JP2004129072A - Sampling frequency conversion device and sampling frequency conversion method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily convert a conversion rate of a sampling frequency with a simplified structure. <P>SOLUTION: On the basis of a sampling frequency Fs<SB>1</SB>of an input signal and a sampling frequency Fs<SB>2</SB>of an output signal there are calculated a ratio R of Fs<SB>1</SB>with respect to Fs<SB>2</SB>, a maximum exponent R<SB>1</SB>of 2 not exceeding R, a ratio R<SB>2</SB>of R with respect to R<SB>1</SB>, and R<SB>3</SB>satisfying R<SB>2</SB>≈R<SB>3</SB>/N and an exponent T of 2, and the input signal is converted to an average signal comprising an average value for every R<SB>1</SB>samples, and thereafter a time position P with T taken as a period is calculated. The time position P is increased for every R3/2, and a linear interpolation on the basis of the time position P is performed for every change of the time position P. <P>COPYRIGHT: (C)2004,JPO

Description

【００２３】
このように、平均信号のサンプリング周波数を１／Ｒ_２倍すると、出力信号のサンプリング周波数Ｆｓ_２を求めることができる。しかしながら、Ｒ_２は、整数と整数との除数であるため、値が小数になり、ハードウェアで演算を実行する際、回路規模が大きくなるという問題がある。そこで、Ｒ_２を整数Ｒ_３と２の巾数との組み合わせで表現する。
【００２４】
Ｒ_２＝Ｒ_３／ｐｏｗ（２，Ｎ）＋Ｒｅ・・・（４）
式（４）において、Ｒ_３、Ｎは、Ｒｅ≒０となるような整数である。式（４）において、Ｒｅ＝０と仮定すると、Ｒ_２＝Ｒ_３／ｐｏｗ（２，Ｎ）となる。サンプリング周波数変換装置１では、平均信号のサンプルの個数をｐｏｗ（２，Ｎ）／Ｒ３倍することにより、平均信号のサンプリング周波数をＦｓ_２に変換できる。
【００２５】
サンプリング周波数変換装置１は、平均信号のサンプリング周波数をｐｏｗ（２，Ｎ）／Ｒ_３倍するために、直線補間を用いる。サンプリング周波数変換装置１は、直線補間に使用される定数として、周期を算出する。周期Ｔは以下の式（５）に基づいて算出される。なお、直線補間の手順については、後述する。
Ｔ＝ｐｏｗ（２，Ｎ）・・・（５）
【００２６】
以上のように、定数Ｒ、Ｒ_１、Ｒ_２、Ｒ_３、Ｎ、Ｔが算出される。なお、ステップＳ１において、Ｆｓ_１およびＦｓ_２の値が変化しない場合には（ステップＳ１；ＮＯ）、サンプリング周波数変換装置１は、定数Ｒ、Ｒ_１、Ｒ_２、Ｒ_３、Ｎ、Ｔの値を更新することなく、ステップＳ３に処理を移行する。
【００２７】
次いで、サンプリング周波数変換装置１は、第２の処理および第３の処理を開始する。第２の処理は、信号の直線補間を行う処理である。第２の処理は、主に、図１のフローチャートのステップＳ４、ステップＳ５、ステップＳ１０、ステップＳ１１に対応する。サンプリング周波数変換装置１はステップＳ４、ステップＳ５において、１回目の直線補間を行い、ステップＳ１０、ステップＳ１１において、２回目の直線補間を行う。サンプリング周波数変換装置１が２回の直線補間を行うのは、直線補間の結果を平均するためであり、これにより、信号のイメージノイズが取り除かれる。
【００２８】
また、第３の処理は、入力信号をＲ１個のサンプルごとに平均をとり、平均信号を生成する処理である。第３の処理は、フローチャートのステップＳ８、ステップＳ１４に対応する。
【００２９】
サンプリング周波数変換装置１が第２の処理として行う直線補間の手順を図２を参照して説明する。図２は、周期Ｍと、平均信号と、出力信号との関係を示す図である。平均信号は、入力信号をＲ_１個のサンプルごとに平均化した信号である。図２は、縦軸を振幅、横軸を時間とするグラフである。図２における、黒丸は平均信号の値を示し、黒四角は出力信号を示している。この図において、Ｉ_１〜Ｉ_４の平均信号が時系列に入力されている。平均信号のサンプリング周期はＴに設定されている。ここで、平均信号の周期を信号の入力された順にＴ_１、Ｔ_２、Ｔ_３と表す。
【００３０】
まず、時間位置Ｐが周期Ｔ_２に存在するとき、サンプリング周波数変換装置１は、Ｉ_２の値を記憶領域Ｂ_２に記憶し、Ｉ_１の値を記憶領域Ｂ_１に記憶する。そして、Ｂ_１、Ｂ_２、Ｔ、Ｐの値を式（６）に代入し、時間位置Ｐにおける直線補間Ｓ_１を算出する。
【００３１】
Ｂ_３＝Ｂ_１×（Ｔ−Ｐ）＋Ｂ_２×Ｐ・・・（６）
【００３２】
ステップＳ４において、直線補間を完了すると、サンプリング周波数変換装置１は、現在のＰの値を式（７）に代入し、Ｐの値を更新する。
Ｐ＝Ｐ＋Ｒ_３／２・・・（７）
そして、Ｐの値がＴより大きくなると（ステップＳ６；ＹＥＳ）、ステップＳ７に処理を移行する。また、Ｐの値がＴを超えない場合には（ステップＳ６；ＮＯ）、サンプリング周波数変換装置１は、処理をステップＳ１０に移行する。
【００３３】
ステップＳ６において、Ｐの値がＴより大きくなった場合、Ｐの時間位置は周期Ｔ_３に移動する。サンプリング周波数変換装置１は、周期Ｔ_３での直線補間を実行するために、Ｂ_１、Ｂ_２に記憶された値を変更する。Ｔ_２の左端の値は、Ｔ_３の右端の値である。そこで、サンプリング周波数変換装置１は、式（８）を用いて、周期Ｔ_２におけるＢ_１の値を記憶領域Ｂ_２に代入し、記憶の時間的移動を行う。（ステップＳ７）。
Ｂ_２＝Ｂ_１・・・（８）
【００３４】
周期Ｔ_３におけるＢ_２の値が設定されると、サンプリング周波数変換装置１は、周期Ｔ_３におけるＢ_１の値を算出する（ステップＳ８）。周期Ｔ_３におけるＢ_１は、Ｒ_１個の入力信号の平均値であり、式（９）をもとに算出することができる。
Ｂ_１＝（Ｉ［ｔ＋０］＋Ｉ［ｔ＋１］＋・・・＋Ｉ［ｔ＋Ｒ_１］）／Ｒ_１・・・（９）
ここで、Ｉ［ｔ］は、入力時刻ｔにおける入力信号と表すため、Ｉ［ｔ］に次いで入力される入力信号は、時系列を持って、Ｉ［ｔ＋０］，Ｉ［ｔ＋１］，・・・，Ｉ［ｔ＋ｎ］となる。
【００３５】
ステップＳ８が終了すると、サンプリング周波数変換装置１は、Ｐの値からＭの値を引き、Ｐの値が０以上Ｍ未満の整数となるように調整する（ステップＳ９）。式（１０）は、Ｐの値を調整するための式である。図２に示すように、式（１０）よって算出されたＰの値は、周期Ｔ_３の時間位置を示している。
Ｐ＝Ｐ−Ｍ・・・（１０）
【００３６】
次いで、サンプリング周波数変換装置１は、２回目の直線補間を行う（ステップＳ１１）。２回目の直線補間は、１回目の直線補間と同様に実行される。ステップＳ１１では、１回目の直線補間の結果と２回目の直線補間の結果との和をＢ_３として出力するため、演算式は式（１１）のように表現される。
Ｂ_３＝Ｂ_３＋Ｂ_１×（Ｍ−Ｐ）＋Ｂ_２×Ｐ・・・（１１）
【００３７】
２回目の直線補間が終了すると、サンプリング周波数変換装置１は、式（６）に従って、Ｐの値を算出し（ステップＳ１１）、Ｐの値がＴより大きい場合には（ステップＳ１２；ＹＥＳ）、記憶領域Ｂ_１に記憶された値を記憶領域Ｂ_２に記憶させるとともに（ステップＳ１３）、新しいＢ_１の算出を行う（ステップＳ１４）。新しいＢ_１を算出すると、サンプリング周波数変換装置１は、Ｐの値からＭの値を引いてＰの値を調整する（ステップＳ１５）。これらの処理によって、Ｂ_１、Ｂ_２、Ｐの値が算出され、次の直線補間が実行できるようになる。なお、ステップＳ１１〜ステップＳ１５までの処理は、それぞれステップＳ５〜ステップＳ９までの処理と同様であるため、詳しい説明を省略する。
【００３８】
次いで、サンプリング周波数変換装置１は、ステップＳ１６に処理を移行し、第４の処理を実行する。第４の処理は、１回目の直線補間と２回目の直線補間の平均をとり、出力信号Ｏを算出する処理である。１回目の直線補間と２回目の直線補間の平均をとる演算は、以下の式（１２）のように表される。
Ｏ＝Ｂ_３／（Ｍ×２）・・・（１２）
Ｂ_３は、１回目の直線補間と２回目の直線補間との和であるため、Ｂ_３を２で割るだけで直線補間の平均は算出される。式（１２）おいて、Ｂ_３をＭ×２で割っているのは、式（７）の直線補間を算出する演算において、式全体をＭで割る演算を省略しているためである。Ｍ×２は２のべき乗であるため、式（１２）の演算は、簡単なビット演算で実行することができる。ステップＳ１６の処理が完了すると、サンプリング周波数変換装置１は、ステップＳ１６で算出した値を出力信号として出力する（ステップＳ１７）。
【００３９】
以下、上述の処理を実行するサンプリング周波数変換装置１の一例について説明する。図３はサンプリング周波数変換装置１の回路構成を示す図である。サンプリング周波数変換装置１の回路は、その処理ごとに４つのブロックに分類される。
【００４０】
図３において、加算器１９と、ＤＱフリップフロップ２０と、除算器２１と、セレクタ２３とは、入力信号の平均値を算出するブロックである。また、乗算器２４と、乗算器２５と、減算器２６と、加算器２７とは、直線補間を行うためのブロックである。また、加算器３２と、ＤＱフリップフロップ３１と、セレクタ３４と、除算器３０とは、直線補間の平均をとるブロックである。ＤＱフリップフロップ２８と、加算器３３とは、時間位置Ｐの算出を行うブロックである。また、マイクロプロセッサ３５は、Ｒ、Ｒ_１、Ｒ_２、Ｒ_３、Ｔ、Ｎの算出を行い、シーケンサ３６は、セレクタの入力信号の制御を行う。
【００４１】
まず、入力信号の平均値を算出する回路について説明する。入力端子１８から信号が入力されると、入力された信号は加算器１９に入力される。加算器１９には、入力信号のほかにセレクタ２３からの信号が入力される。シーケンサ３６は、加算器１９の加算回数がＲ_１に達するまでセレクタ２３のスイッチをＡに設定する。スイッチがＡに設定されている間、加算器１９には、ＤＱフリップフロップ２０に蓄積された信号が出力される。加算器１９は、入力信号とＤＱフリップフロップ２０に蓄積された信号とを加算し、この値をＤＱフリップフロップ２０に蓄積する。シーケンサ３６は、加算器１９の加算数がＲ_１に達すると、セレクタ２３のスイッチをＢに設定し、ＤＱフリップフロップ２０の値をリセットする。そして、ＤＱフリップフロップ２０に累積加算された値は、除算器２１に出力される。除算器２１は、入力された信号をＲ_１で除算する。除算器２１からの出力は、Ｒ_１個のサンプルの平均値になる。
【００４２】
次に、除算器２１から出力された値は、ＤＱフリップフロップ２２および乗算器２４に出力される。ＤＱフリップフロップ２２に出力された値は、１サンプル遅延するため、上述の処理フローにおいてのＢ_１に相当し、乗算器２１に出力された値は遅延がないため、上述の処理フローにおけるＢ_２に相当する。乗算器２４には、ＤＱフリップフロップ２８に格納されたＰの値が出力され、乗算器２４では、入力信号の平均値とＰとの積「Ｂ_２×Ｐ」が算出される。
【００４３】
また、減算器２６において、ＤＱフリップフロップ２８から出力されたＰの値とＭとの差分「Ｔ−Ｐ」が算出され、この値は、乗算器２５に出力される。乗算器２５では、減算器２６からの出力「Ｔ−Ｐ」と入力信号の平均値との積「Ｂ_２×（Ｔ−Ｐ）」が求められる。加算器２７では、乗算器２４からの出力「Ｂ_１×Ｐ」と乗算器２５からの出力「Ｂ_１×（Ｔ−Ｐ）」との和「Ｂ_１×（Ｔ−Ｐ）＋Ｂ_２×Ｐ」を算出する。これにより、直線補間される。
【００４４】
加算器２７によって算出された直線補間の結果は、加算器３２に出力される。加算器３２には、セレクタ３４からの出力が入力される。シーケンサ３６は、加算器３２の加算回数が２回になるまで、セレクタのスイッチをＡにする。スイッチがＡに設定されている間、加算器３２にはＤＱフリップフロップ３１に蓄積された値が出力される。そのため、加算器３２は、加算器２７からの出力とＤＱフリップフロップ３１に蓄積された値とを加算し、この結果をＤＱフリップフロップ３１に蓄積していく。そして、加算器３２の加算回数が２回になると、シーケンサ３６は、セレクタ３４のスイッチをＢに切り換え、ＤＱフリップフロップ３１の値をリセットするとともに、ＤＱフリップフロップ３１に蓄積されていた値を除算器３０に出力する。
【００４５】
除算器３０は、ＤＱフリップフロップ３１から出力された値をＴ×２で除算し、直線補間の結果の平均値を算出する。除算器３０によって算出された値は、出力信号として、出力端子２９を介して外部に出力される。
【００４６】
以上のように、サンプリング周波数変換装置１は、入力信号のサンプリング周波数をＲ_１分の１に変換した後、直線補間を用いて目的のサンプリング周波数に変換する。また、アップサンプリングする場合、サンプリング周波数変換装置１は、直線補間のみを用いて目的のサンプリング周波数に変換する。
【００４７】
サンプリング周波数変換装置１は、Ｒ_１個のサンプルの相加平均を出力信号とすることにより、入力信号のサンプリング周波数をＲ_１分の１に変換する。Ｒ_１サンプルの和を求める演算と、サンプルの和をＲ_１で割る演算とは、単純な回路で実現できる。
【００４８】
また、サンプリング周波数変換装置１は、サンプルの出現する周期をＴに設定し、この周期Ｔに対する時間位置Ｐをもとに直線補間を行う。時間位置Ｐの変位量Ｒ_３／２であり、直線補間はＲ_３／２Ｔの割合で実行される。Ｒ_３、Ｐは整数であり、Ｔは２の巾数であるため、直線補間は２の巾数と整数との四則演算により算出される。このため、直線補間は、単純な回路で実現できる。
【００４９】
また、サンプリング周波数変換装置１は、信号のサンプリング周波数を２×Ｆｓ_２に変換し、変換した信号の２サンプルずつの平均を出力信号として出力する。この処理は、信号に含まれるイメージノイズを除去するために実行される。イメージノイズを回路で除去しようとすると、大きな回路が必要になる。本発明を適用したサンプリング周波数変換装置１は、加算器と記憶素子と乗算器のみでイメージノイズが除去できるため、ハードウェア構成が単純になる。
【００５０】
また、サンプリング周波数変換装置１は、定数Ｒ_１、Ｒ_２、Ｒ_３、Ｔ、Ｎの値をセレクタに入力して、サンプリング周波数の変換レートを制御している。そのため、入力信号のサンプリング周波数Ｆｓ_１と出力信号のサンプリング周波数Ｆｓ_２の変化に応じて定数Ｒ_１、Ｒ_２、Ｒ_３、Ｔ、Ｎを再計算するだけで、サンプリング周波数の変化に対応することができる。
【００５１】
【発明の効果】
上記の課題を解決するため、本発明におけるサンプリング周波数変換装置は、第１のサンプリング周波数でサンプリングされた信号を入力し第２のサンプリング周波数でサンプリングされた信号に変換して出力するサンプリング周波数変換装置であって、第１のサンプリング周波数の第２のサンプリング周波数に対する比（Ｒとする。）を算出する入出力周波数比算出手段と、Ｒを超えない最大の２の巾数（Ｒ_１とする。）を算出する巾数算出手段と、Ｒ_１に対するＲの比（Ｒ_２とする。）を算出する巾数比算出手段と、Ｒ_２を任意の整数Ｒ_３と２の巾数Ｎの逆数とで表される関数で置換する置換手段と、第１のサンプリング周波数でサンプリングされた信号から時系列に連なるＲ_１個の信号値を抽出し、このＲ_１個の信号値ごとに一平均値を算出し、この平均値を平均信号として出力する平均信号算出手段と、第２の巾乗を上記平均信号のサンプリング周期とし、入力信号のサンプリング点に対する出力信号のサンプリング点の相対的な時間位置を算出する時間位置算出手段と、平均信号を算出された時間位置で直線補間し、補間して得た値を出力信号とする。そのため、回路構成が簡単であるだけではなく、入力信号のサンプリング周波数および出力信号のサンプリング周波数の変更が容易なサンプリング周波数変換装置を提供することができる。
【００５２】
また、本発明におけるサンプリング周波数変更方法は、第１のサンプリング周波数でサンプリングされた信号を入力し第２のサンプリング周波数でサンプリングされた信号に変換して出力するサンプリング周波数変換方法であって、第１のサンプリング周波数の第２のサンプリング周波数に対する比（Ｒとする。）を算出する入出力周波数比算出工程と、Ｒを超えない最大の２の巾数（Ｒ_１とする。）を算出する巾数算出工程と、Ｒ_１に対するＲの比（Ｒ_２とする。）を算出する巾数比算出工程と、Ｒ_２を任意の整数Ｒ_３と２の巾数Ｎの逆数とで表される関数で置換する置換工程と、第１のサンプリング周波数でサンプリングされた信号から時系列に連なるＲ_１個の信号値を抽出し、このＲ_１の信号値ごとに一平均値を算出し、この平均値を平均信号として出力する平均信号算出工程と、第２の巾乗を平均信号のサンプリング周期とし、入力信号のサンプリング点に対する出力信号のサンプリング点の相対的な時間位置を算出する時間位置算出工程と、平均信号を算出された時間位置で直線補間し、補間して得た値を上記出力信号とする。そのため、この方法をサンプリング周波数変換装置に適用すると、サンプリング周波数変換装置の回路構成を簡単にするとともに、入力信号のサンプリング周波数および出力信号のサンプリング周波数を容易に変化させることができる。
【図面の簡単な説明】
【図１】サンプリング周波数を変換する手順を示すフローチャートである。
【図２】直線補間の手順を示す図である。
【図３】サンプリング周波数変換装置の回路構成を示す図である。
【符号の説明】
１　サンプリング周波数変換装置、１８　入力端子、１９　加算器、２０　ＤＱフリップフロップ、２１　除算器、２２　ＤＱフリップフロップ、２３　セレクタ、２４　乗算器、２５　乗算器、２６　減算器、２７　加算器、２８　ＤＱフリップフロップ、２９　出力端子、３０　除算器、３１　ＤＱフリップフロップ、３２　加算器、３３　加算器、３４　セレクタ[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a sampling frequency conversion device and a sampling frequency conversion method for resampling a sampling frequency of a sampled time-series signal.
[0002]
[Prior art]
In recent years, the sampling frequency of digital audio signals has been mixed with a large number of sampling frequencies such as 32 kHz for digital video, 44.1 kHz for compact discs, and 96 kHz for DVD-Audio.
[0003]
Therefore, the sampling frequencies of the digital audio signal supplied to the encoding device, the digital audio signal obtained from the decoding device, and the digital audio signal obtained from the decoding device do not always match between the devices. Therefore, when interconnecting electronic devices, it is necessary to reconvert the sampling frequency.
[0004]
Generally, the conversion of the sampling frequency is classified into interpolation and resampling. Interpolation is a process of creating a new continuous function from discrete signal data, and resampling is a process of creating new discrete signal data from a continuous function. In order to create a continuous function from the discrete signal data, a linear combination of the discrete signal data and the interpolation kernel, that is, convolution is performed.
[0005]
[Problems to be solved by the invention]
Conventionally, as a method of converting a sampling frequency, there is a method using a filter bank. In this method, the least common multiple of the sampling frequency of the output signal and the sampling frequency of the input signal is obtained, the input signal is upsampled by the least common multiple, interpolated by a low-pass filter, and downsampled to the sampling frequency of the output signal. I do.
[0006]
If the sampling frequency of the output signal is lower than the sampling frequency of the input signal, it is necessary to perform filtering before downsampling, and the processing load on the sampling frequency conversion device increases.
[0007]
On the other hand, if the sampling frequency of the output signal is higher than the sampling frequency of the input signal, it is necessary to perform filtering before upsampling, and the processing load on the sampling frequency converter increases.
[0008]
As described above, when the sampling frequency is converted using the filter bank, the processing load of the sampling frequency conversion device increases. Therefore, it is necessary to increase the circuit scale and the operating speed.
[0009]
Further, in the method using the filter bank, it is necessary to redesign the filter every time the sampling frequency of the input signal or the sampling frequency of the output signal is changed. In calculating the coefficients of the filter, the design must be made with careful attention to chessboard distortion and the like, which is complicated and requires many processes. A complicated filter has a large input / output delay time, which deteriorates the response characteristics of the entire device.
[0010]
The present invention has been made in view of the above problems, and has a simple circuit configuration, and a sampling frequency conversion device and a sampling frequency conversion that can easily change the sampling frequency of an input signal and the sampling frequency of an output signal. The aim is to provide a method.
[0011]
[Means for Solving the Problems]
In order to solve the above problem, a sampling frequency conversion device according to the present invention is provided with a sampling frequency conversion device that inputs a signal sampled at a first sampling frequency, converts the signal into a signal sampled at a second sampling frequency, and outputs the converted signal. Input / output frequency ratio calculating means for calculating a ratio (R) of the first sampling frequency to the second sampling frequency, and a maximum width of 2 (R ₁ And ) Is calculated, and R ₁ To the ratio of R to (R ₂ And ) For calculating the width ratio ratio; ₂ Is any integer R ₃ And a replacement means for performing replacement by a function represented by a function represented by a reciprocal of the width N of 2 and a signal R sampled at the first sampling frequency. ₁ Signal values are extracted, and this R ₁ Average signal calculation means for calculating an average value for each of the signal values, and outputting the average value as an average signal; an output signal for a sampling point of the input signal, wherein the second power is used as a sampling period of the average signal. And a time position calculating means for calculating a relative time position of the sampling point, and linearly interpolating the average signal at the calculated time position, and use the value obtained by the interpolation as an output signal.
[0012]
Further, the sampling frequency changing method according to the present invention is a sampling frequency conversion method for inputting a signal sampled at a first sampling frequency, converting the signal into a signal sampled at a second sampling frequency, and outputting the converted signal. An input / output frequency ratio calculating step of calculating a ratio (R) of the sampling frequency of the second sampling frequency to the second sampling frequency; ₁ And ) Is calculated, and R is calculated. ₁ To the ratio of R to (R ₂ And ) Is calculated, and R is calculated. ₂ Is any integer R ₃ And a replacement step of performing a replacement with a function represented by a reciprocal of a width N of 2 and an R that continues in time series from a signal sampled at the first sampling frequency. ₁ Signal values are extracted, and this R ₁ Calculating an average value for each signal value, and outputting the average value as an average signal; and sampling the output signal with respect to the sampling point of the input signal using the second power as the sampling period of the average signal. A time position calculating step of calculating a relative time position of a point, linear interpolation is performed on the average signal at the calculated time position, and a value obtained by the interpolation is used as the output signal.
[0013]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, a sampling frequency conversion device to which the present invention is applied will be described. The sampling frequency conversion device mainly converts the sampling frequency by performing four processes. The first processing is a sampling frequency Fs of the input signal. ₁ And the sampling frequency Fs of the output signal ₂ Constants R, R ₁ , R ₂ , R ₃ , N, and T. This processing corresponds to steps S1 and S2 in the flowchart. Here, the constant R is the sampling frequency Fs of the input signal. ₁ Output signal sampling frequency Fs ₂ And R ₁ Is a value obtained by approximating R by a power of 2. ₂ Is R and R ₁ Is a value indicating the error of ₃ And N is R ₂ Is a value used when approximating by an integer and a power of 2, and T is a value indicating a period between samples in linear interpolation.
[0014]
Hereinafter, the four processes executed by the sampling frequency conversion device 1 will be described with reference to the flowchart of FIG. The sampling frequency conversion device 1 outputs the sampling signal Fs of the input signal. ₁ And the sampling frequency Fs of the output signal ₂ Constantly monitor changes in ₁ And / or Fs ₂ Is changed (Step S1; YES), the process proceeds to Step S2, and the constants R, R ₁ , R ₂ , R ₃ , N, T are updated (step S2).
[0015]
In step S2, the sampling frequency converter 1 sets constants R, R ₁ , R ₂ , R ₃ , T are calculated as follows. The sampling frequency conversion device 1 first calculates a constant R. The constant R is the sampling frequency Fs of the input signal. ₁ And the sampling frequency Fs of the output signal ₂ Is obtained by the following equation (1).
R = Fs ₁ / Fs ₂ ... (1)
[0016]
Next, the sampling frequency converter 1 calculates a constant R ₁ Is calculated. Constant R ₁ Is a value obtained by the following equation (2).
R ₁ = Pow (2, floor (log2 (max (1, R))) (2)
Where pow (x, y) is a function that returns x to the power of y
floor (x) is a function that returns the largest integer value not exceeding x
log2 (x) is the logarithm when x is base 2
max (x, y) is a function that returns the larger of x and y
It is.
[0017]
R calculated by equation (2) ₁ Takes different values depending on whether the input signal is down-sampled or up-sampled. R for downsampling ₁ And R for upsampling ₁ The difference between the calculation results and will be described.
[0018]
When downsampling, Fs ₁ > Fs ₂ Therefore, R> 1. At this time, the return value of max (1, R) is R, and R ₁ Is the maximum power of 2 that does not exceed R. When downsampling, the constant R ₁ Is used as the number of samples for averaging the input signal. R ₁ When one average value is obtained from the number of samples, the sampling frequency Fs of the input signal is obtained. ₁ Is Fs ₁ × (1 / R ₁ ). Hereinafter, R ₁ The signal averaged for each sample is referred to as an average signal.
[0019]
On the other hand, when upsampling, Fs ₁ <Fs ₂ And R <1. The return value of max (1, R) is 1, and R ₁ Is 1.
[0020]
When upsampling a signal, R ₁ Is 1. Obtaining the average value of one sample does not change the value of the sample and the number of samples. Therefore, the input signal is output as it is, and the sampling frequency Fs of the input signal is output. ₁ Also does not change.
[0021]
In step S2, the sampling frequency conversion device 1 further calculates R2. R2 is a value obtained by the following equation (3).
R ₂ = R / R ₁ ... (3)
[0022]
R ₂ Is the sampling frequency Fs of the average signal ₁ × (1 / R ₁ ) To Fs ₂ Used as a constant to convert to R ₂ The meaning of is explained using a mathematical expression. In the following equation, the sampling frequency of the average signal is Fs _Mean Expressed by

[0023]
Thus, the sampling frequency of the average signal is 1 / R ₂ When multiplied, the sampling frequency Fs of the output signal ₂ Can be requested. However, R ₂ Is a divisor of an integer and an integer, so that the value becomes a decimal number, and there is a problem that a circuit scale becomes large when performing an operation by hardware. Then, R ₂ Is an integer R ₃ It is expressed by a combination of and a width of 2.
[0024]
R ₂ = R ₃ /Pow(2,N)+Re...(4)
In the formula (4), R ₃ , N are integers such that Re ≒ 0. In equation (4), assuming that Re = 0, R ₂ = R ₃ / Pow (2, N). The sampling frequency conversion device 1 multiplies the number of samples of the average signal by pow (2, N) / R3 to set the sampling frequency of the average signal to Fs. ₂ Can be converted to
[0025]
The sampling frequency converter 1 sets the sampling frequency of the average signal to pow (2, N) / R ₃ To do so, linear interpolation is used. The sampling frequency conversion device 1 calculates a period as a constant used for linear interpolation. The cycle T is calculated based on the following equation (5). The procedure of the linear interpolation will be described later.
T = pow (2, N) (5)
[0026]
As described above, the constants R, R ₁ , R ₂ , R ₃ , N, T are calculated. In step S1, Fs ₁ And Fs ₂ Does not change (step S1; NO), the sampling frequency converter 1 sets the constants R and R ₁ , R ₂ , R ₃ , N, and T, without updating the values, the process proceeds to step S3.
[0027]
Next, the sampling frequency conversion device 1 starts the second processing and the third processing. The second process is a process of performing linear interpolation of a signal. The second process mainly corresponds to step S4, step S5, step S10, and step S11 in the flowchart of FIG. The sampling frequency conversion device 1 performs the first linear interpolation in steps S4 and S5, and performs the second linear interpolation in steps S10 and S11. The reason why the sampling frequency conversion device 1 performs the linear interpolation twice is to average the result of the linear interpolation, thereby removing the image noise of the signal.
[0028]
The third process is a process of averaging the input signal for every R1 samples to generate an average signal. The third process corresponds to steps S8 and S14 in the flowchart.
[0029]
The procedure of the linear interpolation performed by the sampling frequency conversion device 1 as the second process will be described with reference to FIG. FIG. 2 is a diagram showing the relationship between the period M, the average signal, and the output signal. The average signal is calculated by dividing the input signal by R ₁ This is a signal averaged for each sample. FIG. 2 is a graph with the vertical axis representing amplitude and the horizontal axis representing time. In FIG. 2, black circles indicate the value of the average signal, and black squares indicate the output signal. In this figure, I ₁ ~ I ₄ Are input in time series. The sampling period of the average signal is set to T. Here, the cycle of the average signal is set to T in the order of input of the signal. ₁ , T ₂ , T ₃ It expresses.
[0030]
First, the time position P is the period T ₂ , The sampling frequency conversion device 1 ₂ Value of storage area B ₂ And I ₁ Value of storage area B ₁ To memorize. And B ₁ , B ₂ , T, and P are substituted into equation (6) to obtain a linear interpolation S at the time position P. ₁ Is calculated.
[0031]
B ₃ = B ₁ × (TP) + B ₂ × P ・ ・ ・ (6)
[0032]
In step S4, when the linear interpolation is completed, the sampling frequency conversion device 1 substitutes the current value of P into Expression (7) and updates the value of P.
P = P + R ₃ /2...(7)
Then, when the value of P becomes larger than T (step S6; YES), the process proceeds to step S7. If the value of P does not exceed T (step S6; NO), the sampling frequency conversion device 1 shifts the processing to step S10.
[0033]
If the value of P becomes larger than T in step S6, the time position of P is the period T ₃ Move to The sampling frequency converter 1 has a period T ₃ To perform linear interpolation on ₁ , B ₂ Change the value stored in. T ₂ Is the leftmost value of T ₃ Is the rightmost value of Therefore, the sampling frequency conversion device 1 calculates the period T using equation (8). ₂ B in ₁ Value of storage area B ₂ To shift the memory over time. (Step S7).
B ₂ = B ₁ ... (8)
[0034]
Period T ₃ B in ₂ Is set, the sampling frequency converter 1 sets the period T ₃ B in ₁ Is calculated (step S8). Period T ₃ B in ₁ Is R ₁ This is the average value of the input signals and can be calculated based on equation (9).
B ₁ = (I [t + 0] + I [t + 1] +... + I [t + R ₁ ] / R ₁ ... (9)
Here, since I [t] is represented as an input signal at the input time t, the input signal input next to I [t] has a time series of I [t + 0], I [t + 1],. , I [t + n].
[0035]
When step S8 ends, the sampling frequency conversion device 1 subtracts the value of M from the value of P and adjusts the value of P to be an integer greater than or equal to 0 and less than M (step S9). Equation (10) is an equation for adjusting the value of P. As shown in FIG. 2, the value of P calculated by the equation (10) is equal to the period T ₃ Shows the time position of.
P = PM (10)
[0036]
Next, the sampling frequency conversion device 1 performs the second linear interpolation (step S11). The second linear interpolation is performed in the same manner as the first linear interpolation. In step S11, the sum of the result of the first linear interpolation and the result of the second linear interpolation is represented by B ₃ Thus, the operation expression is expressed as in Expression (11).
B ₃ = B ₃ + B ₁ × (MP) + B ₂ × P ... (11)
[0037]
When the second linear interpolation is completed, the sampling frequency conversion device 1 calculates the value of P according to equation (6) (step S11). If the value of P is larger than T (step S12; YES), Storage area B ₁ The value stored in the storage area B ₂ (Step S13), and the new B ₁ Is calculated (step S14). New B ₁ Is calculated, the sampling frequency converter 1 adjusts the value of P by subtracting the value of M from the value of P (step S15). By these processes, B ₁ , B ₂ , P is calculated, and the next linear interpolation can be executed. Note that the processes in steps S11 to S15 are the same as the processes in steps S5 to S9, respectively, and thus detailed description will be omitted.
[0038]
Next, the sampling frequency conversion device 1 shifts the processing to step S16 and executes the fourth processing. The fourth process is a process of calculating an output signal O by averaging the first linear interpolation and the second linear interpolation. The calculation for averaging the first linear interpolation and the second linear interpolation is represented by the following equation (12).
O = B ₃ / (M × 2) (12)
B ₃ Is the sum of the first linear interpolation and the second linear interpolation. ₃ Is simply divided by 2 to calculate the average of the linear interpolation. In equation (12), B ₃ Is divided by M × 2 because the calculation of dividing the entire expression by M is omitted in the calculation of calculating the linear interpolation in Expression (7). Since M × 2 is a power of 2, the operation of Expression (12) can be executed by a simple bit operation. When the processing in step S16 is completed, the sampling frequency conversion device 1 outputs the value calculated in step S16 as an output signal (step S17).
[0039]
Hereinafter, an example of the sampling frequency conversion device 1 that performs the above-described processing will be described. FIG. 3 is a diagram showing a circuit configuration of the sampling frequency conversion device 1. The circuit of the sampling frequency conversion device 1 is classified into four blocks for each processing.
[0040]
3, an adder 19, a DQ flip-flop 20, a divider 21, and a selector 23 are blocks for calculating an average value of an input signal. The multiplier 24, the multiplier 25, the subtractor 26, and the adder 27 are blocks for performing linear interpolation. The adder 32, the DQ flip-flop 31, the selector 34, and the divider 30 are blocks for averaging linear interpolation. The DQ flip-flop 28 and the adder 33 are blocks for calculating the time position P. Further, the microprocessor 35 includes R, R ₁ , R ₂ , R ₃ , T, and N, and the sequencer 36 controls the input signal of the selector.
[0041]
First, a circuit for calculating the average value of the input signal will be described. When a signal is input from the input terminal 18, the input signal is input to the adder 19. A signal from the selector 23 is input to the adder 19 in addition to the input signal. The sequencer 36 determines that the number of additions of the adder 19 is R ₁ The switch of the selector 23 is set to A until it reaches. While the switch is set to A, the signal accumulated in the DQ flip-flop 20 is output to the adder 19. The adder 19 adds the input signal and the signal stored in the DQ flip-flop 20, and stores this value in the DQ flip-flop 20. The sequencer 36 determines that the addition number of the adder 19 is R ₁ , The switch of the selector 23 is set to B, and the value of the DQ flip-flop 20 is reset. The value cumulatively added to the DQ flip-flop 20 is output to the divider 21. The divider 21 converts the input signal to R ₁ Divide by. The output from the divider 21 is R ₁ It is the average of the samples.
[0042]
Next, the value output from the divider 21 is output to the DQ flip-flop 22 and the multiplier 24. Since the value output to the DQ flip-flop 22 is delayed by one sample, B ₁ And the value output to the multiplier 21 has no delay. ₂ Is equivalent to The value of P stored in the DQ flip-flop 28 is output to the multiplier 24, and the product “B” of the average value of the input signal and P is output to the multiplier 24. ₂ × P ”is calculated.
[0043]
Further, the subtracter 26 calculates a difference “TP” between the value of P output from the DQ flip-flop 28 and M, and outputs this value to the multiplier 25. In the multiplier 25, the product “B” of the output “TP” from the subtractor 26 and the average value of the input signal ₂ × (T−P) ”is required. In the adder 27, the output “B” from the multiplier 24 ₁ × P ”and the output“ B ”from the multiplier 25 ₁ × (TP) ”and the sum“ B ₁ × (TP) + B ₂ × P ”is calculated. Thereby, linear interpolation is performed.
[0044]
The result of the linear interpolation calculated by the adder 27 is output to the adder 32. The output from the selector 34 is input to the adder 32. The sequencer 36 sets the selector switch to A until the number of additions of the adder 32 becomes two. While the switch is set to A, the value stored in the DQ flip-flop 31 is output to the adder 32. Therefore, the adder 32 adds the output from the adder 27 and the value stored in the DQ flip-flop 31, and stores the result in the DQ flip-flop 31. Then, when the number of additions of the adder 32 becomes two, the sequencer 36 switches the switch of the selector 34 to B, resets the value of the DQ flip-flop 31, and divides the value stored in the DQ flip-flop 31. Output to the container 30.
[0045]
The divider 30 divides the value output from the DQ flip-flop 31 by T × 2, and calculates an average value of the result of the linear interpolation. The value calculated by the divider 30 is output to the outside via the output terminal 29 as an output signal.
[0046]
As described above, the sampling frequency conversion device 1 sets the sampling frequency of the input signal to R ₁ After the conversion, the data is converted to a target sampling frequency using linear interpolation. When performing upsampling, the sampling frequency conversion device 1 converts the data into a target sampling frequency using only linear interpolation.
[0047]
Sampling frequency conversion device 1 has R ₁ By using the arithmetic mean of the number of samples as the output signal, the sampling frequency of the input signal ₁ Convert to 1 / R ₁ An operation to obtain the sum of the samples, and ₁ The operation of dividing by can be realized by a simple circuit.
[0048]
Further, the sampling frequency conversion device 1 sets the cycle in which the sample appears to T, and performs linear interpolation based on the time position P with respect to this cycle T. Displacement R of time position P ₃ / 2, and the linear interpolation is R ₃ / 2T. R ₃ , P are integers and T is a power of two, so linear interpolation is calculated by four arithmetic operations on the power of two and an integer. Therefore, linear interpolation can be realized with a simple circuit.
[0049]
The sampling frequency conversion device 1 sets the sampling frequency of the signal to 2 × Fs ₂ And outputs an average of every two samples of the converted signal as an output signal. This process is performed to remove image noise included in the signal. To remove image noise by a circuit, a large circuit is required. In the sampling frequency conversion device 1 to which the present invention is applied, since the image noise can be removed only by the adder, the storage element, and the multiplier, the hardware configuration is simplified.
[0050]
In addition, the sampling frequency converter 1 has a constant R ₁ , R ₂ , R ₃ , T, and N are input to the selector to control the conversion rate of the sampling frequency. Therefore, the sampling frequency Fs of the input signal ₁ And the sampling frequency Fs of the output signal ₂ Constant R according to the change of ₁ , R ₂ , R ₃ , T, and N, it is possible to cope with a change in the sampling frequency.
[0051]
【The invention's effect】
In order to solve the above problem, a sampling frequency conversion device according to the present invention is provided with a sampling frequency conversion device that inputs a signal sampled at a first sampling frequency, converts the signal into a signal sampled at a second sampling frequency, and outputs the converted signal. Input / output frequency ratio calculating means for calculating a ratio (R) of the first sampling frequency to the second sampling frequency, and a maximum width of 2 (R ₁ And ) Is calculated, and R ₁ To the ratio of R to (R ₂ And ) For calculating the width ratio ratio; ₂ Is any integer R ₃ And a replacement means for performing replacement by a function represented by a function represented by a reciprocal of the width N of 2 and a signal R sampled at the first sampling frequency. ₁ Signal values are extracted, and this R ₁ Average signal calculation means for calculating an average value for each of the signal values, and outputting the average value as an average signal; an output signal for a sampling point of the input signal, wherein the second power is used as a sampling period of the average signal. And a time position calculating means for calculating a relative time position of the sampling point, and linearly interpolating the average signal at the calculated time position, and use the value obtained by the interpolation as an output signal. Therefore, it is possible to provide a sampling frequency conversion device which not only has a simple circuit configuration but also easily changes the sampling frequency of an input signal and the sampling frequency of an output signal.
[0052]
Further, the sampling frequency changing method according to the present invention is a sampling frequency conversion method for inputting a signal sampled at a first sampling frequency, converting the signal into a signal sampled at a second sampling frequency, and outputting the converted signal. An input / output frequency ratio calculating step of calculating a ratio (R) of the sampling frequency of the second sampling frequency to the second sampling frequency; ₁ And ) Is calculated, and R is calculated. ₁ To the ratio of R to (R ₂ And ) Is calculated, and R is calculated. ₂ Is any integer R ₃ And a replacement step of performing a replacement with a function represented by a reciprocal of a width N of 2 and an R that continues in time series from a signal sampled at the first sampling frequency. ₁ Signal values are extracted, and this R ₁ Calculating an average value for each signal value, and outputting the average value as an average signal; and sampling the output signal with respect to the sampling point of the input signal using the second power as the sampling period of the average signal. A time position calculating step of calculating a relative time position of a point, linear interpolation is performed on the average signal at the calculated time position, and a value obtained by the interpolation is used as the output signal. Therefore, when this method is applied to the sampling frequency converter, the circuit configuration of the sampling frequency converter can be simplified, and the sampling frequency of the input signal and the sampling frequency of the output signal can be easily changed.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a procedure for converting a sampling frequency.
FIG. 2 is a diagram showing a procedure of linear interpolation.
FIG. 3 is a diagram showing a circuit configuration of a sampling frequency conversion device.
[Explanation of symbols]
1 sampling frequency converter, 18 input terminals, 19 adder, 20 DQ flip-flop, 21 divider, 22 DQ flip-flop, 23 selector, 24 multiplier, 25 multiplier, 26 subtractor, 27 adder, 28 DQ flip-flop , 29 output terminals, 30 divider, 31 DQ flip-flop, 32 adder, 33 adder, 34 selector

Claims (12)

A sampling frequency conversion device that inputs a signal sampled at a first sampling frequency, converts the signal into an output signal sampled at a second sampling frequency, and outputs the output signal.
Input / output frequency ratio calculation means for calculating a ratio (R) of the first sampling frequency to the second sampling frequency;
And exponent calculation means for calculating the maximum second width number (and R _1.) Does not exceed the above R,
A width ratio calculating means for calculating a ratio of R (R ₂ to.) With respect to the R _1,
Replacement means for replacing the above R ₂ with a function represented by an arbitrary integer R ₃ and a reciprocal of a width N of 2;
R ₁ signal values connected in a time series are extracted from the signal sampled at the first sampling frequency, an average value is calculated for each of the R ₁ signal values, and the average value is output as an average signal. Average signal calculating means for
Time position calculating means for calculating a relative time position of the output signal with respect to the average signal;
And a linear interpolation means for linearly interpolating the average signal at the time position. The relative time position of the output signal with respect to the average signal is the value of the time position (P) for the width N of 2;
It said time position calculating means, the R ₃ calculates a value V divided by any integer U, sequentially adds the V for any initial value, when the addition result is equal to or greater than N, addition results 2. The sampling frequency conversion apparatus according to claim 1, wherein N is subtracted from, and a time position P which always keeps a value of 0 or more and less than N is calculated. Storage means for storing the average signal;
The signals output to out destination of the stored two average signal to said memory means and B _1, a signal output after the B _2, and the B ₁ and B ₂ between the B ₁ and B ₂ 3. The sampling frequency conversion device according to claim 2, wherein linear interpolation is performed at a time position P located between the two. 4. The sampling frequency conversion device according to claim ₃ , wherein the result of the linear interpolation (B3) is calculated by the following equation (1).
B ₃ = {B ₁ × (NP) + B ₂ × P} / N (1) 3. The sampling frequency converter according to claim 2, further comprising averaging means for averaging a result of said linear interpolation for each U number. A sampling frequency Fs ₁ of the input signal, a monitoring means for monitoring changes in the sampling frequency Fs ₂ of the output signal comprises,
The input / output frequency ratio calculating means, the width number calculating means, the width ratio calculating means, and the replacing means change R, R ₁ , R ₂ , R ₃ each time the Fs ₁ and / or Fs ₂ change. , N is updated. The sampling frequency conversion apparatus according to claim 1, wherein A sampling frequency conversion method for inputting a signal sampled at a first sampling frequency, converting the signal into an output signal sampled at a second sampling frequency, and outputting the output signal,
An input / output frequency ratio calculating step of calculating a ratio (R) of the first sampling frequency to the second sampling frequency;
And exponent calculation means for calculating the maximum second width number (and R _1.) Does not exceed the above R,
(And R _2.) The ratio of R to said R ₁ and width ratio calculating step of calculating a
A replacement step of replacing the above R ₂ by a function represented by an arbitrary integer R ₃ and a reciprocal of a width N of 2;
R ₁ signal values connected in a time series are extracted from the signal sampled at the first sampling frequency, an average value is calculated for each of the R ₁ signal values, and the average value is output as an average signal. Average signal calculating step of
A time position calculating step of calculating a relative time position of the output signal with respect to the average signal;
A linear interpolation step of linearly interpolating the average signal at the time position. The relative time position of the output signal with respect to the average signal is the value of the time position (P) for the width N of 2;
Said time position calculating step, the R ₃ calculates a value V divided by any integer U, sequentially adds the V for any initial value, when the addition result is equal to or greater than N, addition results 8. A sampling frequency conversion method according to claim 7, wherein a time position P is calculated by subtracting N from, and always keeping a value of 0 or more and less than N. Storage means for storing the average signal;
The signals output to out destination of the stored two average signal to said memory means and B _1, a signal output after the B _2, and the B ₁ and B ₂ between the B ₁ and B ₂ 9. The sampling frequency conversion method according to claim 8, wherein linear interpolation is performed at a time position P located therebetween. (And B _3.) The results of the linear interpolation, sampling frequency conversion method according to claim 9, wherein to be calculated by the following equation (1).
B ₃ = {B ₁ × (NP) + B ₂ × P} / N (1) 9. The sampling frequency conversion method according to claim 8, further comprising an averaging step of averaging a result of the linear interpolation for each U number. It includes the sampling frequency Fs ₁ of the input signal, a monitoring step of monitoring changes in the sampling frequency Fs ₂ of the output signal,
The output ratio calculating step, the exponent calculation step, the width ratio calculating step, the displacement step, each time the Fs ₁ and / or Fs _{2 changes, R, R 1, R 2} , R 3, The sampling frequency conversion method according to claim 7, wherein the value of N is updated.

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