JP2005033307A - Design method of digital filter - Google Patents

Design method of digital filter Download PDF

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JP2005033307A
JP2005033307A JP2003193522A JP2003193522A JP2005033307A JP 2005033307 A JP2005033307 A JP 2005033307A JP 2003193522 A JP2003193522 A JP 2003193522A JP 2003193522 A JP2003193522 A JP 2003193522A JP 2005033307 A JP2005033307 A JP 2005033307A
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frequency characteristic
filter
design method
setting value
deconvolution
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JP4214391B2 (en
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Akinori Onuki
昭則 大貫
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ACCUPHASE LABORATORY Inc
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a design method of digital filters capable of easily forming a frequency characteristic close to a setting value with very few effect of adjacent bands without the need for changing the characteristic of the conventional filter single unit, in the digital filter being applied to a graphic equalizer or the like and for forming a composited output frequency characteristic by using a plurality of filter single body units. <P>SOLUTION: In the design method, deconvolution is carried out by using a desired target frequency characteristic formed by a plurality of the filter single body units and respective frequency characteristics of the filter single units, coefficients of each of the filter single body units are set by using respective frequency characteristic setting values of the filter single body units obtained by the deconvolution, and the composited output frequency characteristic is formed on the basis of the coefficients. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【０００１】
【発明の属する技術分野】本発明は、オーディオ機器、映像機器、通信機器等の回路に用いられるデジタル・フィルタに係わり、所望の周波数特性が得られるデジタル・フィルタの設計方法に関する。
【０００２】
【従来の技術】デジタル・フィルタ、例えば、オーディオ機器の音声回路に使用されているグラフィック・イコライザは、周波数特性を変える便利なツールとして古くから活用されている。しかしながら、周波数特性の設定値と実測値に大きな違いがあるのも事実である。従来例において、複数のデジタル・フィルタで構成されたグラフィック・イコライザの周波数特性設定値グラフと実測値グラフに基づいて、この周波数特性の誤差を生ずる原因について詳細に説明する。
【０００３】
（従来例１）
図１０（ａ）に示すようなグラフィック・イコライザ１３の各フィルタ単体１４の振幅特性を周波数特性設定値グラフのように設定したところ、図１０（ｂ）の実測値グラフに示すように実現された従来設計方法による周波数特性１５のカーブには大きな誤差を生じていることがわかる。急激にカーブが変化している部分は特に誤差が大きく設定通りの特性を実現できていない。
【０００４】
（従来例２）
図１１（ａ）に示す周波数特性設定値グラフのように、フィルタ単体１４の１つのバンドのみ振幅を持ち上げることで図１１（ｂ）実測値グラフの従来設計方法による周波数特性１６が確認できる。この実測値グラフの周波数特性を見ると中心周波数ｆ０だけでなく隣接バンドも振幅が増加することがわかる。よってフィルタ単体１４の１つのバンドのみ振幅を持ち上げても、前後数バンドの範囲で振幅が増加して誤差を生じていることが確認できる。
【０００５】
（従来例３）
図１２（ａ）に示す周波数特性設定値グラフのように、７つのフィルタ単体１４の振幅を同じ値に揃えた場合、前記フィルタ単体１４の１つのバンドの時と同様に隣接バンドに影響があり、図１２（ｂ）実測値グラフの従来設計方法による周波数特性１７に示すように両サイドの特性が持ち上がる。また複数個のバンドの振幅を持ち上げると各フィルタの中心周波数の振幅も設定値より大きくなる。これはお互いのバンドが影響し合い、振幅を増加させているからである。
【０００６】
以上説明したように、前記周波数特性設定値グラフのようにフィルタ単体１４の周波数特性を設定しても、設定周波数だけでなく隣接バンドもそれぞれ加算されて前記実測値グラフに示すように隣接バンドの振幅も増減し、所望する周波数特性が得られない。また、隣接バンドの変化しないフィルタを設計したとしても、高次のフィルタが必要となり複雑化して装置が大きくなり高価なコスト負担となる。
【０００７】
【発明が解決しようとする課題】以上説明した現状に鑑み、従来のフィルタ単体の特性を変えることなく、所望の合成出力周波数特性が得られるデジタル・フィルタの設計方法を提供する。
【０００８】
【課題を解決するための手段】本発明者は，上記に鑑み鋭意研究の結果，次の手段によりこの課題を解決した。
（１）グラフィック・イコライザ等に使用される複数のフィルタ単体で合成出力周波数特性を形成するデジタル・フィルタの設計方法において、
前記複数のフィルタ単体で形成される所望の目標周波数特性と、前記複数のフィルタ単体それぞれの周波数特性とで逆たたみ込み演算を行い、該逆たたみ込み演算で求めた前記フィルタ単体のそれぞれの周波数特性設定値によって各フィルタ単体の係数を設定し、それに基づいて合成出力周波数特性を形成することを特徴とするデジタル・フィルタの設計方法であって、従来のフィルタ単体の特性を変えることなく、隣接バンドの影響が極めて少ない、目標周波数特性に近似した特性が容易に形成できる。
【０００９】
（２）前記逆たたみ込み演算で求めた前記フィルタ単体のそれぞれの周波数特性設定値によって各フィルタ単体の係数を設定し、それに基づいて合成出力周波数特性を形成するデジタル・フィルタが、オーディオ機器・映像機器・通信機器等電子機器に組み込まれたデジタル・フィルタに適用できることを特徴とする前項（１）に記載のデジタル・フィルタの設計方法。
【００１０】
【発明の実施の形態】本願発明の実施例図に基づいて詳細に説明する。
図１は本願発明実施例の縦続接続型フィルタの目標周波数特性から「逆たたみ込み演算（＊−１印）」で各フィルタの周波数特性設定値を求める説明図、図２は同発明実施例の「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値によって縦続接続型各フィルタの係数を設定する説明図、図３はフィルタ単体の回路例ブロック図、図４は本願発明実施例の縦続接続型フィルタの目標周波数特性から「逆たたみ込み演算」で各フィルタの周波数特性設定値を求めるフローチャート、図５は縦続接続型フィルタの説明図、図６は縦続接続型フィルタの各フィルタの周波数特性設定値から「たたみ込み演算（＊印）」で合成出力周波数特性を求める説明図、図７は図６で求めた縦続接続型フィルタの合成出力周波数特性から「逆たたみ込み演算（＊−１印）」で各フィルタの周波数特性設定値を求める説明図、図８は本願発明実施例の縦続接続型フィルタの「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値による合成出力周波数特性と、従来方式による各フィルタの周波数特性設定値による合成出力周波数特性との実測結果１の比較グラフ、図９は本願発明実施例の縦続接続型フィルタの「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値による合成出力周波数特性と、従来方式による各フィルタの周波数特性設定値による合成出力周波数特性との実測結果２の比較グラフ、である。
【００１１】
まず現状のグラフィック・イコライザの信号処理を踏まえて、隣接バンドの影響を考慮したフィルタ特性を算出する方法について記述する。なお本実施例ではデジタル信号処理を前提とした、フィルタ単体が加算器と複数の遅延器及び乗算器で構成されたＩＩＲ（Ｉｎｆｉｎｉｔｅ Ｉｍｐｕｌｓｅ Ｒｅｓｐｏｎｓｅ／巡回形）フィルタ・システムを例にして記述する。
【００１２】
図５において、フィルタ単体１の１〜ｎ個による縦続接続型フィルタ３のそれぞれの伝達関数Ｈ１（ｚ）、Ｈ２（ｚ）〜Ｈｎ（ｚ）を設定する。例えば、クオリティ・ファクタＱ＝５，ピークが＋１２ｄＢの２次バンドブースト・フィルタというように設定する。入力信号振幅をＸ（ｚ）、出力信号振幅をＹ（ｚ）、フィルタの伝達関数をＨｎ（ｚ）とすると、伝達関数Ｈ（ｚ）は各フィルタ単体の伝達関数の積で表現できる。
【００１３】
【数１】

Figure 2005033307
【００１４】
ここで、伝達関数を振幅と位相に分解すると、振幅特性Ｍ（ω）は積の形、位相特性θ（ω）は和の形で表現できる。
【００１５】
【数２】
Figure 2005033307
【００１６】
このように、ある周波数での振幅特性は全フィルタの振幅特性の積で表現できる。ここで演算量を軽減するために振幅値を対数スケールに変換する。この変換により振幅特性は全フィルタ特性の和となる。
【００１７】
【数３】
Figure 2005033307
【００１８】
ここで各フィルタの周波数特性設定値とフィルタ単体の周波数特性について検討すると、グラフィック・イコライザの合成出力周波数特性は、フィルタ単体の周波数特性が中心周波数ごとに周波数軸で移動して積分されたものとわかる。したがって各フィルタの振幅値を対数スケールに変換することで積分として扱うことができ、図６のように各フィルタの周波数特性設定値とフィルタ単体の周波数特性５は「たたみ込み」の関係を持っていることが分かる。すなわち、図６（ａ）の各フィルタの周波数特性設定値グラフに示した各フィルタの周波数特性設定値４ａ〜ｉと、図６（ｂ）のフィルタ単体の周波数特性５に基づき「たたみ込み演算（＊印）」すれば、結果として図６（ｃ）に示す「たたみ込み」演算結果による合成出力周波数特性６が算出される。
【００１９】
ここで、グラフィック・イコライザの周波数特性は「たたみ込み」の関係で求められるならば、合成出力周波数特性から各フィルタの周波数特性設定値を求めることも可能になることになる。
【００２０】
各フィルタの周波数特性設定値４ａ〜ｉとフィルタ単体の周波数特性５を「たたみ込み」（＊印）すると合成出力周波数特性６となることから、合成出力周波数特性６をフィルタ単体の周波数特性５で「逆たたみ込み」（＊−１印）した結果は各フィルタの周波数特性設定値４ａ〜ｉとなるのは明白である。その様子を図７に示す。
【００２１】
図７（ｃ）に示す「たたみ込み」演算結果による合成出力周波数特性６と、図７（ｂ）のフィルタ単体の周波数特性５に基づき「逆たたみ込み演算（＊−１印）」すれば、結果として図６（ａ）の各フィルタの周波数特性設定値グラフに示した各フィルタの周波数特性設定値４ａ〜ｉと同様の、図７（ａ）の各フィルタの周波数特性設定値グラフに示した各フィルタの周波数特性設定値４ａ〜ｉが算出される。
【００２２】
ここで合成出力周波数特性を図１（ａ）目標周波数特性７と、図１（ｂ）のフィルタ単体の周波数特性５に基づき「逆たたみ込み演算（＊−１印）」すれば、図１（ｃ）の各フィルタの周波数特性設定値グラフのように隣接バンドへの影響を考慮した各フィルタの周波数特性設定値８ａ〜ｉが求まる。
【００２３】
さらに図１（ａ）の目標周波数特性７から「逆たたみ込み演算（＊−１印）」で求められた図２（ａ）の各フィルタの周波数特性設定値グラフの各フィルタの周波数特性設定値８ａ〜ｉによって図２（ｂ）のように縦続接続型フィルタ３の各フィルタ単体１の係数を設定し、それに基づいて合成出力周波数特性を形成することで誤差を含まないフィルタを実現できる。
【００２４】
すなわち、図３において、１例として、フィルタ単体１は、入力信号Ｘ（ｚ）が乗算器ａ０、遅延器Ｚ−１と直列接続された乗算器ａ１、乗算器ａ１の入力に接続された遅延器Ｚ−１に直列接続された乗算器ａ２のそれぞれを介して加算器１８へ接続され、出力信号Ｙ（ｚ）は遅延器Ｚ−１と直列接続された乗算器ｂ１、乗算器ｂ１の入力に接続された遅延器Ｚ−１に直列接続された乗算器ｂ２のそれぞれを介して加算器１８へ接続された形で構成されている。
ここで上記のように、図１（ａ）の目標周波数特性７から「逆たたみ込み演算（＊−１印）」で求められた図２（ａ）の各フィルタの周波数特性設定値グラフの各フィルタの周波数特性設定値８ａ〜ｉを、前記フィルタ単体１の特性を形成する乗算器ａ０、ａ１、ａ２、ｂ１、ｂ２の係数として設定することで誤差を含まないフィルタを実現できる。
【００２５】
図４は本願発明実施例の縦続接続型フィルタの目標周波数特性から「逆たたみ込み演算」で各フィルタの周波数特性設定値を求めるフローチャートであり、「逆たたみ込み演算」を縦続接続型フィルタに適用する手順は、以下の通りである。
設定手順「ＳＴＡＲＴ」以降、「目標周波数特性を設定」して「振幅値を対数に変換」すると同時に「フィルタ単体の周波数特性を設定」して「振幅値を対数に変換」する。続いて、両者を「逆たたみ込み演算」して得られた各フィルタに設定すべき周波数特性を、グラフィック・イコライザ等ＩＩＲデジタル・フィルタ設計ツール等に入力し、最終的に「各フィルタのフィルタ係数を算出」して「ＳＴＯＰ」する。この結果、目標周波数特性に近似した合成出力周波数特性を実現することができる。
【００２６】
本設計方法によって複雑な伝達関数を実現したフィルタの測定結果を示す。
（実測結果１）
図８において、本図はフィルタ単体７個のバンドの振幅を持ち上げる設定にした場合の実測データで、従来設計方法による合成出力周波数特性９に比べて本願発明設計方法による合成出力周波数特性１０は、隣接バンドの影響が極めて少ない目標周波数特性に近似した周波数特性が形成されていることが分かる。
【００２７】
（実測結果２）
図９において、本図はフィルタ単体１０個のバンド中５個のバンドの振幅を持ち上げ５個のバンドの振幅を下げる設定にした場合の実測データで、上記同様に、従来設計方法による合成出力周波数特性１１に比べて本願発明設計方法による合成出力周波数特性１２は、隣接バンドの影響が極めて少ない目標周波数特性に近似した周波数特性が形成されていることが分かる。
【００２８】
以上、ＩＩＲフィルタ・システム例で説明したが、ＦＩＲ（Ｆｉｎｉｔｅ Ｉｍｐｕｌｓｅ Ｒｅｓｐｏｎｓｅ／非巡回形）フィルタ・システムの設計ツールに適用しても良い。また、並列接続型フィルタに適用することも可能である。
【００２９】
前記逆たたみ込み演算で求めた前記フィルタ単体のそれぞれの周波数特性設定値によって各フィルタ単体の係数を設定し、それに基づいて合成出力周波数特性を形成する前記デジタル・フィルタの設計方法は、オーディオ機器・映像機器・通信機器等電子機器に組み込まれたデジタル・フィルタ全てに適用できる。
【００３０】
【発明の効果】本発明によれば、次のような効果が発揮される。
１）目標とする伝達関数が複雑になっても、容易にフィルタ係数が算出できる。
２）演算時間は伝達関数の複雑さに依らない。
３）所望の合成出力周波数特性が、各フィルタ単体の周波数特性設定値を変えるだけで得られる。
以上のことから、従来のフィルタ単体の特性を変えることなく、隣接バンドの影響が極めて少ない、目標周波数特性に近似した周波数特性を備えたデジタル・フィルタが容易に形成できる。
４）前記デジタル・フィルタの設計方法は、オーディオ機器・映像機器・通信機器等電子機器に組み込まれたデジタル・フィルタ全てに適用できる。
【図面の簡単な説明】
【図１】本願発明実施例の縦続接続型フィルタの目標周波数特性から「逆たたみ込み演算（＊−１印）」で各フィルタの周波数特性設定値を求める説明図。
【図２】同発明実施例の「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値によって縦続接続型各フィルタの係数を設定する説明図。
【図３】フィルタ単体の回路例ブロック図。
【図４】本願発明実施例の縦続接続型フィルタの目標周波数特性から「逆たたみ込み演算」で各フィルタの周波数特性設定値を求めるフローチャート。
【図５】縦続接続型フィルタの説明図。
【図６】縦続接続型フィルタの各フィルタの周波数特性設定値から「たたみ込み演算（＊印）」で合成出力周波数特性を求める説明図。
【図７】図６で求めた縦続接続型フィルタの合成出力周波数特性から「逆たたみ込み演算（＊−１印）」で各フィルタの周波数特性設定値を求める説明図。
【図８】本願発明実施例の縦続接続型フィルタの「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値による合成出力周波数特性と、従来方式による各フィルタの周波数特性設定値による合成出力周波数特性との実測結果１の比較グラフ。
【図９】本願発明実施例の縦続接続型フィルタの「逆たたみ込み演算」で求めた各フィルタの周波数特性設定値による合成出力周波数特性と、従来方式による各フィルタの周波数特性設定値による合成出力周波数特性との実測結果２の比較グラフ。
【図１０】従来例１のグラフィック・イコライザの周波数特性設定値グラフ（ａ）と、実測値グラフ（ｂ）の説明図。
【図１１】従来例２のグラフィック・イコライザの周波数特性設定値グラフ（ａ）と、実測値グラフ（ｂ）の説明図。
【図１２】従来例３のグラフィック・イコライザの周波数特性設定値グラフ（ａ）と、実測値グラフ（ｂ）の説明図。
【符号の説明】
１：フィルタ単体 ２：伝達関数
３：縦続接続型フィルタ ４：周波数特性設定値
５：フィルタ単体の周波数特性 ６：合成出力周波数特性
７：目標周波数特性 ８：周波数特性設定値
９、１１、１５、１６、１７：従来設計方法による合成出力周波数特性
１０、１２：本願発明設計方法による合成出力周波数特性
１３：グラフィック・イコライザ １４：フィルタ単体
１８：加算器[0001]
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital filter used in circuits of audio equipment, video equipment, communication equipment, etc., and to a digital filter design method capable of obtaining a desired frequency characteristic.
[0002]
2. Description of the Related Art Digital filters, such as graphic equalizers used in audio circuits of audio equipment, have long been used as a convenient tool for changing frequency characteristics. However, it is also true that there is a large difference between the set value of the frequency characteristic and the actually measured value. In the conventional example, the cause of the error in the frequency characteristic will be described in detail based on the frequency characteristic setting value graph and the actual measurement value graph of the graphic equalizer constituted by a plurality of digital filters.
[0003]
(Conventional example 1)
When the amplitude characteristic of each filter 14 of the graphic equalizer 13 as shown in FIG. 10A is set as shown in the frequency characteristic setting value graph, it is realized as shown in the actual value graph in FIG. It can be seen that a large error occurs in the curve of the frequency characteristic 15 by the conventional design method. In the portion where the curve changes suddenly, the error is particularly large and the characteristics as set can not be realized.
[0004]
(Conventional example 2)
Like the frequency characteristic setting value graph shown in FIG. 11A, the frequency characteristic 16 according to the conventional design method of the actually measured value graph of FIG. 11B can be confirmed by raising the amplitude of only one band of the filter unit 14. Looking at the frequency characteristics of this measured value graph, it can be seen that not only the center frequency f 0 but also the adjacent bands increase in amplitude. Therefore, even if the amplitude of only one band of the filter unit 14 is increased, it can be confirmed that the amplitude increases in the range of several bands before and after and an error occurs.
[0005]
(Conventional example 3)
As shown in the frequency characteristic setting value graph shown in FIG. 12A, when the amplitudes of the seven single filters 14 are set to the same value, the adjacent bands are affected as in the case of one band of the single filter 14. As shown in FIG. 12B, the frequency characteristics 17 according to the conventional design method in the actual measurement value graph, the characteristics on both sides are raised. Further, when the amplitude of a plurality of bands is raised, the amplitude of the center frequency of each filter becomes larger than the set value. This is because the bands influence each other and increase the amplitude.
[0006]
As described above, even if the frequency characteristic of the filter unit 14 is set as in the frequency characteristic set value graph, not only the set frequency but also the adjacent bands are added, and the adjacent bands are added as shown in the measured value graph. The amplitude also increases or decreases, and the desired frequency characteristics cannot be obtained. Moreover, even if a filter in which the adjacent band does not change is designed, a high-order filter is required and becomes complicated, resulting in a large apparatus and an expensive cost burden.
[0007]
SUMMARY OF THE INVENTION In view of the present situation described above, a digital filter design method capable of obtaining a desired synthesized output frequency characteristic without changing the characteristic of a conventional filter unit is provided.
[0008]
In view of the above, the present inventor has solved this problem by the following means as a result of intensive studies.
(1) In a digital filter design method for forming a composite output frequency characteristic with a plurality of filters used in a graphic equalizer or the like,
A deconvolution operation is performed on a desired target frequency characteristic formed by the plurality of filter units and a frequency characteristic of each of the plurality of filter units, and each frequency characteristic of the filter unit obtained by the deconvolution operation is obtained. A digital filter design method characterized by setting a coefficient of each filter according to a set value and forming a composite output frequency characteristic based on the coefficient, and without changing the characteristics of a conventional filter, Therefore, it is possible to easily form a characteristic approximate to the target frequency characteristic.
[0009]
(2) A digital filter that sets a coefficient of each filter according to a frequency characteristic setting value of each filter obtained by the deconvolution operation and forms a composite output frequency characteristic based on the coefficient, The digital filter design method described in (1) above, which can be applied to a digital filter incorporated in an electronic device such as a device / communication device.
[0010]
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is an explanatory diagram for determining the frequency characteristic setting value of each filter by “deconvolution (* -1 )” from the target frequency characteristic of the cascaded filter of the embodiment of the present invention, and FIG. FIG. 3 is a block diagram of a circuit example of a single filter, and FIG. 4 is a cascade diagram of the embodiment of the present invention. FIG. 5 is an explanatory diagram of the cascade connection type filter, and FIG. 6 is a frequency characteristic of each filter of the cascade connection type filter. The flowchart is for obtaining the frequency characteristic set value of each filter by “deconvolution” from the target frequency characteristic of the connection type filter. FIG. 7 is an explanatory diagram for obtaining a composite output frequency characteristic from a set value by “convolution calculation (marked by *)”, and FIG. 7 shows “deconvolution from the composite output frequency characteristic of the cascaded filter obtained in FIG. FIG. 8 is an explanatory diagram for obtaining the frequency characteristic set value of each filter by “calculation (* -1 )”, and FIG. 8 is the frequency characteristic set value of each filter obtained by “deconvolution calculation” of the cascaded filter of the embodiment of the present invention. FIG. 9 is a comparison graph of the actual measurement result 1 of the synthesized output frequency characteristic by the conventional method and the synthesized output frequency characteristic by the frequency characteristic setting value of each filter according to the conventional method. FIG. 6 is a comparison graph of the actual measurement result 2 between the combined output frequency characteristic based on the frequency characteristic set value of each filter obtained in step 1 and the combined output frequency characteristic based on the frequency characteristic set value of each filter according to the conventional method.
[0011]
First, a method for calculating filter characteristics considering the influence of adjacent bands based on the signal processing of the current graphic equalizer will be described. In the present embodiment, an IIR (Infinite Impulse Response) filter system in which a single filter is composed of an adder, a plurality of delay units, and a multiplier will be described as an example on the premise of digital signal processing.
[0012]
In FIG. 5, transfer functions H1 (z) and H2 (z) to Hn (z) of the cascade connection type filter 3 of 1 to n of the filter units 1 are set. For example, the quality factor is set to Q = 5 and the peak is a +12 dB second-order band boost filter. If the input signal amplitude is X (z), the output signal amplitude is Y (z), and the transfer function of the filter is Hn (z), the transfer function H (z) can be expressed by the product of the transfer functions of the individual filters.
[0013]
[Expression 1]
Figure 2005033307
[0014]
Here, when the transfer function is decomposed into amplitude and phase, the amplitude characteristic M (ω) can be expressed in the form of a product, and the phase characteristic θ (ω) can be expressed in the form of a sum.
[0015]
[Expression 2]
Figure 2005033307
[0016]
Thus, the amplitude characteristic at a certain frequency can be expressed by the product of the amplitude characteristics of all the filters. Here, the amplitude value is converted to a logarithmic scale in order to reduce the calculation amount. By this conversion, the amplitude characteristic becomes the sum of all the filter characteristics.
[0017]
[Equation 3]
Figure 2005033307
[0018]
Considering the frequency characteristic setting value of each filter and the frequency characteristic of the filter alone, the combined output frequency characteristic of the graphic equalizer is that the frequency characteristic of the filter alone is integrated by moving on the frequency axis for each center frequency. Recognize. Therefore, the amplitude value of each filter can be treated as an integral by converting to a logarithmic scale, and the frequency characteristic setting value of each filter and the frequency characteristic 5 of the single filter have a “convolution” relationship as shown in FIG. I understand that. That is, based on the frequency characteristic setting values 4a to 4i of each filter shown in the frequency characteristic setting value graph of each filter in FIG. 6A and the frequency characteristic 5 of the single filter in FIG. As a result, the combined output frequency characteristic 6 based on the “convolution” calculation result shown in FIG. 6C is calculated.
[0019]
Here, if the frequency characteristic of the graphic equalizer is obtained by the “convolution” relationship, the frequency characteristic setting value of each filter can be obtained from the combined output frequency characteristic.
[0020]
When the frequency characteristic setting values 4a to i of each filter and the frequency characteristic 5 of the single filter are “convolved” (marked with *), the combined output frequency characteristic 6 is obtained. It is obvious that the result of “deconvolution” (* −1 ) becomes the frequency characteristic set values 4a to i of each filter. This is shown in FIG.
[0021]
Based on the combined output frequency characteristic 6 based on the result of the “convolution” calculation shown in FIG. 7C and the frequency characteristic 5 of the filter unit shown in FIG. 7B, the “deconvolution calculation (marked with * −1 )” As a result, the frequency characteristic setting value graph of each filter in FIG. 7A is the same as the frequency characteristic setting value 4a to i of each filter shown in the frequency characteristic setting value graph of each filter in FIG. Frequency characteristic setting values 4a to i of each filter are calculated.
[0022]
Here, if the synthesized output frequency characteristic is “deconvolved (* -1 )” based on the target frequency characteristic 7 in FIG. 1 (a) and the frequency characteristic 5 of the single filter in FIG. 1 (b), FIG. As in the frequency characteristic setting value graph of each filter in c), the frequency characteristic setting values 8a to i of each filter in consideration of the influence on adjacent bands are obtained.
[0023]
Furthermore, the frequency characteristic setting value of each filter of the frequency characteristic setting value graph of each filter of FIG. 2A obtained from the target frequency characteristic 7 of FIG. 1A by “deconvolution calculation (* −1 )”. By setting the coefficient of each filter unit 1 of the cascade connection type filter 3 as shown in FIG. 2 (b) by 8a to i and forming the composite output frequency characteristic based on the coefficient, a filter free from errors can be realized.
[0024]
That is, in FIG. 3, connected as an example, filter alone 1, input signal X (z) multiplier a 0, the delay unit Z -1 series-connected multiplier a 1, the input of the multiplier a 1 The output signal Y (z) is connected to the adder 18 via each of the multipliers a 2 connected in series to the delayed delay device Z −1 . The output signal Y (z) is a multiplier b 1 connected in series to the delay device Z −1 . It is configured to be connected to the adder 18 through each of the multipliers b 2 connected in series to the delay device Z -1 connected to the input of the multiplier b 1 .
Here, as described above, each frequency characteristic set value graph of each filter of FIG. 2A obtained from the target frequency characteristic 7 of FIG. 1A by “deconvolution calculation (* -1 mark)”. By setting the frequency characteristic setting values 8a to i of the filter as coefficients of the multipliers a 0 , a 1 , a 2 , b 1 , and b 2 that form the characteristics of the single filter 1 , a filter that does not include an error is realized. it can.
[0025]
FIG. 4 is a flowchart for obtaining the frequency characteristic setting value of each filter by “deconvolution calculation” from the target frequency characteristics of the cascade connection type filter according to the embodiment of the present invention, and applying “deconvolution calculation” to the cascade connection filter. The procedure to do is as follows.
After the setting procedure “START”, “set target frequency characteristic” and “convert amplitude value to logarithm” and “set frequency characteristic of filter alone” and “convert amplitude value to logarithm”. Subsequently, the frequency characteristics to be set for each filter obtained by “deconvolution operation” of both are input to an IIR digital filter design tool such as a graphic equalizer, and finally “filter coefficients of each filter” To "STOP". As a result, a composite output frequency characteristic approximate to the target frequency characteristic can be realized.
[0026]
The measurement result of the filter which realized the complicated transfer function by this design method is shown.
(Measurement result 1)
In FIG. 8, this figure is actual measurement data when setting the amplitude of seven bands of a single filter to be raised. Compared with the synthesized output frequency characteristic 9 by the conventional design method, the synthesized output frequency characteristic 10 by the present invention design method is: It can be seen that a frequency characteristic approximating the target frequency characteristic with very little influence of the adjacent band is formed.
[0027]
(Measurement result 2)
In FIG. 9, this figure shows measured data when the amplitude of five bands out of ten bands of a single filter is raised and the amplitude of the five bands is lowered. Similarly to the above, the synthesized output frequency by the conventional design method is used. It can be seen that, compared to the characteristic 11, the synthesized output frequency characteristic 12 according to the design method of the present invention has a frequency characteristic approximating the target frequency characteristic that is extremely less influenced by adjacent bands.
[0028]
As described above, the example of the IIR filter system has been described. However, the present invention may be applied to a design tool for an FIR (Finite Impulse Response) filter system. Moreover, it is also possible to apply to a parallel connection type filter.
[0029]
The digital filter design method for setting a coefficient of each filter unit based on a frequency characteristic setting value of each filter unit obtained by the deconvolution operation and forming a composite output frequency characteristic based on the coefficient is as follows. It can be applied to all digital filters incorporated in electronic equipment such as video equipment and communication equipment.
[0030]
According to the present invention, the following effects are exhibited.
1) Even if the target transfer function is complicated, the filter coefficient can be easily calculated.
2) The calculation time does not depend on the complexity of the transfer function.
3) A desired combined output frequency characteristic can be obtained by simply changing the frequency characteristic setting value of each filter alone.
From the above, it is possible to easily form a digital filter having a frequency characteristic approximate to the target frequency characteristic, which is extremely less affected by adjacent bands, without changing the characteristic of a conventional filter unit.
4) The digital filter design method can be applied to all digital filters incorporated in electronic equipment such as audio equipment, video equipment, and communication equipment.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram for determining a frequency characteristic set value of each filter by “deconvolution (* −1 )” from a target frequency characteristic of a cascaded filter according to an embodiment of the present invention.
FIG. 2 is an explanatory diagram for setting a coefficient of each cascaded filter according to a frequency characteristic setting value of each filter obtained by “deconvolution calculation” in the embodiment of the present invention.
FIG. 3 is a block diagram of a circuit example of a single filter.
FIG. 4 is a flowchart for obtaining a frequency characteristic setting value of each filter by “deconvolution calculation” from the target frequency characteristic of the cascade connection type filter according to the embodiment of the present invention.
FIG. 5 is an explanatory diagram of a cascade connection type filter.
FIG. 6 is an explanatory diagram for obtaining a composite output frequency characteristic by “convolution calculation (*)” from the frequency characteristic setting value of each filter of the cascade connection type filter.
7 is an explanatory diagram for obtaining a frequency characteristic setting value of each filter by “deconvolution (* −1 )” from the synthesized output frequency characteristic of the cascade connection type filter obtained in FIG. 6;
FIG. 8 shows a combined output frequency characteristic based on the frequency characteristic setting value of each filter obtained by the “deconvolution operation” of the cascaded filter according to the embodiment of the present invention and a combined output based on the frequency characteristic setting value of each filter according to the conventional method. Comparison graph of measurement result 1 with frequency characteristics.
FIG. 9 shows a combined output frequency characteristic based on the frequency characteristic setting value of each filter obtained by the “deconvolution operation” of the cascaded filter of the embodiment of the present invention and a combined output based on the frequency characteristic setting value of each filter according to the conventional method. Comparison graph of measurement result 2 with frequency characteristics.
10 is an explanatory diagram of a frequency characteristic setting value graph (a) and an actual measurement value graph (b) of the graphic equalizer of Conventional Example 1. FIG.
11 is an explanatory diagram of a frequency characteristic setting value graph (a) and an actual measurement value graph (b) of the graphic equalizer of Conventional Example 2. FIG.
12 is an explanatory diagram of a frequency characteristic setting value graph (a) and an actual measurement value graph (b) of the graphic equalizer of Conventional Example 3. FIG.
[Explanation of symbols]
1: Filter unit 2: Transfer function 3: Cascaded filter 4: Frequency characteristic set value 5: Frequency characteristic of filter unit 6: Synthetic output frequency characteristic 7: Target frequency characteristic 8: Frequency characteristic set value 9, 11, 15, 16, 17: Synthetic output frequency characteristic by conventional design method 10, 12: Synthetic output frequency characteristic by present invention design method 13: Graphic equalizer 14: Filter unit 18: Adder

Claims (2)

グラフィック・イコライザ等に使用される複数のフィルタ単体で合成出力周波数特性を形成するデジタル・フィルタの設計方法において、
前記複数のフィルタ単体で形成される所望の目標周波数特性と、前記フィルタ単体それぞれの周波数特性とで逆たたみ込み演算を行い、該逆たたみ込み演算で求めた前記フィルタ単体のそれぞれの周波数特性設定値によって各フィルタ単体の係数を設定し、それに基づいて合成出力周波数特性を形成することを特徴とするデジタル・フィルタの設計方法。In a digital filter design method that forms a composite output frequency characteristic with a plurality of single filters used for graphic equalizers,
Performing a deconvolution operation with a desired target frequency characteristic formed by the plurality of filter units and a frequency characteristic of each of the filter units, and setting each frequency characteristic value of the filter unit obtained by the deconvolution operation A method for designing a digital filter, characterized in that a coefficient of each filter is set according to the above and a combined output frequency characteristic is formed based on the coefficient. 前記逆たたみ込み演算で求めた前記フィルタ単体のそれぞれの周波数特性設定値によって各フィルタ単体の係数を設定し、それに基づいて合成出力周波数特性を形成するデジタル・フィルタが、オーディオ機器・映像機器・通信機器等電子機器に組み込まれたデジタル・フィルタに適用できることを特徴とする請求項１に記載のデジタル・フィルタの設計方法。A digital filter that sets a coefficient of each filter according to the frequency characteristic setting value of each filter obtained by the deconvolution operation, and forms a composite output frequency characteristic based on the coefficient, includes audio equipment, video equipment, and communication. The digital filter design method according to claim 1, wherein the digital filter design method can be applied to a digital filter incorporated in an electronic device such as a device.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2010068319A (en) * 2008-09-11 2010-03-25 Fujitsu Ltd Group delay characteristic compensation apparatus and group delay characteristic compensation method
JP2012213077A (en) * 2011-03-31 2012-11-01 Onkyo Corp Digital signal processing apparatus and digital signal processing method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2010068319A (en) * 2008-09-11 2010-03-25 Fujitsu Ltd Group delay characteristic compensation apparatus and group delay characteristic compensation method
JP2012213077A (en) * 2011-03-31 2012-11-01 Onkyo Corp Digital signal processing apparatus and digital signal processing method

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