連付けられる（逆方向）という意味で、逆順または正順で提示され得る。場合によっては、分析ウインドウ関数および合成ウインドウ関数が同じリストから取得されるが、分析ウインドウ関数が逆方向（または、順方向）に読み取られる一方で、合成ウインドウ関数は順方向（または、逆方向）に読み取られる。
以下の例のうちの少なくとも１つを具現化するために、少なくとも１０個の値（例えば、連続した値）からなる部分的連続を抽出することが、これら１０個の値が０とは異なる場合に可能である（例えば、すべてのサンプルまたは少なくとも大部分のサンプルが、これらの少なくとも１０個の値を形成し得る）。公差または
Figure 0007003261000085
１％を許容することができ、いくつかの場合には
Figure 0007003261000086
０．５％、
Figure 0007003261000087
０．０５％、他の場合には
Figure 0007003261000088
２％、
Figure 0007003261000089
５％、他の場合には０％である。
７．１ 図４および図９に関連する例
例において、－７．０７８５４６７０６５１２３９１ｅ－０４ｆなどの表記は、－７．０７８５４６７０６５１２３９１＊１０－４を意味する。「ｆ」は、浮動小数点での表記を指す（場合によっては、省略されてもよい）。
フレームサイズＮ＝８０についてのウインドウ関数
Figure 0007003261000090
の数値例が、ｎ＝０…２Ｎ－１についての１６０個のエントリによって、ここに提示される。上述したように、最後の値は、常に０であってよい。
-7.078546706512391e-04f, -2.098197727900724e-03f, -4.525198076002370e-03f,
-8.233976327300612e-03f, -1.337713096257934e-02f, -1.999721557401502e-02f,
-2.800909464274782e-02f, -3.721502082245055e-02f, -4.731768261606175e-02f,
-5.794654834034055e-02f, -6.867606753531441e-02f, -7.904647440788692e-02f,
-8.859705468085925e-02f, -9.688303623049199e-02f, -1.034961241263523e-01f,
-1.080766457616878e-01f, -1.103242262600913e-01f, -1.099809851424550e-01f,
-1.068172142230882e-01f, -1.006190418791648e-01f, -9.116452506492527e-02f,
-7.820617483254730e-02f, -6.146688124166948e-02f, -4.063362855701623e-02f,
-1.536329520788766e-02f, +1.470155068746303e-02f, +4.989736509080558e-02f,
+9.050369257152079e-02f, +1.366911019414417e-01f, +1.884686389218322e-01f,
+2.456456803467095e-01f, +3.077789078889820e-01f, +3.741642373060188e-01f,
+4.438114799213576e-01f, +5.154735456539700e-01f, +5.876661722564289e-01f,
+6.587619767809000e-01f, +7.270576699841359e-01f, +7.908752989295335e-01f,
+8.486643364959733e-01f, +8.991320235484349e-01f, +9.413348145272842e-01f,
+9.747634827941575e-01f, +9.994114730415857e-01f, +1.015760373791603e+00f,
+1.024736164069697e+00f, +1.027634294456205e+00f, +1.025991493983836e+00f,
+1.021427210603284e+00f, +1.015439859549357e+00f, +1.009366925499550e+00f,
+1.003508162416449e+00f, +9.988898206257559e-01f, +9.953133902427869e-01f,
+9.925943919208190e-01f, +9.905771957917731e-01f, +9.891371616557014e-01f,
+9.881790747212391e-01f, +9.876249269174586e-01f, +9.874056275509585e-01f,
+9.874524849192456e-01f, +9.876951134084213e-01f, +9.880640617030884e-01f,
+9.884926873551375e-01f, +9.889230031022089e-01f, +9.893074965384659e-01f,
+9.896146331889107e-01f, +9.898319269347060e-01f, +9.899693102025342e-01f,
+9.900603352632121e-01f, +9.901575015155720e-01f, +9.903255289051605e-01f,
+9.906303787150326e-01f, +9.911298894709990e-01f, +9.918665491182922e-01f,
+9.928619727154252e-01f, +9.941156069136238e-01f, +9.956033775539884e-01f,
+9.972793109558521e-01f, +9.990784840729244e-01f, +1.000922365901945e+00f,
+1.002728111386909e+00f, +1.004416038098237e+00f, +1.005919224127911e+00f,
+1.007189345025525e+00f, +1.008200146369426e+00f, +1.008949493525753e+00f,
+1.009458241425143e+00f, +1.009768980817384e+00f, +1.009940336228694e+00f,
+1.010039453539107e+00f, +1.010132323996401e+00f, +1.010272524848519e+00f,
+1.010494354532353e+00f, +1.010808068774316e+00f, +1.011201071127927e+00f,
+1.011641272406023e+00f, +1.012080125934687e+00f, +1.012458183122033e+00f,
+1.012706955800289e+00f, +1.012755013843985e+00f, +1.012530134411619e+00f,
+1.011962331100864e+00f, +1.010982135506986e+00f, +1.009512438049510e+00f,
+1.007460860286395e+00f, +1.004708677491086e+00f, +1.001111413242302e+00f,
+9.965041017623596e-01f, +9.907199995730845e-01f, +9.823765865983288e-01f,
+9.708821747608998e-01f, +9.546732976073705e-01f, +9.321553861564006e-01f,
+9.018003682081348e-01f, +8.623984077953557e-01f, +8.132817365236141e-01f,
+7.544551974836834e-01f, +6.866580716267418e-01f, +6.113488038789190e-01f,
+5.306181649316597e-01f, +4.471309850999502e-01f, +3.639114681156236e-01f,
+2.841647033392408e-01f, +2.110209448747969e-01f, +1.472287968327703e-01f,
+9.482665349502291e-02f, +5.482436608328477e-02f, +2.701461405056264e-02f,
+9.996743588367519e-03f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f
フレームサイズＮ＝１６０についてのウインドウ関数
Figure 0007003261000091
の数値例が、ｎ＝０…２Ｎ－１についての３２０個のエントリによって、ここに提示される。上述したように、最後の値は、常に０であってよい。
-4.619898752628163e-04f, -9.747166718929050e-04f, -1.664473096973725e-03f,
-2.597106916737789e-03f, -3.806285163352241e-03f, -5.324608721716763e-03f,
-7.175885277771099e-03f, -9.382480860899108e-03f, -1.195270300743193e-02f,
-1.489528159506296e-02f, -1.820666399965468e-02f, -2.187570925786862e-02f,
-2.588471937157619e-02f, -3.020862738245264e-02f, -3.481597793538342e-02f,
-3.967067992672979e-02f, -4.472698045914417e-02f, -4.994225863256500e-02f,
-5.526334794593565e-02f, -6.063717235243996e-02f, -6.600961519440657e-02f,
-7.131966266443390e-02f, -7.651178225890490e-02f, -8.152964005319532e-02f,
-8.631137544905677e-02f, -9.080411291245728e-02f, -9.495377758870335e-02f,
-9.870736514214426e-02f, -1.020202684361974e-01f, -1.048438825017798e-01f,
-1.071382314127799e-01f, -1.088690135027248e-01f, -1.099969655786929e-01f,
-1.104898474883336e-01f, -1.103225838568563e-01f, -1.094621746650760e-01f,
-1.078834293141886e-01f, -1.055612509762041e-01f, -1.024650162703341e-01f,
-9.857014566194629e-02f, -9.384684920715425e-02f, -8.826309993000785e-02f,
-8.178792716809512e-02f, -7.438785600211463e-02f, -6.602189797715241e-02f,
-5.665655641133161e-02f, -4.624456893420224e-02f, -3.474585776145929e-02f,
-2.211581608120528e-02f, -8.310425696208936e-03f, +6.717697635290676e-03f,
+2.300642061077823e-02f, +4.060106462625085e-02f, +5.953239090915557e-02f,
+7.983354189816511e-02f, +1.015233140203748e-01f, +1.246171387327525e-01f,
+1.491152519299797e-01f, +1.750067399059861e-01f, +2.022699854906251e-01f,
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フレームサイズＮ＝２４０についてのウインドウ関数
Figure 0007003261000092
の数値例が、ここに提示される（４８０個のサンプル）。
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フレームサイズＮ＝３２０についてのウインドウ関数
Figure 0007003261000093
の数値例が、ここに提示される（６４０個のサンプル）。
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フレームサイズＮ＝４８０についてのウインドウ関数
Figure 0007003261000094
の数値例が、ここに提示される（９６０個のサンプル）。
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フレームサイズＮ＝９６０についてのウインドウ関数
Figure 0007003261000095
の数値例が、ここに提示される（１９２０個のサンプル）。
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７．２ 図２６～図３０に関連する例
フレームサイズＮ＝４０についてのウインドウ関数
Figure 0007003261000096
の数値例が、ｎ＝０…２Ｎ－１についての８０個のエントリによって、ここに提示される。上述したように、最後の値は、０であってよい。
+9.959086585790517e-04, +3.819056787237678e-03, +9.540832613229890e-03,
+1.921659800166160e-02, +3.382719081038548e-02, +5.424831667522354e-02,
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+0.000000000000000e+00, +0.000000000000000e+00.
フレームサイズＮ＝８０についてのウインドウ関数
Figure 0007003261000097
の数値例が、ｎ＝０…２Ｎ－１についての１６０個のエントリによって、ここに提示される。上述したように、最後の値は、０であってよい。
+6.143388180964179e-04, +1.489582832987000e-03, +2.884104959764029e-03,
+4.934298832466617e-03, +7.779130464154915e-03, +1.154910606525086e-02,
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フレームサイズＮ＝１２０についてのウインドウ関数
Figure 0007003261000098
の数値例が、ｎ＝０…２Ｎ－１についての２４０個のエントリによって、ここに提示される。上述したように、最後の値は、０であってよい。
+5.087227626168386e-04, +9.959086585790517e-04, +1.682208006328800e-03,
+2.609697259047744e-03, +3.819056787237678e-03, +5.349319592933909e-03,
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フレームサイズＮ＝１６０についてのウインドウ関数
Figure 0007003261000099
の数値例が、ｎ＝０…２Ｎ－１についての３２０個のエントリによって、ここに提示される。上述したように、最後の値は、０であってよい。
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フレームサイズＮ＝２４０についてのウインドウ関数
Figure 0007003261000100
の数値例が、ここに提示される（４８０個のサンプル）。
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フレームサイズＮ＝３２０についてのウインドウ関数
Figure 0007003261000101
の数値例が、ここに提示される（６４０個のサンプル）。上述したように、最後の値は、０であってよい。
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フレームサイズＮ＝４８０についてのウインドウ関数
Figure 0007003261000102
の数値例が、ここに提示される（９６０個のサンプル）。上述したように、最後の値は、０であってよい。
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フレームサイズＮ＝９６０についてのウインドウ関数の数値例が、ここに提示される（１９２０個のサンプル）。上述したように、最後の値は、０であってよい。
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参考文
［１］ ３ＧＰＰ， “Ｃｏｄｅｃ ｆｏｒ Ｅｎｈａｎｃｅｄ Ｖｏｉｃｅ Ｓｅｒｖｉｃｅｓ （ＥＶＳ）； Ｄｅｔａｉｌｅｄ ａｌｇｏｒｉｔｈｍｉｃ ｄｅｓｃｒｉｐｔｉｏｎ，” ［Ｏｎｌｉｎｅ］． Ａｖａｉｌａｂｌｅ： ｈｔｔｐ：／／ｗｗｗ．３ｇｐｐ．ｏｒｇ／ｆｔｐ／Ｓｐｅｃｓ／ａｒｃｈｉｖｅ／２６＿ｓｅｒｉｅｓ／２６．４４５／２６４４５－ｄ００．ｚｉｐ
［２］ Ｐ． Ｐ． Ｊｕｌｉｅｎ Ｆａｕｒｅ， “Ｄｅｌａｙ－ｏｐｔｉｍｉｚｅｄ ｏｖｅｒｌａｐ ｔｒａｎｓｆｏｒｍ， ｃｏｄｉｎｇ／ｄｅｃｏｄｉｎｇ ｗｅｉｇｈｔｉｎｇ ｗｉｎｄｏｗｓ”． ＵＳ Ｐａｔｅｎｔ ＵＳ８８４７７９５， ２８ ０６ ２０１１
［３］ Ｇｅｉｇｅｒ， Ａｕｄｉｏ Ｃｏｄｉｎｇ ｂａｓｅｄ ｏｎ ｉｎｔｅｇｅｒ ｔｒａｎｓｆｏｒｍ， Ｉｌｍｅｎａｕ： ｈｔｔｐｓ：／／ｗｗｗ．ｄｂ－ｔｈｕｅｒｉｎｇｅｎ．ｄｅ／ｒｅｃｅｉｖｅ／ｄｂｔ＿ｍｏｄｓ＿０００１００５４， ２００４．

Claims (39)

  1. 複数のフレームを含んでいる情報信号をエンコードするための装置（１３０、１３０Ａ、１１０）であって、
    少なくとも４つの地点（＃１、＃２、＃３、＃４）に対応して線形関数（４０’、２４０’）と交差する蛇行部分（４４、６４、２４４）を有している分析ウインドウ関数（４０、５０、７０、２４０）を使用して変調重複変換分析を実行するように構成され、前記情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を、周波数ドメイン（ＦＤ）表現へと変換する変調重複変換ツール（１３１）と、
    前記情報信号またはその処理されたバージョンの前記ＦＤ表現に基づいて、ビットストリームを作成するように構成されたビットストリームライタ（１３７）と
    を備えており、
    前記分析ウインドウ関数は、非対称であるように定義され、
    前記分析ウインドウ関数（４０、２４０）は、前記蛇行部分（４４、９４、２４４）において、
    第１の交差点（＃１）と第２の交差点（＃２）との間の第１の区間（４１、２４１）において前記線形関数（４０’、２４０’）よりも大きくなり、
    前記第２の交差点（＃２）と第３の交差点（＃３）との間の第２の区間（４２、２４２）において前記線形関数（４０’、２４０’）よりも低くなり、
    前記第３の交差点（＃３）と第４の交差点（＃４）との間の第３の区間（４３、２４３）において前記線形関数（４０’、２４０’）よりも大きくなる
    ように定義され、
    前記分析ウインドウ関数は、絶対的な最大値（４１’、２４１’）が前記第１および第３の区間の一方にあるように定義され、
    前記線形関数（４０、２４０）は、定数値１による定数関数である、装置。
  2. 前記分析ウインドウ関数（４０、２４０）は、前記分析ウインドウ関数（４０、２４０）の最大値が同じ時間的瞬間における前記線形関数（４０、２４０）の値を上回ること２５％未満であるように定義される、請求項１に記載の装置。
  3. 前記変調重複変換ツールは、
    時間入力バッファならびに／あるいはコサインまたはサイン値を前記分析ウインドウ関数（４０、５０、７０、２４０）の値でスケーリングする
    ように構成される、請求項１に記載の装置。
  4. 前記変調重複変換ツールは、
    Figure 0007003261000103
    、および
    Figure 0007003261000104
    の形態の入力バッファを使用するように構成され、
    ここで
    Figure 0007003261000105
    は、時間的瞬間
    Figure 0007003261000106
    における前記情報信号または前記情報信号の処理されたバージョンのＴＤサンプルであり、
    Figure 0007003261000107
    は、１フレームにおいて処理されるサンプルの数であり、
    Figure 0007003261000108
    は、変調重複変換ウインドウにおける先頭のゼロの数である、請求項３に記載の装置。
  5. 前記変調重複変換ツール（１３１）は、
    Figure 0007003261000109
    を実行するように構成され、
    ここで
    Figure 0007003261000110
    は、周波数インデックス
    Figure 0007003261000111
    における変調重複変換周波数値であり、
    Figure 0007003261000112
    は、時間的瞬間であり、
    Figure 0007003261000113
    は、前記分析ウインドウ関数であり、
    Figure 0007003261000114
    は、時間入力バッファであり、
    Figure 0007003261000115
    は、１フレームにおいて処理されるサンプルの数である、請求項１に記載の装置。
  6. 周波数ドメイン（ＦＤ）において定義された情報信号またはその処理されたバージョンをデコードするための装置（１４０、１４０Ａ、１２０）であって、
    前記情報信号をエンコードしているビットストリームを読み取るように構成されたビットストリームリーダ（１４１）と、
    少なくとも４つの地点（＃１、＃２、＃３、＃４）に対応して線形関数と交差する蛇行部分（９４）を有している合成ウインドウ関数（９０）を使用して前記情報信号またはその処理されたバージョンについて逆変調重複変換合成を実行するように構成された逆変調重複変換ツール（１４７）と
    を備えており、
    前記合成ウインドウ関数（９０、２９０）は、非対称であるように定義され、
    前記合成ウインドウ関数（９０、２９０）は、前記蛇行部分（４４、９４、２４４）において、
    第１の交差点と第２の交差点との間の第１の区間において前記線形関数よりも大きくなり、
    前記第２の交差点と第３の交差点との間の第２の区間において前記線形関数よりも低くなり、
    前記第３の交差点と第４の交差点との間の第３の区間において前記線形関数よりも大きくなる
    ように定義され、
    前記合成ウインドウ関数は、絶対的な最大値が前記第１および第３の区間の一方にあるように定義され、
    前記線形関数は、定数値１による定数関数である、装置。
  7. 前記合成ウインドウ関数（９０、２９０）は、前記合成ウインドウ関数（９０、２９０）の最大値が同じ時間的瞬間における前記線形関数（９０、２９０）の値を上回ること２５％未満であるように定義される、請求項６に記載の装置。
  8. 前記逆変調重複変換ツール（１４７）は、
    時間ドメインエイリアシングバッファにおける値を前記合成ウインドウ関数（９０）の値でスケーリングする
    ように構成される、請求項６に記載の装置。
  9. 前記逆変調重複変換ツール（１４７）は、
    Figure 0007003261000116
    の形態の時間ドメイン（ＴＤ）信号表現を生成するように構成され、
    ここで
    Figure 0007003261000117
    は、エイリアシングバッファであり、
    Figure 0007003261000118
    は、前記情報信号またはその処理されたバージョンであり、
    Figure 0007003261000119
    は、ＴＤフレームのサンプルの数である、請求項６に記載の装置。
  10. 前記逆変調重複変換ツール（１４７）は、
    時間エイリアシングされたバッファのウインドウ処理（Ｓ１６２）を実行する
    ように構成される、請求項６に記載の装置。
  11. 前記逆変調重複変換ツール（１４７）は、
    Figure 0007003261000120
    を実行することによってウインドウ処理を実行するように構成される、請求項６に記載の装置。
  12. 前記逆変調重複変換ツール（１４７）は、重畳加算演算（Ｓ１６３）を実行するように構成される、請求項６に記載の装置。
  13. 前記逆変調重複変換ツール（１４７）は、重畳加算演算を
    Figure 0007003261000121
    Figure 0007003261000122
    Figure 0007003261000123
    として実行するように構成され、
    ここで
    Figure 0007003261000124
    は、出力値であり、
    Figure 0007003261000125
    は、ウインドウ処理された時間エイリアシングバッファであり、
    Figure 0007003261000126
    は、１フレーム内のサンプルの数である、請求項６に記載の装置。
  14. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、前記蛇行部分（４４、２４４）において、相対的な最大値（４３’、２４３’）が前記第１または第３の区間（４１、４３、２４１、２４３）にあり、相対的な最小値（４２’、２４２’）が前記第２の区間（４２、２４２）にあるように定義される、請求項１または６に記載の装置。
  15. 前記情報信号は、オーディオ信号である、請求項１または６に記載の装置。
  16. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）の最大値が同じ時間的瞬間における前記線形関数の値を上回ること２５％未満であるように定義される、請求項１または６に記載の装置。
  17. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）の最大値（４１’、２４１’）が同じ時間的瞬間における前記線形関数の値を上回ること５％未満であるように定義される、請求項１または６に記載の装置。
  18. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、－３＊１０－４～＋３＊１０－４の間の第２の数値微分を呈するように定義される、請求項１または６に記載の装置。
  19. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、－２＊１０－５～＋２＊１０－５の間の第３の数値微分を呈するように定義される、請求項１または６に記載の装置。
  20. 前記分析ウインドウ関数（４０、２４０）または前記合成ウインドウ関数（９０）は、互いの時間反転バージョンであるように定義される、請求項１または６に記載の装置。
  21. 前記分析ウインドウ関数（４０、６０）または前記合成ウインドウ関数（９０）の値を記憶するための記憶スペース（１１３）
    をさらに備える、請求項１または６に記載の装置。
  22. 前記変調重複変換は、修正離散コサイン変換（ＭＤＣＴ）または修正離散サイン変換（ＭＤＳＴ）であり、前記逆変調重複変換は、逆修正離散コサイン変換（ＩＭＤＣＴ）または逆修正離散サイン変換（ＩＭＤＳＴ）である、請求項１または６に記載の装置。
  23. 前記分析ウインドウ関数（４０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -7.078546706512391e-04f, -2.098197727900724e-03f, -4.525198076002370e-03f,
    -8.233976327300612e-03f, -1.337713096257934e-02f, -1.999721557401502e-02f,
    -2.800909464274782e-02f, -3.721502082245055e-02f, -4.731768261606175e-02f,
    -5.794654834034055e-02f, -6.867606753531441e-02f, -7.904647440788692e-02f,
    -8.859705468085925e-02f, -9.688303623049199e-02f, -1.034961241263523e-01f,
    -1.080766457616878e-01f, -1.103242262600913e-01f, -1.099809851424550e-01f,
    -1.068172142230882e-01f, -1.006190418791648e-01f, -9.116452506492527e-02f,
    -7.820617483254730e-02f, -6.146688124166948e-02f, -4.063362855701623e-02f,
    -1.536329520788766e-02f, +1.470155068746303e-02f, +4.989736509080558e-02f,
    +9.050369257152079e-02f, +1.366911019414417e-01f, +1.884686389218322e-01f,
    +2.456456803467095e-01f, +3.077789078889820e-01f, +3.741642373060188e-01f,
    +4.438114799213576e-01f, +5.154735456539700e-01f, +5.876661722564289e-01f,
    +6.587619767809000e-01f, +7.270576699841359e-01f, +7.908752989295335e-01f,
    +8.486643364959733e-01f, +8.991320235484349e-01f, +9.413348145272842e-01f,
    +9.747634827941575e-01f, +9.994114730415857e-01f, +1.015760373791603e+00f,
    +1.024736164069697e+00f, +1.027634294456205e+00f, +1.025991493983836e+00f,
    +1.021427210603284e+00f, +1.015439859549357e+00f, +1.009366925499550e+00f,
    +1.003508162416449e+00f, +9.988898206257559e-01f, +9.953133902427869e-01f,
    +9.925943919208190e-01f, +9.905771957917731e-01f, +9.891371616557014e-01f,
    +9.881790747212391e-01f, +9.876249269174586e-01f, +9.874056275509585e-01f,
    +9.874524849192456e-01f, +9.876951134084213e-01f, +9.880640617030884e-01f,
    +9.884926873551375e-01f, +9.889230031022089e-01f, +9.893074965384659e-01f,
    +9.896146331889107e-01f, +9.898319269347060e-01f, +9.899693102025342e-01f,
    +9.900603352632121e-01f, +9.901575015155720e-01f, +9.903255289051605e-01f,
    +9.906303787150326e-01f, +9.911298894709990e-01f, +9.918665491182922e-01f,
    +9.928619727154252e-01f, +9.941156069136238e-01f, +9.956033775539884e-01f,
    +9.972793109558521e-01f, +9.990784840729244e-01f, +1.000922365901945e+00f,
    +1.002728111386909e+00f, +1.004416038098237e+00f, +1.005919224127911e+00f,
    +1.007189345025525e+00f, +1.008200146369426e+00f, +1.008949493525753e+00f,
    +1.009458241425143e+00f, +1.009768980817384e+00f, +1.009940336228694e+00f,
    +1.010039453539107e+00f, +1.010132323996401e+00f, +1.010272524848519e+00f,
    +1.010494354532353e+00f, +1.010808068774316e+00f, +1.011201071127927e+00f,
    +1.011641272406023e+00f, +1.012080125934687e+00f, +1.012458183122033e+00f,
    +1.012706955800289e+00f, +1.012755013843985e+00f, +1.012530134411619e+00f,
    +1.011962331100864e+00f, +1.010982135506986e+00f, +1.009512438049510e+00f,
    +1.007460860286395e+00f, +1.004708677491086e+00f, +1.001111413242302e+00f,
    +9.965041017623596e-01f, +9.907199995730845e-01f, +9.823765865983288e-01f,
    +9.708821747608998e-01f, +9.546732976073705e-01f, +9.321553861564006e-01f,
    +9.018003682081348e-01f, +8.623984077953557e-01f, +8.132817365236141e-01f,
    +7.544551974836834e-01f, +6.866580716267418e-01f, +6.113488038789190e-01f,
    +5.306181649316597e-01f, +4.471309850999502e-01f, +3.639114681156236e-01f,
    +2.841647033392408e-01f, +2.110209448747969e-01f, +1.472287968327703e-01f,
    +9.482665349502291e-02f, +5.482436608328477e-02f, +2.701461405056264e-02f,
    +9.996743588367519e-03f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f
    である、請求項１または６に記載の装置。
  24. 前記分析ウインドウ関数（４０、６０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -4.619898752628163e-04f, -9.747166718929050e-04f, -1.664473096973725e-03f,
    -2.597106916737789e-03f, -3.806285163352241e-03f, -5.324608721716763e-03f,
    -7.175885277771099e-03f, -9.382480860899108e-03f, -1.195270300743193e-02f,
    -1.489528159506296e-02f, -1.820666399965468e-02f, -2.187570925786862e-02f,
    -2.588471937157619e-02f, -3.020862738245264e-02f, -3.481597793538342e-02f,
    -3.967067992672979e-02f, -4.472698045914417e-02f, -4.994225863256500e-02f,
    -5.526334794593565e-02f, -6.063717235243996e-02f, -6.600961519440657e-02f,
    -7.131966266443390e-02f, -7.651178225890490e-02f, -8.152964005319532e-02f,
    -8.631137544905677e-02f, -9.080411291245728e-02f, -9.495377758870335e-02f,
    -9.870736514214426e-02f, -1.020202684361974e-01f, -1.048438825017798e-01f,
    -1.071382314127799e-01f, -1.088690135027248e-01f, -1.099969655786929e-01f,
    -1.104898474883336e-01f, -1.103225838568563e-01f, -1.094621746650760e-01f,
    -1.078834293141886e-01f, -1.055612509762041e-01f, -1.024650162703341e-01f,
    -9.857014566194629e-02f, -9.384684920715425e-02f, -8.826309993000785e-02f,
    -8.178792716809512e-02f, -7.438785600211463e-02f, -6.602189797715241e-02f,
    -5.665655641133161e-02f, -4.624456893420224e-02f, -3.474585776145929e-02f,
    -2.211581608120528e-02f, -8.310425696208936e-03f, +6.717697635290676e-03f,
    +2.300642061077823e-02f, +4.060106462625085e-02f, +5.953239090915557e-02f,
    +7.983354189816511e-02f, +1.015233140203748e-01f, +1.246171387327525e-01f,
    +1.491152519299797e-01f, +1.750067399059861e-01f, +2.022699854906251e-01f,
    +2.308655379767671e-01f, +2.607365124918583e-01f, +2.918144694729168e-01f,
    +3.240095704645023e-01f, +3.572175180786021e-01f, +3.913146885756875e-01f,
    +4.261571642320424e-01f, +4.615925445090212e-01f, +4.974471592901086e-01f,
    +5.335326819631583e-01f, +5.696546730080154e-01f, +6.056083823929643e-01f,
    +6.411830842823245e-01f, +6.761653499550255e-01f, +7.103400549562944e-01f,
    +7.434943718765665e-01f, +7.754281892901473e-01f, +8.059437233154637e-01f,
    +8.348589373399948e-01f, +8.620108336276733e-01f, +8.872599706865123e-01f,
    +9.104863121445679e-01f, +9.315962496426278e-01f, +9.505220861927248e-01f,
    +9.672366712325431e-01f, +9.817397501303696e-01f, +9.940557180662704e-01f,
    +1.004247514102417e+00f, +1.012407428282884e+00f, +1.018650990561848e+00f,
    +1.023118841384460e+00f, +1.025972450969440e+00f, +1.027397523939210e+00f,
    +1.027585830688143e+00f, +1.026738673647482e+00f, +1.025061777648234e+00f,
    +1.022756514615106e+00f, +1.020009139549275e+00f, +1.016996499560845e+00f,
    +1.013915946100629e+00f, +1.011044869639164e+00f, +1.007773858455400e+00f,
    +1.004848753962734e+00f, +1.002245009135684e+00f, +9.999393169239009e-01f,
    +9.979055415627330e-01f, +9.961203379971326e-01f, +9.945597525471822e-01f,
    +9.932031606606762e-01f, +9.920297273323891e-01f, +9.910230654424902e-01f,
    +9.901668953434221e-01f, +9.894488374513719e-01f, +9.888556356037892e-01f,
    +9.883778520531268e-01f, +9.880051626345804e-01f, +9.877295459610343e-01f,
    +9.875412739766566e-01f, +9.874329809802893e-01f, +9.873949921033299e-01f,
    +9.874197049003676e-01f, +9.874973205882319e-01f, +9.876201238703241e-01f,
    +9.877781920433015e-01f, +9.879637979933339e-01f, +9.881678007807095e-01f,
    +9.883835200189653e-01f, +9.886022219397892e-01f, +9.888182771263505e-01f,
    +9.890247977602895e-01f, +9.892178658748239e-01f, +9.893923680007577e-01f,
    +9.895463342815009e-01f, +9.896772011542693e-01f, +9.897859195209235e-01f,
    +9.898725363809847e-01f, +9.899410789223559e-01f, +9.899945557067980e-01f,
    +9.900394023736973e-01f, +9.900814722948890e-01f, +9.901293790312005e-01f,
    +9.901902265696609e-01f, +9.902734448815004e-01f, +9.903862280081246e-01f,
    +9.905379830873822e-01f, +9.907348826312993e-01f, +9.909842592301273e-01f,
    +9.912905118607647e-01f, +9.916586940166509e-01f, +9.920906151219310e-01f,
    +9.925887208794144e-01f, +9.931516528513824e-01f, +9.937790866568735e-01f,
    +9.944668184371617e-01f, +9.952116634297566e-01f, +9.960068616185641e-01f,
    +9.968461329825753e-01f, +9.977203369515556e-01f, +9.986213520769593e-01f,
    +9.995382582242990e-01f, +1.000461955079660e+00f, +1.001380551217109e+00f,
    +1.002284871786226e+00f, +1.003163845364970e+00f, +1.004009147462043e+00f,
    +1.004811375053364e+00f, +1.005563968008037e+00f, +1.006259855360867e+00f,
    +1.006895570408563e+00f, +1.007466616298057e+00f, +1.007972441990187e+00f,
    +1.008411468616852e+00f, +1.008786009787269e+00f, +1.009097763850333e+00f,
    +1.009351762546296e+00f, +1.009552401900961e+00f, +1.009707093778162e+00f,
    +1.009822090220407e+00f, +1.009906958448099e+00f, +1.009969021400474e+00f,
    +1.010017890428877e+00f, +1.010060809299530e+00f, +1.010106564965965e+00f,
    +1.010161131093372e+00f, +1.010231078494249e+00f, +1.010319484524512e+00f,
    +1.010430470494512e+00f, +1.010564099281000e+00f, +1.010721360243234e+00f,
    +1.010899655674578e+00f, +1.011096993993037e+00f, +1.011308167670753e+00f,
    +1.011529185153809e+00f, +1.011753008569803e+00f, +1.011973876511603e+00f,
    +1.012182837094955e+00f, +1.012373028737774e+00f, +1.012535058602453e+00f,
    +1.012660975529858e+00f, +1.012740575296603e+00f, +1.012765922449960e+00f,
    +1.012726958954961e+00f, +1.012615904116265e+00f, +1.012422888521601e+00f,
    +1.012140460211194e+00f, +1.011758810583150e+00f, +1.011269960947744e+00f,
    +1.010663676735228e+00f, +1.009930754807923e+00f, +1.009058249873833e+00f,
    +1.008034308295421e+00f, +1.006843352506855e+00f, +1.005470005637052e+00f,
    +1.003894772403371e+00f, +1.002098854400575e+00f, +1.000060686758758e+00f,
    +9.977600196406868e-01f, +9.951746430061121e-01f, +9.922861082472264e-01f,
    +9.890757868707590e-01f, +9.847362453480265e-01f, +9.798613526271561e-01f,
    +9.741378617337759e-01f, +9.673331975559332e-01f, +9.592539757044516e-01f,
    +9.496984081652284e-01f, +9.384634163826711e-01f, +9.253567968750328e-01f,
    +9.101986790930605e-01f, +8.928338316495705e-01f, +8.731437835983047e-01f,
    +8.510420440685049e-01f, +8.264839911291133e-01f, +7.994681492797084e-01f,
    +7.700431275216928e-01f, +7.383028603058783e-01f, +7.043814340356083e-01f,
    +6.684616478236647e-01f, +6.307755329382612e-01f, +5.915799587176216e-01f,
    +5.511703155400274e-01f, +5.098915423728179e-01f, +4.681017110047964e-01f,
    +4.261772971493010e-01f, +3.845172335531009e-01f, +3.435228672445613e-01f,
    +3.036004651973099e-01f, +2.651434678028531e-01f, +2.285283969438072e-01f,
    +1.941021906320984e-01f, +1.621735416384830e-01f, +1.330015240938615e-01f,
    +1.067840430193724e-01f, +8.365057236623041e-02f, +6.365188111381356e-02f,
    +4.676538412257621e-02f, +3.288072750732215e-02f, +2.183057564646270e-02f,
    +1.336381425803019e-02f, +6.758124889697787e-03f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f
    である、請求項１または６に記載の装置。
  25. 前記分析ウインドウ関数（４０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -3.613496418928369e-04f, -7.078546706512391e-04f, -1.074443637110903e-03f,
    -1.533478537964509e-03f, -2.098197727900724e-03f, -2.778420871815740e-03f,
    -3.584129920673041e-03f, -4.525198076002370e-03f, -5.609327243712055e-03f,
    -6.843234536105624e-03f, -8.233976327300612e-03f, -9.785314755557023e-03f,
    -1.149880303071551e-02f, -1.337713096257934e-02f, -1.542181679511618e-02f,
    -1.762979910961727e-02f, -1.999721557401502e-02f, -2.252080561390149e-02f,
    -2.519406300389030e-02f, -2.800909464274782e-02f, -3.095765092956728e-02f,
    -3.402996266948349e-02f, -3.721502082245055e-02f, -4.050053247568393e-02f,
    -4.387219218706189e-02f, -4.731768261606175e-02f, -5.082325342672667e-02f,
    -5.437166635159518e-02f, -5.794654834034055e-02f, -6.153426201732499e-02f,
    -6.511708163113709e-02f, -6.867606753531441e-02f, -7.219447805250771e-02f,
    -7.565695975592170e-02f, -7.904647440788692e-02f, -8.234442557322251e-02f,
    -8.553324579905185e-02f, -8.859705468085925e-02f, -9.152091100798199e-02f,
    -9.428847446755965e-02f, -9.688303623049198e-02f, -9.929123258537813e-02f,
    -1.015008467688577e-01f, -1.034961241263523e-01f, -1.052637003544443e-01f,
    -1.067939984687745e-01f, -1.080766457616878e-01f, -1.090997300590506e-01f,
    -1.098524491515805e-01f, -1.103242262600913e-01f, -1.105084619148789e-01f,
    -1.103977408741932e-01f, -1.099809851424550e-01f, -1.092492774392824e-01f,
    -1.081974227416502e-01f, -1.068172142230882e-01f, -1.050995803285455e-01f,
    -1.030360111111103e-01f, -1.006190418791648e-01f, -9.784120023411771e-02f,
    -9.469304216883027e-02f, -9.116452506492527e-02f, -8.724644532866996e-02f,
    -8.293043914044632e-02f, -7.820617483254730e-02f, -7.306142427456862e-02f,
    -6.748468182105991e-02f, -6.146688124166948e-02f, -5.499497258200362e-02f,
    -4.805444424454820e-02f, -4.063362855701623e-02f, -3.272045590229335e-02f,
    -2.430122582451853e-02f, -1.536329520788766e-02f, -5.891434269890659e-03f,
    +4.126595858583295e-03f, +1.470155068746303e-02f, +2.584738191459814e-02f,
    +3.757652772246801e-02f, +4.989736509080558e-02f, +6.282034030592902e-02f,
    +7.635397728566121e-02f, +9.050369257152079e-02f, +1.052747118478660e-01f,
    +1.206703467513333e-01f, +1.366911019414417e-01f, +1.533343890681390e-01f,
    +1.705954709184399e-01f, +1.884686389218322e-01f, +2.069449962574092e-01f,
    +2.260093000067393e-01f, +2.456456803467095e-01f, +2.658346019332584e-01f,
    +2.865543814049772e-01f, +3.077789078889820e-01f, +3.294769437072290e-01f,
    +3.516171481750350e-01f, +3.741642373060188e-01f, +3.970739591211551e-01f,
    +4.203043046885219e-01f, +4.438114799213576e-01f, +4.675442291623012e-01f,
    +4.914498631045615e-01f, +5.154735456539700e-01f, +5.395557644293222e-01f,
    +5.636399817032525e-01f, +5.876661722564289e-01f, +6.115695310143157e-01f,
    +6.352890592874099e-01f, +6.587619767809000e-01f, +6.819230974423550e-01f,
    +7.047092819314779e-01f, +7.270576699841359e-01f, +7.489068963384272e-01f,
    +7.701990187606995e-01f, +7.908752989295335e-01f, +8.108788692151807e-01f,
    +8.301579139160681e-01f, +8.486643364959733e-01f, +8.663548164329093e-01f,
    +8.831896853053627e-01f, +8.991320235484349e-01f, +9.141540563656075e-01f,
    +9.282282546151819e-01f, +9.413348145272842e-01f, +9.534619388400459e-01f,
    +9.646048250501910e-01f, +9.747634827941575e-01f, +9.839435385219192e-01f,
    +9.921529097154242e-01f, +9.994114730415857e-01f, +1.005746084650236e+00f,
    +1.011183971347815e+00f, +1.015760373791603e+00f, +1.019515072412387e+00f,
    +1.022490937034641e+00f, +1.024736164069697e+00f, +1.026304095700693e+00f,
    +1.027250978292214e+00f, +1.027634294456205e+00f, +1.027511063644843e+00f,
    +1.026942795115598e+00f, +1.025991493983836e+00f, +1.024716149969084e+00f,
    +1.023175976163407e+00f, +1.021427210603284e+00f, +1.019521566634239e+00f,
    +1.017510118327508e+00f, +1.015439859549357e+00f, +1.013460916839174e+00f,
    +1.011654901040475e+00f, +1.009366925499550e+00f, +1.007263182132894e+00f,
    +1.005313192386866e+00f, +1.003508162416449e+00f, +1.001840787319378e+00f,
    +1.000303927234380e+00f, +9.988898206257559e-01f, +9.975915283480670e-01f,
    +9.964015284765968e-01f, +9.953133902427869e-01f, +9.943201078053212e-01f,
    +9.934158959186011e-01f, +9.925943919208190e-01f, +9.918510277326026e-01f,
    +9.911797988363887e-01f, +9.905771957917731e-01f, +9.900381047643838e-01f,
    +9.895594394179152e-01f, +9.891371616557014e-01f, +9.887684373604154e-01f,
    +9.884497924570929e-01f, +9.881790747212391e-01f, +9.879528358230726e-01f,
    +9.877691368590689e-01f, +9.876249269174586e-01f, +9.875179947346887e-01f,
    +9.874458127312921e-01f, +9.874056275509585e-01f, +9.873951115886979e-01f,
    +9.874115368168944e-01f, +9.874524849192456e-01f, +9.875149888347144e-01f,
    +9.875968894760857e-01f, +9.876951134084213e-01f, +9.878075819424549e-01f,
    +9.879311998177238e-01f, +9.880640617030884e-01f, +9.882032571565917e-01f,
    +9.883471084085503e-01f, +9.884926873551375e-01f, +9.886386592120545e-01f,
    +9.887825578295630e-01f, +9.889230031022089e-01f, +9.890581715933395e-01f,
    +9.891867674284610e-01f, +9.893074965384659e-01f, +9.894196399062921e-01f,
    +9.895220757174378e-01f, +9.896146331889107e-01f, +9.896970346678272e-01f,
    +9.897692596535289e-01f, +9.898319269347060e-01f, +9.898852572653667e-01f,
    +9.899307640365727e-01f, +9.899693102025343e-01f, +9.900025692522435e-01f,
    +9.900321562263099e-01f, +9.900603352632121e-01f, +9.900889812894406e-01f,
    +9.901206586012907e-01f, +9.901575015155720e-01f, +9.902023946214220e-01f,
    +9.902575406142213e-01f, +9.903255289051605e-01f, +9.904087914462694e-01f,
    +9.905096491583045e-01f, +9.906303787150326e-01f, +9.907727108894024e-01f,
    +9.909387444078919e-01f, +9.911298894709990e-01f, +9.913476318763218e-01f,
    +9.915928560402563e-01f, +9.918665491182922e-01f, +9.921691315380984e-01f,
    +9.925010851461232e-01f, +9.928619727154252e-01f, +9.932519181564613e-01f,
    +9.936700207375173e-01f, +9.941156069136238e-01f, +9.945873147903244e-01f,
    +9.950837402063278e-01f, +9.956033775539884e-01f, +9.961439922621166e-01f,
    +9.967034533921340e-01f, +9.972793109558521e-01f, +9.978690858367024e-01f,
    +9.984697087896268e-01f, +9.990784840729244e-01f, +9.996919011206490e-01f,
    +1.000308193833526e+00f, +1.000922365901945e+00f, +1.001532636590676e+00f,
    +1.002135464655177e+00f, +1.002728111386909e+00f, +1.003307449770187e+00f,
    +1.003870934089686e+00f, +1.004416038098237e+00f, +1.004940548815171e+00f,
    +1.005442141810160e+00f, +1.005919224127911e+00f, +1.006370303149314e+00f,
    +1.006793927824538e+00f, +1.007189345025525e+00f, +1.007555573455895e+00f,
    +1.007892674961336e+00f, +1.008200146369426e+00f, +1.008478423284851e+00f,
    +1.008727884997619e+00f, +1.008949493525753e+00f, +1.009144112734761e+00f,
    +1.009313224929575e+00f, +1.009458241425143e+00f, +1.009581280555682e+00f,
    +1.009684090687164e+00f, +1.009768980817384e+00f, +1.009838308708799e+00f,
    +1.009894548257807e+00f, +1.009940336228694e+00f, +1.009977916643680e+00f,
    +1.010010230290263e+00f, +1.010039453539107e+00f, +1.010068202038694e+00f,
    +1.010098388689342e+00f, +1.010132323996401e+00f, +1.010171656775640e+00f,
    +1.010218096148412e+00f, +1.010272524848519e+00f, +1.010336490294771e+00f,
    +1.010410221483215e+00f, +1.010494354532353e+00f, +1.010588873699422e+00f,
    +1.010693501186928e+00f, +1.010808068774316e+00f, +1.010931436739342e+00f,
    +1.011062876503041e+00f, +1.011201071127927e+00f, +1.011344700694417e+00f,
    +1.011491904228184e+00f, +1.011641272406023e+00f, +1.011790282474963e+00f,
    +1.011937567254485e+00f, +1.012080125934687e+00f, +1.012216235487353e+00f,
    +1.012342907951334e+00f, +1.012458183122033e+00f, +1.012558879696851e+00f,
    +1.012642857380847e+00f, +1.012706955800289e+00f, +1.012748952907404e+00f,
    +1.012765799894453e+00f, +1.012755013843985e+00f, +1.012713798678211e+00f,
    +1.012639775003457e+00f, +1.012530134411619e+00f, +1.012382309473470e+00f,
    +1.012194068117524e+00f, +1.011962331100864e+00f, +1.011685173724601e+00f,
    +1.011359143572147e+00f, +1.010982135506986e+00f, +1.010550715971368e+00f,
    +1.010062133151922e+00f, +1.009512438049510e+00f, +1.008898689394160e+00f,
    +1.008215923600973e+00f, +1.007460860286395e+00f, +1.006627741823389e+00f,
    +1.005712337656749e+00f, +1.004708677491086e+00f, +1.003611467285588e+00f,
    +1.002414286392268e+00f, +1.001111413242302e+00f, +9.996961651093181e-01f,
    +9.981625949525345e-01f, +9.965041017623596e-01f, +9.947148884277037e-01f,
    +9.927891912841345e-01f, +9.907199995730845e-01f, +9.884793707533194e-01f,
    +9.855347660016696e-01f, +9.823765865983286e-01f, +9.789747333404933e-01f,
    +9.751623811486372e-01f, +9.708821747608998e-01f, +9.660805524695870e-01f,
    +9.606976399184645e-01f, +9.546732976073706e-01f, +9.479479345282376e-01f,
    +9.404609052933396e-01f, +9.321553861564006e-01f, +9.229775478442888e-01f,
    +9.128745354570823e-01f, +9.018003682081348e-01f, +8.897163275605041e-01f,
    +8.765908974996186e-01f, +8.623984077953557e-01f, +8.471200801854385e-01f,
    +8.307479727020245e-01f, +8.132817365236141e-01f, +7.947291447585267e-01f,
    +7.751108841891807e-01f, +7.544551974836834e-01f, +7.327963552921717e-01f,
    +7.101790843209148e-01f, +6.866580716267418e-01f, +6.622962432368731e-01f,
    +6.371684119604742e-01f, +6.113488038789190e-01f, +5.849206604934815e-01f,
    +5.579747428663487e-01f, +5.306181649316717e-01f, +5.029523957059122e-01f,
    +4.750868825511614e-01f, +4.471309850999535e-01f, +4.192049917945288e-01f,
    +3.914252910998820e-01f, +3.639114681156252e-01f, +3.367837772954476e-01f,
    +3.101627843160973e-01f, +2.841647033392418e-01f, +2.589033711808454e-01f,
    +2.344880603710975e-01f, +2.110209448747974e-01f, +1.885997642296488e-01f,
    +1.673100807904834e-01f, +1.472287968327706e-01f, +1.284223074167396e-01f,
    +1.109422548710344e-01f, +9.482665349502306e-02f, +8.009914366829558e-02f,
    +6.676765847398403e-02f, +5.482436608328485e-02f, +4.424588851571281e-02f,
    +3.499361000717621e-02f, +2.701461405056267e-02f, +2.024370180670145e-02f,
    +1.460796755137538e-02f, +9.996743588367531e-03f, +5.305235098871444e-03f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f
    である、請求項１または６に記載の装置。
  26. 前記分析ウインドウ関数（４０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -3.021153494057143e-04f, -5.867737487939294e-04f, -8.366504004139796e-04f,
    -1.126635355725494e-03f, -1.470492941694331e-03f, -1.873473391018495e-03f,
    -2.339292362082021e-03f, -2.872008069419264e-03f, -3.476256385086407e-03f,
    -4.155963816705528e-03f, -4.914563787665504e-03f, -5.755172503953251e-03f,
    -6.680623380533122e-03f, -7.693816924650567e-03f, -8.796760749750191e-03f,
    -9.990503073705982e-03f, -1.127574117138621e-02f, -1.265334152129685e-02f,
    -1.412438986522702e-02f, -1.568889620430290e-02f, -1.734512089366117e-02f,
    -1.909097368362797e-02f, -2.092546711168754e-02f, -2.284684792818856e-02f,
    -2.485207716234951e-02f, -2.693746704328349e-02f, -2.909952486193999e-02f,
    -3.133504629493832e-02f, -3.363960728361352e-02f, -3.600820974457969e-02f,
    -3.843601741746971e-02f, -4.091746034850161e-02f, -4.344654894948344e-02f,
    -4.601786724624048e-02f, -4.862598509282497e-02f, -5.126474204655663e-02f,
    -5.392644753556616e-02f, -5.660384311081047e-02f, -5.929116747072080e-02f,
    -6.198268202511926e-02f, -6.467025548071184e-02f, -6.734542216184526e-02f,
    -7.000099017198280e-02f, -7.263057011354321e-02f, -7.522784961377151e-02f,
    -7.778525942347714e-02f, -8.029480247839878e-02f, -8.274924535373614e-02f,
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    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f
    である、請求項１または６に記載の装置。
  27. 前記分析ウインドウ関数（４０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -2.353032150516754e-04f, -4.619898752628163e-04f, -6.262931535610879e-04f,
    -7.929180432976445e-04f, -9.747166718929050e-04f, -1.180256894474562e-03f,
    -1.409209039594871e-03f, -1.664473096973725e-03f, -1.946591608170231e-03f,
    -2.257081732588478e-03f, -2.597106916737789e-03f, -2.967607624839524e-03f,
    -3.370454877988472e-03f, -3.806285163352241e-03f, -4.276873767639064e-03f,
    -4.782469904501813e-03f, -5.324608721716763e-03f, -5.903403814095400e-03f,
    -6.520419726599805e-03f, -7.175885277771099e-03f, -7.871422820642307e-03f,
    -8.606586039759667e-03f, -9.382480860899108e-03f, -1.019827182163307e-02f,
    -1.105520547739066e-02f, -1.195270300743193e-02f, -1.289205910303846e-02f,
    -1.387263484323160e-02f, -1.489528159506296e-02f, -1.595856621933800e-02f,
    -1.706288556735433e-02f, -1.820666399965468e-02f, -1.939065975232718e-02f,
    -2.061355417582714e-02f, -2.187570925786862e-02f, -2.317526315266411e-02f,
    -2.451227449041489e-02f, -2.588471937157619e-02f, -2.729263737090799e-02f,
    -2.873390902713615e-02f, -3.020862738245264e-02f, -3.171440372994384e-02f,
    -3.325098858986303e-02f, -3.481597793538342e-02f, -3.640892406933019e-02f,
    -3.802742318209150e-02f, -3.967067992672979e-02f, -4.133575417353826e-02f,
    -4.302203371734278e-02f, -4.472698045914417e-02f, -4.645022292934329e-02f,
    -4.818891490266687e-02f, -4.994225863256500e-02f, -5.170690802826666e-02f,
    -5.348162036097223e-02f, -5.526334794593565e-02f, -5.705123152423822e-02f,
    -5.884271749745559e-02f, -6.063717235243996e-02f, -6.243104027829089e-02f,
    -6.422303545004304e-02f, -6.600961519440657e-02f, -6.778962269634495e-02f,
    -6.955996868581379e-02f, -7.131966266443390e-02f, -7.306581273272733e-02f,
    -7.479758913001458e-02f, -7.651178225890490e-02f, -7.820711420768856e-02f,
    -7.988010693411644e-02f, -8.152964005319532e-02f, -8.315237353264004e-02f,
    -8.474728946770714e-02f, -8.631137544905677e-02f, -8.784374452959058e-02f,
    -8.934164364321417e-02f, -9.080411291245728e-02f, -9.222795761428432e-02f,
    -9.361232867223340e-02f, -9.495377758870335e-02f, -9.625155313139856e-02f,
    -9.750284620437569e-02f, -9.870736514214426e-02f, -9.986271288271026e-02f,
    -1.009680221406219e-01f, -1.020202684361974e-01f, -1.030183804850491e-01f,
    -1.039596356759290e-01f, -1.048438825017798e-01f, -1.056686838192766e-01f,
    -1.064342821660323e-01f, -1.071382314127799e-01f, -1.077799961121537e-01f,
    -1.083570625865931e-01f, -1.088690135027248e-01f, -1.093135588677235e-01f,
    -1.096903559498340e-01f, -1.099969655786929e-01f, -1.102332261219973e-01f,
    -1.103972812085189e-01f, -1.104898474883336e-01f, -1.105086416532167e-01f,
    -1.104537426996073e-01f, -1.103225838568563e-01f, -1.101145827722143e-01f,
    -1.098276928170364e-01f, -1.094621746650760e-01f, -1.090163960055733e-01f,
    -1.084908852561722e-01f, -1.078834293141886e-01f, -1.071937180231978e-01f,
    -1.064196358069465e-01f, -1.055612509762041e-01f, -1.046162812518618e-01f,
    -1.035849043557610e-01f, -1.024650162703341e-01f, -1.012568997532046e-01f,
    -9.995864571932928e-02f, -9.857014566194627e-02f, -9.708911135857967e-02f,
    -9.551545820689084e-02f, -9.384684920715425e-02f, -9.208300062891550e-02f,
    -9.022171021406450e-02f, -8.826309993000785e-02f, -8.620493821803937e-02f,
    -8.404742152815330e-02f, -8.178792716809512e-02f, -7.942625026703617e-02f,
    -7.695980775819990e-02f, -7.438785600211463e-02f, -7.170797002873608e-02f,
    -6.891994783815969e-02f, -6.602189797715241e-02f, -6.301349420724424e-02f,
    -5.989191912667712e-02f, -5.665655641133161e-02f, -5.330406164482222e-02f,
    -4.983427241976235e-02f, -4.624456893420224e-02f, -4.253455686336916e-02f,
    -3.870195772538443e-02f, -3.474585776145929e-02f, -3.066341518682682e-02f,
    -2.645425077642105e-02f, -2.211581608120528e-02f, -1.764740541599136e-02f,
    -1.304581363895818e-02f, -8.310425696208936e-03f, -3.438268661133170e-03f,
    +1.570315476576933e-03f, +6.717697635290676e-03f, +1.200477020244778e-02f,
    +1.743398319747869e-02f, +2.300642061077823e-02f, +2.872481423270595e-02f,
    +3.458896350634671e-02f, +4.060106462625085e-02f, +4.676102915752826e-02f,
    +5.307133911821893e-02f, +5.953239090915557e-02f, +6.614647812869151e-02f,
    +7.291293184312803e-02f, +7.983354189816511e-02f, +8.690807412770696e-02f,
    +9.413813765275064e-02f, +1.015233140203748e-01f, +1.090651518336202e-01f,
    +1.167626546016197e-01f, +1.246171387327525e-01f, +1.326272948938113e-01f,
    +1.407938190608664e-01f, +1.491152519299797e-01f, +1.575921408388593e-01f,
    +1.662224799248571e-01f, +1.750067399059861e-01f, +1.839431938620024e-01f,
    +1.930318183054904e-01f, +2.022699854906251e-01f, +2.116567430906184e-01f,
    +2.211888523410642e-01f, +2.308655379767671e-01f, +2.406837992341654e-01f,
    +2.506420640291662e-01f, +2.607365124918583e-01f, +2.709659073501196e-01f,
    +2.813259021832532e-01f, +2.918144694729168e-01f, +3.024270279840051e-01f,
    +3.131603499997996e-01f, +3.240095704645023e-01f, +3.349719592361666e-01f,
    +3.460422935204829e-01f, +3.572175180786021e-01f, +3.684915649120530e-01f,
    +3.798595119591716e-01f, +3.913146885756875e-01f, +4.028532873867052e-01f,
    +4.144688328137527e-01f, +4.261571642320424e-01f, +4.379113897565727e-01f,
    +4.497256320417501e-01f, +4.615925445090212e-01f, +4.735067030065239e-01f,
    +4.854600184866710e-01f, +4.974471592901086e-01f, +5.094597228333853e-01f,
    +5.214909841729947e-01f, +5.335326819631583e-01f, +5.455789811615239e-01f,
    +5.576217157959890e-01f, +5.696546730080154e-01f, +5.816685576268035e-01f,
    +5.936560624526468e-01f, +6.056083823929643e-01f, +6.175192060085208e-01f,
    +6.293796611336280e-01f, +6.411830842823245e-01f, +6.529203544876097e-01f,
    +6.645840786371451e-01f, +6.761653499550255e-01f, +6.876573952173626e-01f,
    +6.990511539119996e-01f, +7.103400549562944e-01f, +7.215149331458728e-01f,
    +7.325691772738999e-01f, +7.434943718765665e-01f, +7.542846327442048e-01f,
    +7.649313654540612e-01f, +7.754281892901473e-01f, +7.857670170752049e-01f,
    +7.959414651061612e-01f, +8.059437233154637e-01f, +8.157687070715176e-01f,
    +8.254086223972127e-01f, +8.348589373399948e-01f, +8.441125827416620e-01f,
    +8.531651194538425e-01f, +8.620108336276733e-01f, +8.706456337542150e-01f,
    +8.790631561061171e-01f, +8.872599706865123e-01f, +8.952313288619367e-01f,
    +9.029751680353524e-01f, +9.104863121445679e-01f, +9.177625550620636e-01f,
    +9.247997426966093e-01f, +9.315962496426278e-01f, +9.381494858921667e-01f,
    +9.444588390359354e-01f, +9.505220861927248e-01f, +9.563402921286364e-01f,
    +9.619114522936701e-01f, +9.672366712325431e-01f, +9.723156637834687e-01f,
    +9.771501187120180e-01f, +9.817397501303696e-01f, +9.860865871353246e-01f,
    +9.901906380163595e-01f, +9.940557180662704e-01f, +9.976842395284637e-01f,
    +1.001080961257010e+00f, +1.004247514102417e+00f, +1.007188578458507e+00f,
    +1.009906654565108e+00f, +1.012407428282884e+00f, +1.014694702432600e+00f,
    +1.016774659209400e+00f, +1.018650990561848e+00f, +1.020330464463111e+00f,
    +1.021817328911793e+00f, +1.023118841384460e+00f, +1.024240262467000e+00f,
    +1.025189721888128e+00f, +1.025972450969440e+00f, +1.026596938589443e+00f,
    +1.027069179375841e+00f, +1.027397523939210e+00f, +1.027587902203109e+00f,
    +1.027648951922701e+00f, +1.027585830688143e+00f, +1.027408519661012e+00f,
    +1.027122986826984e+00f, +1.026738673647482e+00f, +1.026261663878092e+00f,
    +1.025701002415063e+00f, +1.025061777648234e+00f, +1.024353980976701e+00f,
    +1.023582385618774e+00f, +1.022756514615106e+00f, +1.021880604350422e+00f,
    +1.020963871317665e+00f, +1.020009139549275e+00f, +1.019027285501251e+00f,
    +1.018019442784231e+00f, +1.016996499560845e+00f, +1.015957433206324e+00f,
    +1.014923441259795e+00f, +1.013915946100629e+00f, +1.013047565149327e+00f,
    +1.012216130365610e+00f, +1.011044869639164e+00f, +1.009914592130044e+00f,
    +1.008824888092573e+00f, +1.007773858455400e+00f, +1.006761700412993e+00f,
    +1.005786648810854e+00f, +1.004848753962734e+00f, +1.003946083413733e+00f,
    +1.003078846506546e+00f, +1.002245009135684e+00f, +1.001444733905817e+00f,
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    +9.985548127155425e-01f, +9.979055415627330e-01f, +9.972842679758880e-01f,
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    +4.820662943337458e-01f, +4.681017110048007e-01f, +4.541216995958746e-01f,
    +4.401421815729068e-01f, +4.261772971493010e-01f, +4.122417888542512e-01f,
    +3.983499612526493e-01f, +3.845172335531009e-01f, +3.707583717376236e-01f,
    +3.570886786795506e-01f, +3.435228672445627e-01f, +3.300763764703638e-01f,
    +3.167640325043893e-01f, +3.036004651973109e-01f, +2.905996158436682e-01f,
    +2.777758503744847e-01f, +2.651434678028531e-01f, +2.527161881181577e-01f,
    +2.405069849650012e-01f, +2.285283969438072e-01f, +2.167933432162879e-01f,
    +2.053139897833021e-01f, +1.941021906320988e-01f, +1.831680872008943e-01f,
    +1.725221947208913e-01f, +1.621735416384834e-01f, +1.521320683467849e-01f,
    +1.424052801149985e-01f, +1.330015240938615e-01f, +1.239260664828526e-01f,
    +1.151858295527293e-01f, +1.067840430193724e-01f, +9.872637505002878e-02f,
    +9.101379000888035e-02f, +8.365057236623055e-02f, +7.663508305536153e-02f,
    +6.997033405748826e-02f, +6.365188111381365e-02f, +5.768176015814392e-02f,
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    +1.592127815153420e-02f, +1.336381425803020e-02f, +1.108558877807282e-02f,
    +8.943474189364638e-03f, +6.758124889697787e-03f, +3.504438130619497e-03f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
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    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
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    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
    +0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f
    である、請求項１または６に記載の装置。
  28. 前記分析ウインドウ関数（４０）または前記合成ウインドウ関数（９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    -1.596869453315999e-04, -3.021153494057143e-04, -4.142323860121641e-04,
    -5.058484031439142e-04, -5.867737487939294e-04, -6.666034929771656e-04,
    -7.499813122143762e-04, -8.366504004139794e-04, -9.273096237893370e-04,
    -1.023773491532728e-03, -1.126635355725494e-03, -1.235247794937702e-03,
    -1.349627853510606e-03, -1.470492941694331e-03, -1.598145399394582e-03,
    -1.732450700747454e-03, -1.873473391018495e-03, -2.021493133113876e-03,
    -2.176721793926887e-03, -2.339292362082021e-03, -2.509298051958086e-03,
    -2.686801873698675e-03, -2.872008069419264e-03, -3.065254982136409e-03,
    -3.266686736002951e-03, -3.476256385086407e-03, -3.694123506258334e-03,
    -3.920651988943251e-03, -4.155963816705528e-03, -4.399940204176431e-03,
    -4.652692827862344e-03, -4.914563787665504e-03, -5.185653529531935e-03,
    -5.465821495567872e-03, -5.755172503953251e-03, -6.054056765330685e-03,
    -6.362583863449497e-03, -6.680623380533122e-03, -7.008304674718039e-03,
    -7.346013465075499e-03, -7.693816924650567e-03, -8.051465262788033e-03,
    -8.419001443263380e-03, -8.796760749750191e-03, -9.184751507972289e-03,
    -9.582657230262597e-03, -9.990503073705982e-03, -1.040865597419619e-02,
    -1.083716113754551e-02, -1.127574117138621e-02, -1.172444049589271e-02,
    -1.218362542421523e-02, -1.265334152129685e-02, -1.313331245904876e-02,
    -1.362355747138776e-02, -1.412438986522702e-02, -1.463576680723352e-02,
    -1.515729094197161e-02, -1.568889620430290e-02, -1.623084814367250e-02,
    -1.678306524600559e-02, -1.734512089366117e-02, -1.791696516251699e-02,
    -1.849892453107246e-02, -1.909097368362797e-02, -1.969273308274951e-02,
    -2.030414376031160e-02, -2.092546711168754e-02, -2.155660557689242e-02,
    -2.219710359529686e-02, -2.284684792818856e-02, -2.350606779320675e-02,
    -2.417463749934085e-02, -2.485207716234951e-02, -2.553826580898371e-02,
    -2.623344061522424e-02, -2.693746704328349e-02, -2.764983997782559e-02,
    -2.837043858580717e-02, -2.909952486193998e-02, -2.983695676902939e-02,
    -3.058218787751172e-02, -3.133504629493832e-02, -3.209573641742117e-02,
    -3.286409853195186e-02, -3.363960728361352e-02, -3.442207835192332e-02,
    -3.521166997276568e-02, -3.600820974457969e-02, -3.681119317395579e-02,
    -3.762042487257546e-02, -3.843601741746971e-02, -3.925772507976759e-02,
    -4.008494689009130e-02, -4.091746034850161e-02, -4.175542154425013e-02,
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    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00.
    である、請求項１または６に記載の装置。
  29. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +9.959086585790517e-04, +3.819056787237678e-03, +9.540832613229890e-03,
    +1.921659800166160e-02, +3.382719081038548e-02, +5.424831667522354e-02,
    +8.120777668775610e-02, +1.152171887125930e-01, +1.564942331034909e-01,
    +2.049363422022628e-01, +2.601166575816199e-01, +3.212814164616093e-01,
    +3.873472997948746e-01, +4.569497078592333e-01, +5.285192958868393e-01,
    +6.003522489375573e-01, +6.706896380227332e-01, +7.378044458510402e-01,
    +8.000925313431716e-01, +8.561409184410547e-01, +9.048272294524792e-01,
    +9.453685031730190e-01, +9.773507430600533e-01, +1.000800872826561e+00,
    +1.016171590112097e+00, +1.024315247630982e+00, +1.026415431432931e+00,
    +1.023858366571912e+00, +1.018135705524407e+00, +1.010794822557756e+00,
    +1.003406509762925e+00, +9.967831265986109e-01, +9.920995520917141e-01,
    +9.892206942816891e-01, +9.879658322200813e-01, +9.881273531631907e-01,
    +9.894805541465801e-01, +9.917849916000535e-01, +9.947847580943504e-01,
    +9.982119669301160e-01, +1.001791235858836e+00, +1.005242583245485e+00,
    +1.008283053756130e+00, +1.010631281038659e+00, +1.012015300253356e+00,
    +1.012180753005270e+00, +1.010896765282633e+00, +1.007963362035220e+00,
    +1.003227255072391e+00, +9.966050551498514e-01, +9.868284225039941e-01,
    +9.731250287581631e-01, +9.540636479502398e-01, +9.283864275822276e-01,
    +8.950916858157935e-01, +8.534769362643825e-01, +8.032090930429980e-01,
    +7.444735201251689e-01, +6.780787033699449e-01, +6.053970453856138e-01,
    +5.282077505750667e-01, +4.486552956056635e-01, +3.691875990296312e-01,
    +2.924566408966777e-01, +2.210718537110463e-01, +1.573148583944309e-01,
    +1.030525757797768e-01, +5.982732244758054e-02, +2.871831923385133e-02,
    +9.683884928956490e-03, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00.
    である、請求項１または６に記載の装置。
  30. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +6.143388180964179e-04, +1.489582832987000e-03, +2.884104959764029e-03,
    +4.934298832466617e-03, +7.779130464154915e-03, +1.154910606525086e-02,
    +1.637155619860352e-02, +2.237116158648752e-02, +2.966159685753317e-02,
    +3.835663329277230e-02, +4.855610986150206e-02, +6.035055738891727e-02,
    +7.382288203064732e-02, +8.903563687211119e-02, +1.060356225286319e-01,
    +1.248534855777947e-01, +1.454931890869180e-01, +1.679435556337752e-01,
    +1.921728622634411e-01, +2.181238261985594e-01, +2.457259744642953e-01,
    +2.748839432649996e-01, +3.054824712370942e-01, +3.373873799614014e-01,
    +3.704415932452488e-01, +4.044749630814483e-01, +4.393004362003260e-01,
    +4.747225454237193e-01, +5.105341492548225e-01, +5.465201916422433e-01,
    +5.824658100332457e-01, +6.181452662624718e-01, +6.533411462740817e-01,
    +6.878367295965062e-01, +7.214176027060971e-01, +7.538887973483771e-01,
    +7.850546571907628e-01, +8.147397447696774e-01, +8.427819363777799e-01,
    +8.690376742017057e-01, +8.933935477349644e-01, +9.157483563218768e-01,
    +9.360270196617569e-01, +9.541731142261065e-01, +9.701635474343885e-01,
    +9.840036439809510e-01, +9.957199420334376e-01, +1.005374268639838e+00,
    +1.013046655758663e+00, +1.018843380560658e+00, +1.022896948293643e+00,
    +1.025355286710874e+00, +1.026382881625701e+00, +1.026155530733488e+00,
    +1.024853974580724e+00, +1.022664602721801e+00, +1.019779396547454e+00,
    +1.016391686789653e+00, +1.012697033320358e+00, +1.008885191761748e+00,
    +1.005378742804807e+00, +1.001563778373068e+00, +9.982531564931281e-01,
    +9.954346644968789e-01, +9.930950268060122e-01, +9.912170911359961e-01,
    +9.897805192546195e-01, +9.887624937408933e-01, +9.881383235740961e-01,
    +9.878819413827574e-01, +9.879662130250981e-01, +9.883630508181326e-01,
    +9.890434070785485e-01, +9.899772316163624e-01, +9.911334564321237e-01,
    +9.924800441092685e-01, +9.939841207305906e-01, +9.956121471675398e-01,
    +9.973300590248015e-01, +9.991033633647473e-01, +1.000897441314013e+00,
    +1.002677088643863e+00, +1.004407190937699e+00, +1.006052289109999e+00,
    +1.007576934100958e+00, +1.008945862447015e+00, +1.010124241309341e+00,
    +1.011077969726137e+00, +1.011773962181442e+00, +1.012180362866919e+00,
    +1.012266707295288e+00, +1.012004064757857e+00, +1.011365223023975e+00,
    +1.010324996851905e+00, +1.008860731864438e+00, +1.006952983357691e+00,
    +1.004586273379809e+00, +1.001749900308864e+00, +9.984386632116344e-01,
    +9.946500332901397e-01, +9.895756853352172e-01, +9.838303127859196e-01,
    +9.769999155793757e-01, +9.689141159310996e-01, +9.594038121639412e-01,
    +9.483086322505029e-01, +9.354860218216989e-01, +9.208101305030523e-01,
    +9.041732260327581e-01, +8.854882249661838e-01, +8.646864947605046e-01,
    +8.417237467711145e-01, +8.165875713256009e-01, +7.892986353718001e-01,
    +7.599171886893816e-01, +7.285474515411827e-01, +6.953282935906302e-01,
    +6.604334017809461e-01, +6.240661431421666e-01, +5.864461424698465e-01,
    +5.478160663871147e-01, +5.084499758302218e-01, +4.686361426418982e-01,
    +4.286789889246253e-01, +3.889032719013045e-01, +3.496431418636314e-01,
    +3.112360816586544e-01, +2.740128472224535e-01, +2.382847225401666e-01,
    +2.043379825955252e-01, +1.724305860483632e-01, +1.427939789949265e-01,
    +1.156385879569741e-01, +9.115821766571995e-02, +6.952749039054593e-02,
    +5.088975408628225e-02, +3.533430192568954e-02, +2.286680405144430e-02,
    +1.338005016725895e-02, +6.640506529168652e-03, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  31. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +5.087227626168386e-04, +9.959086585790517e-04, +1.682208006328800e-03,
    +2.609697259047744e-03, +3.819056787237678e-03, +5.349319592933909e-03,
    +7.243906383895192e-03, +9.540832613229890e-03, +1.227637642543709e-02,
    +1.548950238899404e-02, +1.921659800166160e-02, +2.349369619441617e-02,
    +2.835199581667961e-02, +3.382719081038548e-02, +3.994939538719628e-02,
    +4.674775238543380e-02, +5.424831667522354e-02, +6.247770776443612e-02,
    +7.145835917501348e-02, +8.120777668775610e-02, +9.174400412319896e-02,
    +1.030764959637497e-01, +1.152171887125930e-01, +1.281665713944242e-01,
    +1.419264381068653e-01, +1.564942331034909e-01, +1.718593189799504e-01,
    +1.880134254543744e-01, +2.049363422022628e-01, +2.226123055761096e-01,
    +2.410151242797736e-01, +2.601166575816199e-01, +2.798871008989962e-01,
    +3.002880135563586e-01, +3.212814164616093e-01, +3.428208463088390e-01,
    +3.648596557863134e-01, +3.873472997948746e-01, +4.102294951869188e-01,
    +4.334494534591082e-01, +4.569497078592333e-01, +4.806696403251166e-01,
    +5.045473815014847e-01, +5.285192958868393e-01, +5.525196099932443e-01,
    +5.764872452085427e-01, +6.003522489375573e-01, +6.240509872809882e-01,
    +6.475182586093196e-01, +6.706896380227332e-01, +6.935029068990036e-01,
    +7.158927516396895e-01, +7.378044458510402e-01, +7.591787241845952e-01,
    +7.799586608897265e-01, +8.000925313431716e-01, +8.195318652294690e-01,
    +8.382288957404715e-01, +8.561409184410547e-01, +8.732316951214179e-01,
    +8.894702022170831e-01, +9.048272294524792e-01, +9.192736375782965e-01,
    +9.327940405054362e-01, +9.453685031730190e-01, +9.569883933538136e-01,
    +9.676486424195593e-01, +9.773507430600533e-01, +9.861027831072527e-01,
    +9.939122412655677e-01, +1.000800872826561e+00, +1.006787811971719e+00,
    +1.011901269172423e+00, +1.016171590112097e+00, +1.019636414864842e+00,
    +1.022336613864005e+00, +1.024315247630982e+00, +1.025621299895396e+00,
    +1.026303439275662e+00, +1.026415431432931e+00, +1.026007933174836e+00,
    +1.025137435167917e+00, +1.023858366571912e+00, +1.022226936424625e+00,
    +1.020300550334848e+00, +1.018135705524407e+00, +1.015792146756340e+00,
    +1.013325966774524e+00, +1.010794822557756e+00, +1.008265131568879e+00,
    +1.006046874304407e+00, +1.003406509762925e+00, +1.000977398831985e+00,
    +9.987704535700208e-01, +9.967831265986109e-01, +9.950118905889862e-01,
    +9.934523971504882e-01, +9.920995520917141e-01, +9.909475998606236e-01,
    +9.899902426925508e-01, +9.892206942816891e-01, +9.886318043013834e-01,
    +9.882160904669929e-01, +9.879658322200813e-01, +9.878730767519871e-01,
    +9.879296932443894e-01, +9.881273531631907e-01, +9.884575535474619e-01,
    +9.889115869213529e-01, +9.894805541465801e-01, +9.901553455166457e-01,
    +9.909266562913843e-01, +9.917849916000535e-01, +9.927206838643636e-01,
    +9.937239208721489e-01, +9.947847580943504e-01, +9.958931493776203e-01,
    +9.970389567617592e-01, +9.982119669301160e-01, +9.994020338838508e-01,
    +1.000598323893564e+00, +1.001791235858836e+00, +1.002969837054169e+00,
    +1.004123786397111e+00, +1.005242583245485e+00, +1.006315717067918e+00,
    +1.007332693127034e+00, +1.008283053756130e+00, +1.009156423082384e+00,
    +1.009942535308151e+00, +1.010631281038659e+00, +1.011212744622770e+00,
    +1.011677230257499e+00, +1.012015300253356e+00, +1.012217779097186e+00,
    +1.012275790821109e+00, +1.012180753005270e+00, +1.011924425888915e+00,
    +1.011498917644724e+00, +1.010896765282633e+00, +1.010110965619444e+00,
    +1.009135094671655e+00, +1.007963362035220e+00, +1.006590756505588e+00,
    +1.005013115379014e+00, +1.003227255072391e+00, +1.001231060075500e+00,
    +9.990235555436858e-01, +9.966050551498514e-01, +9.939894706113089e-01,
    +9.904539200261149e-01, +9.868284225039941e-01, +9.827716736909488e-01,
    +9.782206672373213e-01, +9.731250287581631e-01, +9.674323528812744e-01,
    +9.610947043524248e-01, +9.540636479502398e-01, +9.462952991190324e-01,
    +9.377489107516087e-01, +9.283864275822276e-01, +9.181762606422500e-01,
    +9.070861558801854e-01, +8.950916858157935e-01, +8.821696237804294e-01,
    +8.683025287048570e-01, +8.534769362643825e-01, +8.376852006833730e-01,
    +8.209275259764013e-01, +8.032090930429980e-01, +7.845450482523652e-01,
    +7.649554851899686e-01, +7.444735201251689e-01, +7.231348066419057e-01,
    +7.009860555207412e-01, +6.780787033699450e-01, +6.544686506489734e-01,
    +6.302212149502727e-01, +6.053970453856138e-01, +5.800715766089168e-01,
    +5.543129276657669e-01, +5.282077505750727e-01, +5.018369724442092e-01,
    +4.752902962082383e-01, +4.486552956056652e-01, +4.220281118338883e-01,
    +3.955057965950340e-01, +3.691875990296320e-01, +3.431732847389720e-01,
    +3.175633015043183e-01, +2.924566408966782e-01, +2.679463783886042e-01,
    +2.441231331518492e-01, +2.210718537110466e-01, +1.988719153219592e-01,
    +1.775967625327044e-01, +1.573148583944310e-01, +1.380903364946733e-01,
    +1.199837497591550e-01, +1.030525757797769e-01, +8.735085011789188e-02,
    +7.292811584897502e-02, +5.982732244758056e-02, +4.808178837444506e-02,
    +3.771135297837851e-02, +2.871831923385135e-02, +2.108352028641225e-02,
    +1.476289412849005e-02, +9.683884928956495e-03, +5.642168789286858e-03,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  32. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +4.595886345493055e-04, +7.919323614002698e-04, +1.227927169310031e-03,
    +1.783653266717233e-03, +2.479549413444207e-03, +3.329799454594261e-03,
    +4.353535478916468e-03, +5.564965156664018e-03, +6.986108359341676e-03,
    +8.629882322202329e-03, +1.051343406844975e-02, +1.265082642578719e-02,
    +1.506090447446532e-02, +1.775591229287213e-02, +2.075475983187825e-02,
    +2.406813715401559e-02, +2.771207863541604e-02, +3.169933248543932e-02,
    +3.604609640533871e-02, +4.076128638095439e-02, +4.586038120884381e-02,
    +5.135136676471998e-02, +5.724780220726930e-02, +6.355854744461048e-02,
    +7.029450733434550e-02, +7.745987198268531e-02, +8.506635369887924e-02,
    +9.311641620512773e-02, +1.016162955027316e-01, +1.105690806271684e-01,
    +1.199789286645804e-01, +1.298417294090302e-01, +1.401623800497866e-01,
    +1.509371564593891e-01, +1.621632295622287e-01, +1.738354123649302e-01,
    +1.859520359191026e-01, +1.985008828937603e-01, +2.114778554475382e-01,
    +2.248732557074316e-01, +2.386763947872762e-01, +2.528729453658238e-01,
    +2.674547009618951e-01, +2.824031465430401e-01, +2.977050145264297e-01,
    +3.133419120661713e-01, +3.292976696294886e-01, +3.455490160824131e-01,
    +3.620795045342974e-01, +3.788648665671841e-01, +3.958851576591690e-01,
    +4.131143794748322e-01, +4.305308301005456e-01, +4.481076715576617e-01,
    +4.658227790464821e-01, +4.836466393241829e-01, +5.015564851667653e-01,
    +5.195228071176610e-01, +5.375197039843709e-01, +5.555183841040963e-01,
    +5.734957812557457e-01, +5.914186654649489e-01, +6.092622887527459e-01,
    +6.269981160888640e-01, +6.446002007776794e-01, +6.620384583071039e-01,
    +6.792906550106088e-01, +6.963256426589250e-01, +7.131194393772130e-01,
    +7.296469905863920e-01, +7.458864594794676e-01, +7.618094719403713e-01,
    +7.773958448163656e-01, +7.926208751337592e-01, +8.074666387233143e-01,
    +8.219101564897180e-01, +8.359343163788637e-01, +8.495180470826319e-01,
    +8.626485837105826e-01, +8.753083234662220e-01, +8.874884715160425e-01,
    +8.991737724042251e-01, +9.103527429187326e-01, +9.210144133066616e-01,
    +9.311556192776946e-01, +9.407644740241826e-01, +9.498382236872068e-01,
    +9.583732599601223e-01, +9.663690412284377e-01, +9.738235617865406e-01,
    +9.807442506043361e-01, +9.871297972052695e-01, +9.929872268444632e-01,
    +9.983241398929388e-01, +1.003150760219063e+00, +1.007473713377193e+00,
    +1.011309151636166e+00, +1.014666681083198e+00, +1.017563337333301e+00,
    +1.020014681326785e+00, +1.022039872150903e+00, +1.023654257342442e+00,
    +1.024881624147540e+00, +1.025739288978437e+00, +1.026250709375593e+00,
    +1.026436666375082e+00, +1.026320857404224e+00, +1.025922917798664e+00,
    +1.025269979527211e+00, +1.024382188798244e+00, +1.023284940887058e+00,
    +1.022000829220643e+00, +1.020555973231408e+00, +1.018971390778550e+00,
    +1.017275179369116e+00, +1.015489129111694e+00, +1.013639356938881e+00,
    +1.011747750709711e+00, +1.009840844244693e+00, +1.007939764480188e+00,
    +1.006407400915498e+00, +1.004374825095777e+00, +1.002469814737132e+00,
    +1.000689073754539e+00, +9.990346001249977e-01, +9.975024904153303e-01,
    +9.960941547576162e-01, +9.948051243621099e-01, +9.936362728142866e-01,
    +9.925826537087717e-01, +9.916447007525191e-01, +9.908170758245324e-01,
    +9.900998445795673e-01, +9.894873685512386e-01, +9.889794323427195e-01,
    +9.885701787626714e-01, +9.882591911282058e-01, +9.880404423341358e-01,
    +9.879133688360181e-01, +9.878718098237022e-01, +9.879150762106034e-01,
    +9.880368938846610e-01, +9.882364564839506e-01, +9.885073687439192e-01,
    +9.888487088987707e-01, +9.892539488627546e-01, +9.897220412447528e-01,
    +9.902463287269285e-01, +9.908256340476208e-01, +9.914531811725067e-01,
    +9.921276814881759e-01, +9.928422499725458e-01, +9.935955098307742e-01,
    +9.943804814776256e-01, +9.951957244449919e-01, +9.960341878404958e-01,
    +9.968943831870675e-01, +9.977692009836100e-01, +9.986571134591464e-01,
    +9.995509738170480e-01, +1.000449227898040e+00, +1.001344692310058e+00,
    +1.002235786606954e+00, +1.003115291715261e+00, +1.003981602446902e+00,
    +1.004827468041713e+00, +1.005651275972376e+00, +1.006445772052972e+00,
    +1.007209352772459e+00, +1.007934783656087e+00, +1.008620496650569e+00,
    +1.009259314290145e+00, +1.009849742422788e+00, +1.010384692193296e+00,
    +1.010862783160582e+00, +1.011277044709547e+00, +1.011626247430694e+00,
    +1.011903571699736e+00, +1.012107954864219e+00, +1.012232755709885e+00,
    +1.012277089047072e+00, +1.012234505114778e+00, +1.012104319978655e+00,
    +1.011880293122688e+00, +1.011561972516341e+00, +1.011143373963981e+00,
    +1.010624321020038e+00, +1.009999148545101e+00, +1.009268031808824e+00,
    +1.008425698479647e+00, +1.007472774447058e+00, +1.006404483571931e+00,
    +1.005222003295591e+00, +1.003921160689206e+00, +1.002503762756151e+00,
    +1.000966332772540e+00, +9.993114007411373e-01, +9.975362702189898e-01,
    +9.956442306333592e-01, +9.936333924912825e-01, +9.908677480361242e-01,
    +9.882326326262749e-01, +9.853620567056602e-01, +9.822305093671991e-01,
    +9.788185853162172e-01, +9.751026333215268e-01, +9.710631852370086e-01,
    +9.666759668947944e-01, +9.619242192293307e-01, +9.567841986369235e-01,
    +9.512394303101863e-01, +9.452700238623795e-01, +9.388615698236068e-01,
    +9.319946435581106e-01, +9.246592033932568e-01, +9.168383396399868e-01,
    +9.085218034087421e-01, +8.996967011299613e-01, +8.903562054918268e-01,
    +8.804877931535187e-01, +8.700884209228057e-01, +8.591492134848259e-01,
    +8.476686394755906e-01, +8.356428970797861e-01, +8.230753889817990e-01,
    +8.099649296155544e-01, +7.963204506324437e-01, +7.821460539775005e-01,
    +7.674541821769616e-01, +7.522563457568547e-01, +7.365702052057368e-01,
    +7.204090552899627e-01, +7.037975107157410e-01, +6.867542812151157e-01,
    +6.693041888771051e-01, +6.514710959179395e-01, +6.332854832820911e-01,
    +6.147685389896460e-01, +5.959553778639692e-01, +5.768737955463938e-01,
    +5.575534287167304e-01, +5.380320138068979e-01, +5.183454027643563e-01,
    +4.985259415650634e-01, +4.786156067459849e-01, +4.586473038370941e-01,
    +4.386643656872842e-01, +4.187046888325280e-01, +3.988123056192917e-01,
    +3.790262923635886e-01, +3.593914828698096e-01, +3.399474132903109e-01,
    +3.207392420889753e-01, +3.018061113177048e-01, +2.831905952786929e-01,
    +2.649288369241889e-01, +2.470608550624402e-01, +2.296201119084317e-01,
    +2.126433716126151e-01, +1.961601816145380e-01, +1.802035203864437e-01,
    +1.647996883470626e-01, +1.499787548077656e-01, +1.357643522991611e-01,
    +1.221842534547464e-01, +1.092601994264172e-01, +9.701788451015501e-02,
    +8.547680283183663e-02, +7.465976378295235e-02, +6.458254322751883e-02,
    +5.526281189874138e-02, +4.670976978373095e-02, +3.893244425578719e-02,
    +3.192976013776996e-02, +2.569810636390756e-02, +2.022259265088492e-02,
    +1.548317776486452e-02, +1.144924909653903e-02, +8.076482660383199e-03,
    +5.300044080947794e-03, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  33. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +4.090106504820579e-04, +6.143388180964179e-04, +8.571759876954877e-04,
    +1.147015057857495e-03, +1.489582832987000e-03, +1.889770382231583e-03,
    +2.353000800169909e-03, +2.884104959764029e-03, +3.488213786635855e-03,
    +4.170040431489613e-03, +4.934298832466617e-03, +5.787076505403503e-03,
    +6.733811743137561e-03, +7.779130464154915e-03, +8.927044958757816e-03,
    +1.018202888968871e-02, +1.154910606525086e-02, +1.303349217699797e-02,
    +1.463951288465963e-02, +1.637155619860352e-02, +1.823455383898077e-02,
    +2.023309488998589e-02, +2.237116158648752e-02, +2.465237348403478e-02,
    +2.708101935270475e-02, +2.966159685753317e-02, +3.239884850877327e-02,
    +3.529601774976465e-02, +3.835663329277230e-02, +4.158447932459513e-02,
    +4.498322421745353e-02, +4.855610986150206e-02, +5.230596475016741e-02,
    +5.623624576084146e-02, +6.035055738891727e-02, +6.465186317477950e-02,
    +6.914195749790462e-02, +7.382288203064732e-02, +7.869709331995660e-02,
    +8.376761638427657e-02, +8.903563687211118e-02, +9.450199243028472e-02,
    +1.001680193006426e-01, +1.060356225286319e-01, +1.121060220821844e-01,
    +1.183788547045326e-01, +1.248534855777947e-01, +1.315302847610869e-01,
    +1.384103079528939e-01, +1.454931890869180e-01, +1.527772946853750e-01,
    +1.602608842337125e-01, +1.679435556337752e-01, +1.758245615079801e-01,
    +1.839020119821303e-01, +1.921728622634411e-01, +2.006344295681524e-01,
    +2.092853879977170e-01, +2.181238261985594e-01, +2.271462264407930e-01,
    +2.363479205237173e-01, +2.457259744642953e-01, +2.552771551741124e-01,
    +2.649981094228982e-01, +2.748839432649996e-01, +2.849296444030153e-01,
    +2.951306505827265e-01, +3.054824712370942e-01, +3.159799638238941e-01,
    +3.266169794538543e-01, +3.373873799614014e-01, +3.482855915638277e-01,
    +3.593057693987583e-01, +3.704415932452488e-01, +3.816862385160692e-01,
    +3.930329782788047e-01, +4.044749630814483e-01, +4.160051103939122e-01,
    +4.276159595085598e-01, +4.393004362003260e-01, +4.510516333434032e-01,
    +4.628616046119925e-01, +4.747225454237193e-01, +4.866266705542529e-01,
    +4.985664508456704e-01, +5.105341492548225e-01, +5.225212793188740e-01,
    +5.345190505841265e-01, +5.465201916422433e-01, +5.585172769552711e-01,
    +5.705021536899105e-01, +5.824658100332457e-01, +5.943991720381216e-01,
    +6.062948176207270e-01, +6.181452662624718e-01, +6.299422016714543e-01,
    +6.416768736044914e-01, +6.533411462740817e-01, +6.649277540000037e-01,
    +6.764292700223311e-01, +6.878367295965062e-01, +6.991421467689277e-01,
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    +8.604920874939698e-01, +8.690376742017057e-01, +8.773720451249032e-01,
    +8.854927938913381e-01, +8.933935477349644e-01, +9.010727088526728e-01,
    +9.085249398881980e-01, +9.157483563218768e-01, +9.227413839712016e-01,
    +9.295017469413066e-01, +9.360270196617569e-01, +9.423143052164881e-01,
    +9.483629792665091e-01, +9.541731142261065e-01, +9.597438382130120e-01,
    +9.650738394220176e-01, +9.701635474343885e-01, +9.750143364412617e-01,
    +9.796277191617885e-01, +9.840036439809510e-01, +9.881426772731259e-01,
    +9.920470446911211e-01, +9.957199420334376e-01, +9.991640812275709e-01,
    +1.002381307710643e+00, +1.005374268639838e+00, +1.008146718214831e+00,
    +1.010703123647275e+00, +1.013046655758663e+00, +1.015181271161417e+00,
    +1.017111643578857e+00, +1.018843380560658e+00, +1.020381713994816e+00,
    +1.021731101971518e+00, +1.022896948293643e+00, +1.023885455671576e+00,
    +1.024702974608899e+00, +1.025355286710874e+00, +1.025848243050604e+00,
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    +1.025395432284244e+00, +1.024853974580724e+00, +1.024213482124578e+00,
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    +1.020806917660529e+00, +1.019779396547454e+00, +1.018695995335235e+00,
    +1.017564416918053e+00, +1.016391686789653e+00, +1.015184918030332e+00,
    +1.013950835315021e+00, +1.012697033320358e+00, +1.011430749860716e+00,
    +1.010158346781076e+00, +1.008885191761748e+00, +1.007592718305943e+00,
    +1.006805603478092e+00, +1.005378742804807e+00, +1.004049051787112e+00,
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    +9.993014844615166e-01, +9.982531564931281e-01, +9.972595460676951e-01,
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    +9.883042028597552e-01, +9.881383235740961e-01, +9.880133161159576e-01,
    +9.879281898513085e-01, +9.878819413827574e-01, +9.878735508484809e-01,
    +9.879019873841568e-01, +9.879662130250981e-01, +9.880651778500144e-01,
    +9.881978162133899e-01, +9.883630508181326e-01, +9.885597957603544e-01,
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    +1.005515557572658e+00, +1.006052289109999e+00, +1.006575635258931e+00,
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    +1.009754742820913e+00, +1.010124241309341e+00, +1.010468769795370e+00,
    +1.010787087537248e+00, +1.011077969726137e+00, +1.011340205650538e+00,
    +1.011572597114216e+00, +1.011773962181442e+00, +1.011943138906979e+00,
    +1.012078982659783e+00, +1.012180362866919e+00, +1.012246166897464e+00,
    +1.012275305013586e+00, +1.012266707295288e+00, +1.012219319453278e+00,
    +1.012132107622966e+00, +1.012004064757857e+00, +1.011834207632025e+00,
    +1.011621572933544e+00, +1.011365223023975e+00, +1.011064253702468e+00,
    +1.010717792733157e+00, +1.010324996851905e+00, +1.009885057526159e+00,
    +1.009397209381147e+00, +1.008860731864438e+00, +1.008274947065247e+00,
    +1.007639223374887e+00, +1.006952983357691e+00, +1.006215708265639e+00,
    +1.005426938305289e+00, +1.004586273379809e+00, +1.003693377657581e+00,
    +1.002747984657666e+00, +1.001749900308864e+00, +1.000699003803502e+00,
    +9.995952485989262e-01, +9.984386632116344e-01, +9.972293415774932e-01,
    +9.959672769174924e-01, +9.946500332901397e-01, +9.932403996813470e-01,
    +9.912511516117244e-01, +9.895756853352172e-01, +9.877713214760662e-01,
    +9.858577479051078e-01, +9.838303127859196e-01, +9.816822625580078e-01,
    +9.794074486605805e-01, +9.769999155793757e-01, +9.744528356359687e-01,
    +9.717597500340699e-01, +9.689141159310996e-01, +9.659101618500662e-01,
    +9.627421831412876e-01, +9.594038121639412e-01, +9.558889978382734e-01,
    +9.521922434090249e-01, +9.483086322505029e-01, +9.442332539187503e-01,
    +9.399607238929982e-01, +9.354860218216989e-01, +9.308052967663477e-01,
    +9.259146970284931e-01, +9.208101305030523e-01, +9.154873597416558e-01,
    +9.099426066529104e-01, +9.041732260327581e-01, +8.981763729936715e-01,
    +8.919490241013392e-01, +8.854882249661838e-01, +8.787919436722827e-01,
    +8.718585835568161e-01, +8.646864947605047e-01, +8.572738135700366e-01,
    +8.496195859658071e-01, +8.417237467711145e-01, +8.335862715770727e-01,
    +8.252074428838668e-01, +8.165875713256009e-01, +8.077280370477699e-01,
    +7.986311592191131e-01, +7.892986353718001e-01, +7.797330954210866e-01,
    +7.699379531983687e-01, +7.599171886893816e-01, +7.496758423734833e-01,
    +7.392176841476761e-01, +7.285474515411827e-01, +7.176714478163359e-01,
    +7.065962311464494e-01, +6.953282935906302e-01, +6.838739059112046e-01,
    +6.722395305539791e-01, +6.604334017809461e-01, +6.484643596235256e-01,
    +6.363395004626368e-01, +6.240661431421666e-01, +6.116530334821534e-01,
    +5.991098644638286e-01, +5.864461424698465e-01, +5.736694851703749e-01,
    +5.607881029948401e-01, +5.478160663871271e-01, +5.347619788897301e-01,
    +5.216365147692703e-01, +5.084499758302256e-01, +4.952135086430446e-01,
    +4.819387562519412e-01, +4.686361426419003e-01, +4.553170769563941e-01,
    +4.419939954454178e-01, +4.286789889246267e-01, +4.153837786572842e-01,
    +4.021211063103491e-01, +3.889032719013054e-01, +3.757425439137077e-01,
    +3.626515183776310e-01, +3.496431418636322e-01, +3.367290822653354e-01,
    +3.239228075238623e-01, +3.112360816586549e-01, +2.986807941537710e-01,
    +2.862694673284843e-01, +2.740128472224539e-01, +2.619228330079575e-01,
    +2.500098438708934e-01, +2.382847225401669e-01, +2.267578490199104e-01,
    +2.154390996938547e-01, +2.043379825955254e-01, +1.934636765792024e-01,
    +1.828250319214460e-01, +1.724305860483634e-01, +1.622886348529314e-01,
    +1.524071880359812e-01, +1.427939789949266e-01, +1.334565845242183e-01,
    +1.244023922999665e-01, +1.156385879569742e-01, +1.071721547807196e-01,
    +9.900985872728905e-02, +9.115821766572002e-02, +8.362344855837105e-02,
    +7.641140367416376e-02, +6.952749039054598e-02, +6.297656454790079e-02,
    +5.676284244020858e-02, +5.088975408628229e-02, +4.535983304624439e-02,
    +4.017457306236873e-02, +3.533430192568957e-02, +3.083806062123772e-02,
    +2.668355420358626e-02, +2.286680405144430e-02, +1.938236337675363e-02,
    +1.622312720409645e-02, +1.338005016725895e-02, +1.084218595595746e-02,
    +8.596753980908744e-03, +6.640506529168652e-03, +5.172703110468352e-03,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  34. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +3.821992968116373e-04, +5.337292962876158e-04, +7.010318350640769e-04,
    +8.910357994632938e-04, +1.107726421735994e-03, +1.354305556720234e-03,
    +1.632968062524617e-03, +1.944392065549996e-03, +2.291251920978034e-03,
    +2.676357471188558e-03, +3.102160324883627e-03, +3.569302917352426e-03,
    +4.080147004222224e-03, +4.637409387087253e-03, +5.243697651112320e-03,
    +5.900394401532485e-03, +6.609908124535202e-03, +7.375089966000295e-03,
    +8.197610411215884e-03, +9.078195201482999e-03, +1.001888876231112e-02,
    +1.102272421949215e-02, +1.209201783148431e-02, +1.322773320467288e-02,
    +1.443170227861997e-02, +1.570673344965518e-02, +1.705481769961258e-02,
    +1.847711280171765e-02, +1.997546609433320e-02, +2.155255505248360e-02,
    +2.320993080187466e-02, +2.494800748775296e-02, +2.676898100961685e-02,
    +2.867550388692567e-02, +3.066976865911597e-02, +3.275241094528637e-02,
    +3.492474656851959e-02, +3.718932683936013e-02, +3.954748420753697e-02,
    +4.200013716597904e-02, +4.454866443036003e-02, +4.719547798640356e-02,
    +4.994161943600844e-02, +5.278755308483513e-02, +5.573471840677637e-02,
    +5.878567633813699e-02, +6.194176167634657e-02, +6.520301218579141e-02,
    +6.857009288032996e-02, +7.204473108503576e-02, +7.562815385274406e-02,
    +7.932038618419741e-02, +8.312281225703541e-02, +8.703660776989294e-02,
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    +1.038112769854394e-01, +1.082885168352610e-01, +1.128793060660070e-01,
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    +7.005478826218464e-01, +7.089444008783498e-01, +7.172765338080037e-01,
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    +1.012146211141323e+00, +1.012209509774826e+00, +1.012252080651208e+00,
    +1.012273461473019e+00, +1.012274179329824e+00, +1.012253779830287e+00,
    +1.012210860152664e+00, +1.012144976732521e+00, +1.012056685871527e+00,
    +1.011945565763788e+00, +1.011810229432951e+00, +1.011650280893217e+00,
    +1.011466289818154e+00, +1.011257880752579e+00, +1.011023694799342e+00,
    +1.010763375755366e+00, +1.010477533938561e+00, +1.010165826445586e+00,
    +1.009826955798404e+00, +1.009460591235290e+00, +1.009067412134881e+00,
    +1.008647118373303e+00, +1.008198467170796e+00, +1.007721196075366e+00,
    +1.007216031301935e+00, +1.006682757156533e+00, +1.006120180721864e+00,
    +1.005528123164754e+00, +1.004907385380564e+00, +1.004257813991292e+00,
    +1.003578321293819e+00, +1.002868793771428e+00, +1.002130123378852e+00,
    +1.001362250678481e+00, +1.000564166270619e+00, +9.997358689793686e-01,
    +9.988783302889642e-01, +9.979915852192069e-01, +9.970747197397686e-01,
    +9.961277448216609e-01, +9.951529474418550e-01, +9.941541831614942e-01,
    +9.930678080460911e-01, +9.914646039976289e-01, +9.902352352689523e-01,
    +9.889131869680553e-01, +9.875383274623817e-01, +9.861028679251979e-01,
    +9.846041087188396e-01, +9.830394337851476e-01, +9.814052410296346e-01,
    +9.796987091039431e-01, +9.779184677896273e-01, +9.760616740194450e-01,
    +9.741245958128935e-01, +9.721043782586516e-01, +9.699991325531057e-01,
    +9.678068213341133e-01, +9.655234943873925e-01, +9.631470850364502e-01,
    +9.606758082762421e-01, +9.581070287387355e-01, +9.554372064329766e-01,
    +9.526641870716750e-01, +9.497868942084339e-01, +9.468034353946915e-01,
    +9.437103240778303e-01, +9.405054771915659e-01, +9.371877218082764e-01,
    +9.337553821450042e-01, +9.302057763482381e-01, +9.265373496318979e-01,
    +9.227494594741956e-01, +9.188401295674290e-01, +9.148067377557749e-01,
    +9.106476709258303e-01, +9.063629680720371e-01, +9.019514987490371e-01,
    +8.974108808873397e-01, +8.927398817643528e-01, +8.879382683346716e-01,
    +8.830050715882986e-01, +8.779385355821995e-01, +8.727379973888942e-01,
    +8.674038889082810e-01, +8.619352566808824e-01, +8.563305243162549e-01,
    +8.505893287555129e-01, +8.447127297770400e-01, +8.387007637143140e-01,
    +8.325523768291013e-01, +8.262677444285360e-01, +8.198478927378535e-01,
    +8.132935411236417e-01, +8.066040997239516e-01, +7.997809105802602e-01,
    +7.928255537687610e-01, +7.857391245481645e-01, +7.785212684545030e-01,
    +7.711744403395434e-01, +7.637008160854790e-01, +7.561026668755407e-01,
    +7.483805701761127e-01, +7.405363749469933e-01, +7.325730245135402e-01,
    +7.244930008228270e-01, +7.162980305440977e-01, +7.079910089690906e-01,
    +6.995757887359807e-01, +6.910546259244099e-01, +6.824295471401947e-01,
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    +6.469573547411541e-01, +6.378629377753962e-01, +6.286855280775698e-01,
    +6.194273058858271e-01, +6.100922809170846e-01, +6.006842631336996e-01,
    +5.912087588215279e-01, +5.816678990293079e-01, +5.720650011081139e-01,
    +5.624031153715043e-01, +5.526906296747590e-01, +5.429296335729603e-01,
    +5.331253296256703e-01, +5.232805923025862e-01, +5.134010079652535e-01,
    +5.034916218473681e-01, +4.935565059779637e-01, +4.835996679580253e-01,
    +4.736270399539165e-01, +4.636428606356920e-01, +4.536519115376573e-01,
    +4.436589520558524e-01, +4.336702110092904e-01, +4.236905139305571e-01,
    +4.137241358370227e-01, +4.037764981593496e-01, +3.938536636599411e-01,
    +3.839608678121244e-01, +3.741023650337649e-01, +3.642834353302138e-01,
    +3.545105744959439e-01, +3.447887254766501e-01, +3.351225758795436e-01,
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    +2.971215837581699e-01, +2.878124834032541e-01, +2.785898831431837e-01,
    +2.694592444601873e-01, +2.604240268886858e-01, +2.514886909115454e-01,
    +2.426587307354934e-01, +2.339385917103926e-01, +2.253316454409216e-01,
    +2.168420127437019e-01, +2.084745870335012e-01, +2.002332724591125e-01,
    +1.921209969418307e-01, +1.841414579810840e-01, +1.762991374092108e-01,
    +1.685975427109672e-01, +1.610392647455030e-01, +1.536276387455411e-01,
    +1.463667950599712e-01, +1.392599476606262e-01, +1.323093893293405e-01,
    +1.255182155111708e-01, +1.188903216873086e-01, +1.124286726877977e-01,
    +1.061353122093495e-01, +1.000130754353283e-01, +9.406556557413207e-02,
    +8.829543394466104e-02, +8.270438757849530e-02, +7.729486433686703e-02,
    +7.206998099643687e-02, +6.703183558090599e-02, +6.218153160076208e-02,
    +5.752079270262547e-02, +5.305187265543024e-02, +4.877591488398974e-02,
    +4.469299727922282e-02, +4.080367800167831e-02, +3.710883802024244e-02,
    +3.360819061792393e-02, +3.030027537135876e-02, +2.718416076819826e-02,
    +2.425872983336823e-02, +2.152170070657780e-02, +1.896992105664512e-02,
    +1.660053693426304e-02, +1.441002712765955e-02, +1.239334766429038e-02,
    +1.054549096241532e-02, +8.862485552559351e-03, +7.329085750247888e-03,
    +5.896299968476346e-03, +4.914753459788711e-03, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  35. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +3.538498803770035e-04, +4.595886345493055e-04, +5.595519647227489e-04,
    +6.718404887323839e-04, +7.919323614002698e-04, +9.254835101516548e-04,
    +1.069418485858920e-03, +1.227927169310031e-03, +1.398277791978983e-03,
    +1.584491535026729e-03, +1.783653266717233e-03, +1.999873692180148e-03,
    +2.230687004705732e-03, +2.479549413444207e-03, +2.744274680521470e-03,
    +3.028517203082985e-03, +3.329799454594260e-03, +3.651493788541270e-03,
    +3.991659081158673e-03, +4.353535478916468e-03, +4.734803493964832e-03,
    +5.139354888882466e-03, +5.564965156664017e-03, +6.015065135312130e-03,
    +6.487669532207667e-03, +6.986108359341676e-03, +7.507986430774601e-03,
    +8.056692238103912e-03, +8.629882322202329e-03, +9.230898632007642e-03,
    +9.857619542786990e-03, +1.051343406844975e-02, +1.119617236058772e-02,
    +1.190938692951881e-02, +1.265082642578719e-02, +1.342375201935177e-02,
    +1.422598597626579e-02, +1.506090447446532e-02, +1.592611511144210e-02,
    +1.682519266177794e-02, +1.775591229287213e-02, +1.872166356881472e-02,
    +1.972014746423546e-02, +2.075475983187825e-02, +2.182299926812682e-02,
    +2.292828566629717e-02, +2.406813715401559e-02, +2.524583465017564e-02,
    +2.645943128544517e-02, +2.771207863541604e-02, +2.900157039370381e-02,
    +3.033143686044867e-02, +3.169933248543932e-02, +3.310834554878132e-02,
    +3.455615910816914e-02, +3.604609640533871e-02, +3.757564512209753e-02,
    +3.914808612511974e-02, +4.076128638095439e-02, +4.241834056741758e-02,
    +4.411695502674887e-02, +4.586038120884381e-02, +4.764607953574337e-02,
    +4.947719681327219e-02, +5.135136676471998e-02, +5.327183246133368e-02,
    +5.523619574402436e-02, +5.724780220726930e-02, +5.930419525733627e-02,
    +6.140861916695377e-02, +6.355854744461048e-02, +6.575698564821578e-02,
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    +9.038399472465716e-02, +9.311641620512773e-02, +9.590005739506280e-02,
    +9.873233942897164e-02, +1.016162955027316e-01, +1.045493607096311e-01,
    +1.075345731608719e-01, +1.105690806271684e-01, +1.136556251529813e-01,
    +1.167913767515824e-01, +1.199789286645804e-01, +1.232155302990620e-01,
    +1.265040684552515e-01, +1.298417294090302e-01, +1.332315661550852e-01,
    +1.366709127560524e-01, +1.401623800497866e-01, +1.437031543339276e-01,
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    +2.203627179356420e-01, +2.248732557074316e-01, +2.294303802774835e-01,
    +2.340304946493155e-01, +2.386763947872762e-01, +2.433647632018021e-01,
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    +2.625518239753811e-01, +2.674547009618951e-01, +2.723969864831702e-01,
    +2.773809014717047e-01, +2.824031465430401e-01, +2.874658392896952e-01,
    +2.925657097525320e-01, +2.977050145264297e-01, +3.028802866809923e-01,
    +3.080937708388026e-01, +3.133419120661713e-01, +3.186267330325243e-01,
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    +3.401004975161905e-01, +3.455490160824131e-01, +3.510297825670005e-01,
    +3.565392648316303e-01, +3.620795045342974e-01, +3.676468198385683e-01,
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    +5.135297950483941e-01, +5.195228071176610e-01, +5.255203889406241e-01,
    +5.315186369941947e-01, +5.375197039843709e-01, +5.435197203416460e-01,
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    +6.033245382283379e-01, +6.092622887527459e-01, +6.151869491458284e-01,
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    +1.001597808884145e+00, +1.003150760219063e+00, +1.004646500318265e+00,
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    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00
    である、請求項１または６に記載の装置。
  36. 前記分析ウインドウ関数（２４０）または前記合成ウインドウ関数（２９０）は、±１％の公差にて、以下の値によって形成される正順または逆順の連続を少なくとも含み、あるいは０でない場合の以下の値のうちの１０個の部分的連続を少なくとも含み、前記以下の値は、
    +3.235700349233950e-04, +3.821992968116373e-04, +4.346763076430269e-04,
    +4.841399974556557e-04, +5.337292962876158e-04, +5.864735900759105e-04,
    +6.428827504324996e-04, +7.010318350640768e-04, +7.608344672311270e-04,
    +8.240821499679188e-04, +8.910357994632938e-04, +9.604008359868557e-04,
    +1.032187650884365e-03, +1.107726421735994e-03, +1.187132578842487e-03,
    +1.269300730654068e-03, +1.354305556720234e-03, +1.443403284874795e-03,
    +1.536663296357133e-03, +1.632968062524617e-03, +1.732380147404573e-03,
    +1.836145247521724e-03, +1.944392065549996e-03, +2.056125836181849e-03,
    +2.171386021601719e-03, +2.291251920978034e-03, +2.415808383814314e-03,
    +2.544144440874477e-03, +2.676357471188558e-03, +2.813551797283812e-03,
    +2.955803613263345e-03, +3.102160324883627e-03, +3.252661103181324e-03,
    +3.408341073385241e-03, +3.569302917352426e-03, +3.734713566068289e-03,
    +3.904659832213214e-03, +4.080147004222224e-03, +4.261212283030981e-03,
    +4.446929867132814e-03, +4.637409387087253e-03, +4.833793064672789e-03,
    +5.036194779738963e-03, +5.243697651112321e-03, +5.456361749675164e-03,
    +5.675227929566806e-03, +5.900394401532485e-03, +6.131014766883671e-03,
    +6.367178191275927e-03, +6.609908124535202e-03, +6.859253963058476e-03,
    +7.114293307371561e-03, +7.375089966000295e-03, +7.642693523739984e-03,
    +7.917171839712018e-03, +8.197610411215884e-03, +8.484065880416487e-03,
    +8.777567475206218e-03, +9.078195201482999e-03, +9.385078909241503e-03,
    +9.698299554301988e-03, +1.001888876231112e-02, +1.034691797503113e-02,
    +1.068149963936024e-02, +1.102272421949215e-02, +1.137165918496004e-02,
    +1.172838973544289e-02, +1.209201783148431e-02, +1.246260014549782e-02,
    +1.284114967210881e-02, +1.322773320467288e-02, +1.362147156562462e-02,
    +1.402244719763268e-02, +1.443170227861997e-02, +1.484928966105225e-02,
    +1.527427503031274e-02, +1.570673344965518e-02, +1.614774906895406e-02,
    +1.659741217225623e-02, +1.705481769961258e-02, +1.752003567982498e-02,
    +1.799411192217523e-02, +1.847711280171765e-02, +1.896812570518296e-02,
    +1.946722405557199e-02, +1.997546609433320e-02, +2.049290306467406e-02,
    +2.101858037652682e-02, +2.155255505248360e-02, +2.209589582354997e-02,
    +2.264866778978731e-02, +2.320993080187466e-02, +2.377971919482778e-02,
    +2.435904568934701e-02, +2.494800748775296e-02, +2.554578281793083e-02,
    +2.615244880416785e-02, +2.676898100961685e-02, +2.739542549965559e-02,
    +2.803090209537370e-02, +2.867550388692567e-02, +2.933029464839461e-02,
    +2.999535245144327e-02, +3.066976865911597e-02, +3.135358217583060e-02,
    +3.204778132642869e-02, +3.275241094528637e-02, +3.346657321987338e-02,
    +3.419033915994245e-02, +3.492474656851959e-02, +3.566984393450434e-02,
    +3.642469098112518e-02, +3.718932683936013e-02, +3.796477227376223e-02,
    +3.875111047720054e-02, +3.954748420753697e-02, +4.035395199977597e-02,
    +4.117148855800665e-02, +4.200013716597904e-02, +4.283901138210502e-02,
    +4.368817991890082e-02, +4.454866443036003e-02, +4.542050595471842e-02,
    +4.630276577789394e-02, +4.719547798640356e-02, +4.809965043366945e-02,
    +4.901533344583754e-02, +4.994161943600844e-02, +5.087856571149934e-02,
    +5.182719384692941e-02, +5.278755308483513e-02, +5.375872122678868e-02,
    +5.474076083738614e-02, +5.573471840677637e-02, +5.674064972230924e-02,
    +5.775761981233486e-02, +5.878567633813699e-02, +5.982584998609648e-02,
    +6.087818970335195e-02, +6.194176167634657e-02, +6.301659162319866e-02,
    +6.410366584958441e-02, +6.520301218579141e-02, +6.631369927165530e-02,
    +6.743573988811077e-02, +6.857009288032996e-02, +6.971680213521406e-02,
    +7.087499583595998e-02, +7.204473108503576e-02, +7.322699135891000e-02,
    +7.442178588912410e-02, +7.562815385274406e-02, +7.684615718122945e-02,
    +7.807687861830234e-02, +7.932038618419741e-02, +8.057572953286415e-02,
    +8.184289534616669e-02, +8.312281225703541e-02, +8.441550376460240e-02,
    +8.572008755967025e-02, +8.703660776989294e-02, +8.836603137189772e-02,
    +8.970833701278809e-02, +9.106251913073614e-02, +9.242858978650852e-02,
    +9.380757856153675e-02, +9.519952848393795e-02, +9.660349396690321e-02,
    +9.801949952722568e-02, +9.944854075501454e-02, +1.008906469288751e-01,
    +1.023448810132759e-01, +1.038112769854394e-01, +1.052908387348570e-01,
    +1.067835785257166e-01, +1.082885168352610e-01, +1.098056403352340e-01,
    +1.113359035023070e-01, +1.128793060660070e-01, +1.144348917022365e-01,
    +1.160026418427939e-01, +1.175834766182813e-01, +1.191773817925584e-01,
    +1.207834098631640e-01, +1.224015773361210e-01, +1.240328627276697e-01,
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    +1.410428901194039e-01, +1.428131506368226e-01, +1.445965317426731e-01,
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    +1.518555991923989e-01, +1.537021065265166e-01, +1.555605782414143e-01,
    +1.574309942903742e-01, +1.593143180431248e-01, +1.612105639985474e-01,
    +1.631187954209520e-01, +1.650390046254505e-01, +1.669721131327860e-01,
    +1.689180947901775e-01, +1.708759773387028e-01, +1.728457537748600e-01,
    +1.748283801430888e-01, +1.768238156096776e-01, +1.788310228663131e-01,
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    +3.469162810132548e-01, +3.496568059948401e-01, +3.524044231246164e-01,
    +3.551590444946287e-01, +3.579215403419018e-01, +3.606918060977176e-01,
    +3.634687629020059e-01, +3.662523018706806e-01, +3.690432842592497e-01,
    +3.718416007949022e-01, +3.746461722601965e-01, +3.774569030021080e-01,
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    +9.019912955294541e-02, +8.829543394466111e-02, +8.641126446867767e-02,
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    +4.603205697395506e-02, +4.469299727922284e-02, +4.337512126408456e-02,
    +4.207843336193631e-02, +4.080367800167834e-02, +3.955086170148164e-02,
    +3.831925359021936e-02, +3.710883802024247e-02, +3.592031377191350e-02,
    +3.475367083924110e-02, +3.360819061792393e-02, +3.248382426594506e-02,
    +3.138119240391853e-02, +3.030027537135876e-02, +2.924041340892334e-02,
    +2.820153617857359e-02, +2.718416076819826e-02, +2.618823091914950e-02,
    +2.521312012928253e-02, +2.425872983336824e-02, +2.332548569166988e-02,
    +2.241332520509764e-02, +2.152170070657781e-02, +2.065047207339204e-02,
    +1.979990274080047e-02, +1.896992105664513e-02, +1.816012507709582e-02,
    +1.737032543754079e-02, +1.660053693426305e-02, +1.585068068878849e-02,
    +1.512059554489944e-02, +1.441002712765956e-02, +1.371861264850595e-02,
    +1.304629624757017e-02, +1.239334766429038e-02, +1.175941174949483e-02,
    +1.114348079271000e-02, +1.054549096241532e-02, +9.966369456231951e-03,
    +9.405876078723861e-03, +8.862485552559351e-03, +8.334801852513261e-03,
    +7.821914540064593e-03, +7.329085750247891e-03, +6.866427280374203e-03,
    +6.407912160580299e-03, +5.896299968476348e-03, +5.431884551945897e-03,
    +5.251971150005845e-03, +4.914753459788713e-03, +3.326211257672788e-03,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
    +0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00.
    である、請求項１または６に記載の装置。
  37. 複数のフレームを含んでいる情報信号をエンコードするための方法であって、
    少なくとも４つの地点（＃１、＃２、＃３、＃４）に対応して線形関数（４０’、２４０’）を通過する蛇行部分（４４、２４４）を有している分析ウインドウ関数（４０、５０、２４０、７０）を使用して前記情報信号またはその処理されたバージョンの時間ドメイン（ＴＤ）表現を周波数ドメイン（ＦＤ）表現へと変換するための修正コサイン変換（ＭＤＣＴ）分析を実行すること
    を含んでおり、
    前記分析ウインドウ関数は、非対称であるように定義され、
    前記分析ウインドウ関数（４０、２４０）は、前記蛇行部分（４４、９４、２４４）において、
    第１の交差点（＃１）と第２の交差点（＃２）との間の第１の区間（４１、２４１）において前記線形関数（４０’、２４０’）よりも大きくなり、
    前記第２の交差点（＃２）と第３の交差点（＃３）との間の第２の区間（４２、２４２）において前記線形関数（４０’、２４０’）よりも低くなり、
    前記第３の交差点（＃３）と第４の交差点（＃４）との間の第３の区間（４３、２４３）において前記線形関数（４０’、２４０’）よりも大きくなる
    ように定義され、
    前記分析ウインドウ関数は、絶対的な最大値（４１’、２４１’）が前記第１および第３の区間の一方にあるように定義され、
    前記線形関数（４０、２４０）は、定数値１による定数関数である、方法。
  38. 周波数ドメイン（ＦＤ）において定義された情報信号またはその処理されたバージョンをデコードするための方法であって、
    少なくとも４つの地点（＃１、＃２、＃３、＃４）に対応して線形関数を通過する蛇行部分（９４）を有している合成ウインドウ関数（９０）を使用して情報信号またはその処理されたバージョンのＦＤ表現を時間ドメイン（ＴＤ）表現へと変換するための逆修正コサイン変換（ＭＤＣＴ）合成を実行すること
    を含んでおり、
    前記合成ウインドウ関数（９０、２９０）は、前記蛇行部分において、
    第１の交差点と第２の交差点との間の第１の区間において前記線形関数よりも大きくなり、
    前記第２の交差点と第３の交差点との間の第２の区間において前記線形関数よりも低くなり、
    前記第３の交差点と第４の交差点との間の第３の区間において前記線形関数よりも大きくなる
    ように定義され、
    前記合成ウインドウ関数は、絶対的な最大値が前記第１および第３の区間の一方にあるように定義され、
    前記線形関数は、定数値１による定数関数である、
    方法。
  39. プロセッサ上で実行されたときに請求項３７または３８に記載の方法を前記プロセッサに実行させる命令を格納した非一時的な記憶ユニット。
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