JP3881836B2 - Frequency interpolation device, frequency interpolation method, and recording medium - Google Patents

Frequency interpolation device, frequency interpolation method, and recording medium Download PDF

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Publication number
JP3881836B2
JP3881836B2 JP2000324641A JP2000324641A JP3881836B2 JP 3881836 B2 JP3881836 B2 JP 3881836B2 JP 2000324641 A JP2000324641 A JP 2000324641A JP 2000324641 A JP2000324641 A JP 2000324641A JP 3881836 B2 JP3881836 B2 JP 3881836B2
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interpolated
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JP2002132298A (en
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寧 佐藤
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Kenwood KK
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Kenwood KK
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Priority to PCT/JP2001/005523 priority patent/WO2002035517A1/en
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Description

【0001】
【発明の属する技術分野】
この発明は、変調された信号のスペクトル分布を改善する周波数補間装置及び周波数補間方法に関する。
【0002】
【従来の技術】
MP3(MPEG1 audio layer 3)形式のデータの配信、及び、FM(Frequency Modulation)放送やテレビジョン音声多重放送等の手法による音楽などの供給が近年盛んになっている。これらの手法では、帯域が過度に広くなることによるデータ量の増大や占有帯域幅の広がりを避けるため、一般に、供給する対象の音楽等のうち約15kHz以上の周波数成分が除去されている。
【0003】
このように、一定値以上の周波数成分が除去された音楽等は通常、音質が悪い。そこで、除去された周波数成分に代わる信号を加算することが考えられる。このための手法としては、特開平7−93900号公報に開示されている手法がある。
特開平7−93900号公報に開示されている手法は、PCMディジタルオーディオ信号をローパスフィルタに通して得られる出力オーディオ信号を、当該出力信号の絶対値成分を含む信号を乗算することにより歪みを生じさせる、という手法である。
【0004】
【発明が解決しようとする課題】
しかし、特開平7−93900号公報のオーディオ信号再生装置は、出力オーディオ信号の波形を絶対値回路等を用いて歪ませることにより高調波を発生させるに過ぎないものであって、この高調波は元のオーディオ信号に含まれているものに近似し得るものであるかは分からない。
【0005】
この発明は、上記実状に鑑みてなされたものであり、原信号の帯域を制限した信号を用いて得られる変調波から原信号に近い信号を復元できるようにするための周波数補間装置及び周波数補間方法を提供することを目的とする。
また、この発明は、オーディオ信号を高音質で復元するための周波数補間装置及び周波数補間方法を提供することを目的とする。
【0006】
【課題を解決するための手段】
上記目的を達成するべく、この発明の第1の観点に係る周波数補間装置は、
補間される対象である被補間信号のうち第1の帯域内の成分を抽出する第1のフィルタと、
前記被補間信号のうち第2の帯域内の成分を抽出する第2のフィルタと、
前記第1及び第2のフィルタが抽出した各前記成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成する混合部と、
前記混合により得られる信号のうち第3の帯域内の成分を抽出する第3のフィルタと、
前記第3のフィルタが抽出した前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する加算部と、を備える、
ことを特徴とする。
【0007】
このような周波数補間装置によれば、被補間信号を構成する成分又はその高調波成分同士の和又は差にあたる成分が被補間信号に追加され、帯域が拡張される。追加された成分は、被補間信号の一部分の高調波成分とみなし得るので、被補間信号が帯域を制限された信号である場合、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号に近いものとなる。従って、被補間信号がオーディオ信号を表すものであれば、帯域が拡張された後の被補間信号を用いてオーディオ信号を復元することにより、オーディオ信号が高音質で復元される。
【0008】
前記第1の帯域が占める帯域幅は、前記第2の帯域が占める帯域幅に実質的に等しく、
前記第1の帯域の上限は前記第2の帯域の下限に実質的に等しく、
前記第2の帯域の上限は被補間信号のスペクトルの分布の上限に実質的に等しく、
前記第3の帯域の下限は前記第2の帯域の上限に実質的に等しく、
前記第3の帯域が占める帯域幅は、前記第1の帯域が占める帯域幅の2倍に実質的に等しいものであれば、入力被補間信号に追加される成分は、被補間信号の一部分の高調波成分に特によく近似し得る可能性が高い。また、入力被補間信号に追加される成分のスペクトルは、被補間信号のスペクトルと、高周波側で隙間なく隣接するものとなる。従って、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号により近いものとなる。
【0009】
前記第1のフィルタは、自己に供給される指示に応答して、前記第1の帯域の上限及び下限を変化させる手段を備え、
前記第2のフィルタは、自己に供給される指示に応答して、前記第2の帯域の上限及び下限を変化させる手段を備え、
前記第3のフィルタは、自己に供給される指示に応答して、前記第3の帯域の上限及び下限を変化させる手段を備えていてもよい。
この場合、前記周波数補間装置は、前記被補間信号を取得して、取得した当該被補間信号のスペクトルの分布の上限を特定し、特定した結果に基づいて、前記第1乃至第3の帯域の上限及び下限を決定し、前記第1のフィルタに、前記第1の帯域の上限及び下限を自己が決定した値とする指示を供給し、前記第2のフィルタに、前記第2の帯域の上限及び下限を自己が決定した値とする指示を供給し、前記第3のフィルタに、前記第3の帯域の上限及び下限を自己が決定した値とする指示を供給する解析手段を備えることにより、第1乃至第3のフィルタの通過帯域を自ら最適化する。
【0010】
前記周波数補間装置は、前記被補間信号のスペクトルの包絡線を表す包絡線情報を抽出し、前記第3のフィルタが抽出した成分を取得し、取得した当該成分のスペクトルの強度が前記包絡線情報が示す包絡線により表される強度に実質的に等しくなるように当該成分をフィルタリングして前記加算部に供給するイコライズ手段を備え、
前記加算部は、前記イコライズ手段がフィルタリングした前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成するものとしてもよい。
このような構成を有することにより、前記周波数補間装置は、被補間信号に追加されるべき成分を、被補間信号のスペクトルの包絡線に沿うようにして被補間信号に追加する。従って、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号により近いものとなる。
【0011】
前記加算部は、前記第3の帯域内の成分と実質的に同相になるように前記被補間信号を遅延させる遅延部を備え、前記第3の帯域内の成分及び前記遅延部が遅延させた前記被補間信号の和を表す前記出力信号を生成するものであれば、第1乃至第3のフィルタ及び混合部のうちいずれかが信号の遅延を発生させるものであっても、加算部が正確に被補間信号の帯域の拡張を行う。
【0012】
また、この発明の第2の観点に係る周波数補間方法は、
補間される対象である被補間信号のうち第1の帯域内の成分を抽出し、
前記被補間信号のうち第2の帯域内の成分を抽出し、
抽出された前記第1及び第2の帯域内の各成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成し、
前記混合により得られる信号のうち第3の帯域内の成分を抽出し、
抽出された前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する、
ことを特徴とする。
【0013】
このような周波数補間方法によれば、被補間信号を構成する成分又はその高調波成分同士の和又は差にあたる成分が被補間信号に追加され、帯域が拡張される。追加された成分は、被補間信号の一部分の高調波成分とみなし得るので、被補間信号が帯域を制限された信号である場合、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号に近いものとなる。従って、被補間信号がオーディオ信号を表すものであれば、帯域が拡張された後の被補間信号を用いてオーディオ信号を復元することにより、オーディオ信号が高音質で復元される。
【0014】
前記第1の帯域が占める帯域幅は、前記第2の帯域が占める帯域幅に実質的に等しく、
前記第1の帯域の上限は前記第2の帯域の下限に実質的に等しく、
前記第2の帯域の上限は被補間信号のスペクトルの分布の上限に実質的に等しく、
前記第3の帯域の下限は前記第2の帯域の上限に実質的に等しく、
前記第3の帯域が占める帯域幅は、前記第1の帯域が占める帯域幅の2倍に実質的に等しいものであれば、入力被補間信号に追加される成分は、被補間信号の一部分の高調波成分に特によく近似し得る可能性が高い。また、入力被補間信号に追加される成分のスペクトルは、被補間信号のスペクトルと、高周波側で隙間なく隣接するものとなる。従って、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号により近いものとなる。
【0015】
前記被補間信号を取得して、取得した当該被補間信号のスペクトルの分布の上限を特定し、特定した結果に基づいて、前記第1乃至第3の帯域の上限及び下限を決定し、決定結果に従って、前記第1乃至第3の帯域の上限及び下限を変化させるものとすれば、第1乃至第3の帯域が最適化される。
【0016】
前記被補間信号のスペクトルの包絡線を表す包絡線情報を抽出し、前記第3のフィルタが抽出した成分を取得し、取得した当該成分のスペクトルの強度が前記包絡線情報が示す包絡線により表される強度に実質的に等しくなるように当該成分をフィルタリングし、
フィルタリングした前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成するようにしてもよい。
こうすることにより、被補間信号に追加されるべき成分は、被補間信号のスペクトルの包絡線に沿うようにして被補間信号に追加される。従って、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号により近いものとなる。
【0017】
前記第3の帯域内の成分と実質的に同相になるように前記被補間信号を遅延させ、前記第3の帯域内の成分及び遅延させた前記被補間信号の和を表す前記出力信号を生成するようにすれば、第1乃至第3の帯域内の成分の抽出や第1及び第2の帯域内の各成分の混合の工程で信号の遅延が発生する場合であっても、被補間信号の帯域の拡張が正確に行われる。
【0018】
また、この発明の第3の観点に係るコンピュータ読み取り可能な記録媒体は、
コンピュータを、
補間される対象である被補間信号のうち第1の帯域内の成分を抽出する第1のフィルタと、
前記被補間信号のうち第2の帯域内の成分を抽出する第2のフィルタと、
前記第1及び第2のフィルタが抽出した各前記成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成する混合部と、
前記混合により得られる信号のうち第3の帯域内の成分を抽出する第3のフィルタと、
前記第3のフィルタが抽出した前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する加算部と、
して機能させるためのプログラムを記録したことを特徴とする。
【0019】
このような記録媒体に記録されたプログラムを実行するコンピュータは、被補間信号を構成する成分又はその高調波成分同士の和又は差にあたる成分を被補間信号に追加し、被補間信号の帯域を拡張する。追加された成分は、被補間信号の一部分の高調波成分とみなし得るので、被補間信号が帯域を制限された信号である場合、帯域が拡張された後の被補間信号は、帯域が制限される前の原信号に近いものとなる。従って、被補間信号がオーディオ信号を表すものであれば、帯域が拡張された後の被補間信号を用いてオーディオ信号を復元することにより、オーディオ信号が高音質で復元される。
【0020】
【発明の実施の形態】
以下に、図面を参照して、この発明の実施の形態に係る周波数補間装置を、周波数補間器を例として説明する。
【0021】
図1は、この発明の実施の形態に係る周波数補間器の構成を示す図である。
図示するように、この周波数補間器は、BPF(バンドパスフィルタ)1A、1B及び4と、遅延部2と、混合部3と、加算部5とより構成されている。
【0022】
BPF1A及び1Bは、いずれも、この周波数補間器により周波数の補間を受ける対象の信号(入力信号)を同時に供給される。そして、各々、自己に供給された信号のうち、各自に固有の通過帯域内の成分を通過させ混合部3へと供給し、他の成分を実質的に遮断する。
【0023】
なお、入力信号は音声等を表す信号からなる。入力信号が表す音声等のスペクトル分布は、例えば、元の音声等のうち一定値以上(例えば、14kHz以上)の周波数成分が除去されたものに相当するものとする。
【0024】
BPF1A及び1Bの通過帯域の範囲は、図2に示すように、
(1) BPF1Aの通過帯域(図2において「BA」として示す帯域)の上限の周波数が、BPF1Bの通過帯域(図2において「BB」として示す帯域)の下限の周波数にほぼ等しく、
(2) BPF1Aの通過帯域の幅が、周波数の補間を施すことによって入力信号に追加される成分が占める帯域(図2において「Badd」として示す帯域)の帯域幅の2分の1にほぼ等しく、
(3) BPF1Bの通過帯域の上限の周波数が、入力信号が占める帯域(図2において「Bin」として示す帯域)の上限の周波数にほぼ等しく、
(4) BPF1Bの通過帯域の幅が、BPF1Aの通過帯域の幅にほぼ等しい、
という関係にある。
【0025】
すなわち、BPF1Aの通過帯域の下限の周波数をfAL、BPF1Aの通過帯域の上限の周波数をfAH、BPF1Bの通過帯域の下限の周波数をfBL、BPF1Bの通過帯域の上限の周波数をfBH、入力信号が占める帯域の上限をfIN、周波数の補間により入力信号に追加される成分が占める帯域幅をwとすると、fAL、fAH、fBL、fBH、fIN、及びwの各値の間には数式1〜数式3に示す関係がある。
【0026】
【数1】
AH=fBL
【数2】
BH=fIN
【数3】
(fAH−fAL)=(fBH−fBL)=(w/2)
【0027】
遅延部2は、BPF1A及び1Bに供給されたものと同一の入力信号を、BPF1A及び1Bと同時に供給される。そして、自己に供給された信号を遅延させて加算部5に供給する。
遅延部2が信号を遅延させる時間の長さは、BPF1A及び1Bに供給された信号の成分が混合部3及びBPF4を経て加算部5に供給されるまでに経過する時間の長さに実質的に等しいものとする。
また、遅延部2から加算部5に供給される遅延された入力信号の位相と、BPF4から加算部5に供給される信号の位相とは、加算部5に同時に供給されるもの同士の間では、実質的に同相であるものとする。
【0028】
混合部3は、BPF1A及び1Bより供給された成分を互いに混合することにより、BPF1Aを通過した成分又はその高調波とBPF1Bを通過した成分又はその高調波との積を表す信号を生成し、生成した信号をBPF4に供給する。
【0029】
BPF4は、混合部3より供給された成分のうち、周波数の下限がfINで周波数の上限が(fIN+w)である帯域を占める成分を通過させ加算部5に供給し、他の成分を実質的に遮断する。
【0030】
加算部5は、遅延部2から自己に供給される遅延された入力信号とBPF4から供給される成分との和を表す信号を生成し、この周波数補間器の出力信号として出力する。
【0031】
周波数の補間を施された後の入力信号(すなわち出力信号)は、BPF1Aを通過した入力信号の成分又はその高調波とBPF1Bを通過した入力信号の成分又はその高調波との積のうち、周波数の下限がfINで周波数の上限が(fIN+w)である帯域を占める成分を、入力信号に追加して得られる信号より構成される。
入力信号に追加された成分は、入力信号の一部の高調波成分より構成されるので、入力信号が帯域を制限された信号である場合、出力信号は、帯域が制限される前の入力信号に近いものとなる。
【0032】
なお、この周波数補間器の構成は上述のものに限られない。
例えば、BPF1A、BPF1B、遅延部2、混合部3、BPF4及び加算部5の機能の一部又は全部を、DSP(Digital Signal Processor)やCPU(Central Processing Unit)が行ってもよい。
【0033】
また、fAL、fAH、fBL、fBH、fIN、及びwの各値は、必ずしも数式1〜数式3に示す関係を有する必要はない。
しかし、これらの各値が数式1〜数式3に示す関係を有する場合、BPF1A及び1Bを通過する入力信号の成分は、入力信号自体の一部分の高調波成分とみなしうる可能性が高い。また、BPF4を通過する成分のスペクトルは、入力信号のスペクトルに、高周波側で隙間なく隣接するものとなる。従って、入力信号が、帯域を制限されたオーディオ信号を表すものである場合、出力信号は、帯域が制限される前の入力信号により近いものとなる。
【0034】
また、BPF1A、1B及び4は、各自に供給される指示に従って各自の通過帯域を公知の手法により変化させるものであってもよい。そして、この周波数補間器は、BPF1A、1B及び4に、各々の通過帯域を変化させる指示を供給する制御部を備えていてもよい。
【0035】
この制御部は、例えば、フーリエ変換部及び解析部からなるものとし、いずれも、例えばDSPあるいはCPU等より構成されるものとする。
フーリエ変換部は、入力信号を取得してフーリエ変換し、フーリエ変換の結果得られるスペクトルを表す信号を生成するものとする。解析部は、フーリエ変換部が生成した信号が示すスペクトルの成分のうち最も周波数が高い成分を特定し、特定したスペクトルの周波数を上述のfINの値として決定する。次に、解析部は、決定したfINの値と、入力信号に追加する成分の周波数の上限を示す所定値とに基づき、上述のwの値を決定し、決定したfIN及びwの値に基づき、更にfAL、fAH、fBL及びfBHの値を決定する。そして、決定したfAL及びfAHの値がBPF1Aの通過帯域の下限及び上限となるよう通過帯域を変化させる指示を、BPF1Aに供給する。BPF1Bには、決定したfBL及びfBHの値がBPF1Bの通過帯域の下限及び上限となるように通過帯域を変化させる指示を供給する。BPF4には、決定したfIN及び(fIN+w)の値がBPF4の通過帯域の下限及び上限となるように通過帯域を変化させる指示を供給する。
【0036】
また、この周波数補間器は、入力信号に追加する成分のスペクトルの強度を、入力信号のスペクトルの包絡線に外挿することにより決定するようにしてもよい。
具体的には、例えば、この周波数補間器はイコライザを備え、このイコライザは、BPF4が加算部5に供給すべき成分を、自己に供給される信号が示す周波数特性に合致するようにフィルタリングしてから加算部5に供給するものとする。一方、上述の解析部は、上述のフーリエ変換部が生成した信号に基づき回帰計算の処理を行うことにより、入力信号のスペクトルの包絡線をなす関数を特定し、特定した関数に基づき、下限の周波数がfINで上限の周波数が(fIN+w)である帯域内の出力信号の周波数特性を決定する。そして、決定結果を示す信号を上述のイコライザに供給するものとする。
【0037】
以上、この発明の実施の形態を説明したが、この発明にかかる周波数補間装置は、専用のシステムによらず、通常のコンピュータシステムを用いて実現可能である。
例えば、パーソナルコンピュータやマイクロコンピュータに上述のBPF1A、1B及び4や、遅延部2や、混合部3や、加算部5や、制御部や、イコライザの動作を実行するためのプログラムを格納した媒体(CD−ROM、MO、フロッピーディスク等)から該プログラムをインストールすることにより、上述の処理を実行する周波数補間器を構成することができる。
【0038】
また、例えば、通信回線の掲示板(BBS)に該プログラムを掲示し、これを通信回線を介して配信してもよく、また、該プログラムを表す信号により搬送波を変調し、得られた変調波を伝送し、この変調波を受信した装置が変調波を復調して該プログラムを復元するようにしてもよい。
そして、このプログラムを起動し、OSの制御下に、他のアプリケーションプログラムと同様に実行することにより、上述の処理を実行することができる。
【0039】
なお、OSが処理の一部を分担する場合、あるいは、OSが本願発明の1つの構成要素の一部を構成するような場合には、記録媒体には、その部分をのぞいたプログラムを格納してもよい。この場合も、この発明では、その記録媒体には、コンピュータが実行する各機能又はステップを実行するためのプログラムが格納されているものとする。
【0040】
【発明の効果】
以上の説明のように、この発明によれば、原信号の帯域を制限した信号を用いて得られる変調波から原信号に近い信号を復元できるようにするための周波数補間装置及び周波数補間方法が実現される。
また、この発明によれば、オーディオ信号を高音質で復元するための周波数補間装置及び周波数補間方法が実現される。
【図面の簡単な説明】
【図1】この発明の実施の形態に係る周波数補間器の構成を示す図である。
【図2】入力信号及び入力信号に追加される成分が占める帯域と、BPFの通過帯域とを示すグラフである。
【符号の説明】
1A、1B、4 BPF
2 遅延部
3 混合部
5 加算部
[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a frequency interpolation apparatus and a frequency interpolation method for improving the spectral distribution of a modulated signal.
[0002]
[Prior art]
In recent years, distribution of data in the MP3 (MPEG1 audio layer 3) format and supply of music and the like by techniques such as FM (Frequency Modulation) broadcasting and television audio multiplex broadcasting have become popular. In these methods, in order to avoid an increase in the amount of data and an increase in occupied bandwidth due to an excessively wide band, generally, a frequency component of about 15 kHz or more is removed from music to be supplied.
[0003]
As described above, music or the like from which frequency components of a certain value or more are removed usually has poor sound quality. Therefore, it is conceivable to add a signal in place of the removed frequency component. As a technique for this purpose, there is a technique disclosed in JP-A-7-93900.
The technique disclosed in Japanese Patent Laid-Open No. 7-93900 causes distortion by multiplying an output audio signal obtained by passing a PCM digital audio signal through a low-pass filter by a signal including an absolute value component of the output signal. It is a technique of letting.
[0004]
[Problems to be solved by the invention]
However, the audio signal reproduction device disclosed in Japanese Patent Laid-Open No. 7-93900 merely generates harmonics by distorting the waveform of the output audio signal using an absolute value circuit or the like. It is not known whether it can be approximated to that contained in the original audio signal.
[0005]
The present invention has been made in view of the above circumstances, and a frequency interpolation device and a frequency interpolation for enabling restoration of a signal close to the original signal from a modulated wave obtained by using a signal in which the band of the original signal is limited It aims to provide a method.
Another object of the present invention is to provide a frequency interpolation device and a frequency interpolation method for restoring an audio signal with high sound quality.
[0006]
[Means for Solving the Problems]
In order to achieve the above object, a frequency interpolation apparatus according to the first aspect of the present invention provides:
A first filter for extracting a component in the first band from the interpolated signal to be interpolated;
A second filter for extracting a component in a second band from the interpolated signal;
By mixing the components extracted by the first and second filters , the product of the component in the first band or its harmonic and the component in the second band or its harmonic is represented. A mixing section for generating a signal ;
A third filter for extracting a component in a third band from the signal obtained by the mixing;
An adder that generates an output signal representing a sum of the component in the third band extracted by the third filter and the interpolated signal;
It is characterized by that.
[0007]
According to such a frequency interpolation apparatus, a component constituting the interpolated signal or a component corresponding to the sum or difference of its harmonic components is added to the interpolated signal, and the band is expanded. Since the added component can be regarded as a harmonic component of a part of the interpolated signal, when the interpolated signal is a band-limited signal, the interpolated signal after the band is expanded is band-limited. It is close to the original signal. Therefore, if the interpolated signal represents an audio signal, the audio signal is restored using the interpolated signal whose band has been expanded, thereby restoring the audio signal with high sound quality.
[0008]
The bandwidth occupied by the first band is substantially equal to the bandwidth occupied by the second band;
The upper limit of the first band is substantially equal to the lower limit of the second band;
The upper limit of the second band is substantially equal to the upper limit of the spectrum distribution of the interpolated signal,
The lower limit of the third band is substantially equal to the upper limit of the second band;
If the bandwidth occupied by the third band is substantially equal to twice the bandwidth occupied by the first band, then the component added to the input interpolated signal is part of the interpolated signal. There is a high possibility of being able to approximate the harmonic component particularly well. Further, the spectrum of the component added to the input interpolated signal is adjacent to the interpolated signal spectrum without any gap on the high frequency side. Therefore, the interpolated signal after the band is expanded is closer to the original signal before the band is limited.
[0009]
The first filter includes means for changing an upper limit and a lower limit of the first band in response to an instruction supplied to the first filter,
The second filter comprises means for changing the upper and lower limits of the second band in response to an instruction supplied to the second filter;
The third filter may include means for changing an upper limit and a lower limit of the third band in response to an instruction supplied to the third filter.
In this case, the frequency interpolation device acquires the interpolated signal, specifies the upper limit of the spectrum distribution of the acquired interpolated signal, and, based on the specified result, the first to third bands. An upper limit and a lower limit are determined, an instruction is supplied to the first filter so that the upper limit and the lower limit of the first band are self-determined values, and an upper limit of the second band is supplied to the second filter And an analyzing means for supplying an instruction to set the lower limit to a value determined by itself, and to supply an instruction to set the upper limit and the lower limit of the third band to values determined by the self, to the third filter, The passbands of the first to third filters are optimized by themselves.
[0010]
The frequency interpolation device extracts envelope information representing an envelope of a spectrum of the interpolated signal, acquires a component extracted by the third filter, and an intensity of the acquired spectrum of the component is the envelope information Comprising equalizing means for filtering the component to be substantially equal to the intensity represented by the envelope indicated by
The adding unit may generate an output signal representing a sum of the component in the third band filtered by the equalizing unit and the interpolated signal.
By having such a configuration, the frequency interpolation device adds the component to be added to the interpolated signal to the interpolated signal along the spectrum envelope of the interpolated signal. Therefore, the interpolated signal after the band is expanded is closer to the original signal before the band is limited.
[0011]
The adding unit includes a delay unit that delays the interpolated signal so as to be substantially in phase with the component in the third band, and the component in the third band and the delay unit are delayed. As long as the output signal representing the sum of the interpolated signals is generated, even if any one of the first to third filters and the mixing unit generates a signal delay, the adding unit is accurate. Then, the band of the interpolated signal is expanded.
[0012]
The frequency interpolation method according to the second aspect of the present invention is as follows:
Extracting the component in the first band from the interpolated signal to be interpolated,
Extracting a component in a second band from the interpolated signal;
By mixing the extracted components in the first band and the second band, the product of the component in the first band or its harmonic and the component in the second band or its harmonic is obtained. Generates a signal that represents
Extracting a component in the third band from the signal obtained by the mixing;
Generating an output signal representing a sum of the extracted component in the third band and the interpolated signal;
It is characterized by that.
[0013]
According to such a frequency interpolation method, components constituting the interpolated signal or components corresponding to the sum or difference of their harmonic components are added to the interpolated signal, and the band is expanded. Since the added component can be regarded as a harmonic component of a part of the interpolated signal, when the interpolated signal is a band-limited signal, the interpolated signal after the band is expanded is band-limited. It is close to the original signal. Therefore, if the interpolated signal represents an audio signal, the audio signal is restored using the interpolated signal whose band has been expanded, thereby restoring the audio signal with high sound quality.
[0014]
The bandwidth occupied by the first band is substantially equal to the bandwidth occupied by the second band;
The upper limit of the first band is substantially equal to the lower limit of the second band;
The upper limit of the second band is substantially equal to the upper limit of the spectrum distribution of the interpolated signal,
The lower limit of the third band is substantially equal to the upper limit of the second band;
If the bandwidth occupied by the third band is substantially equal to twice the bandwidth occupied by the first band, then the component added to the input interpolated signal is part of the interpolated signal. There is a high possibility of being able to approximate the harmonic component particularly well. Further, the spectrum of the component added to the input interpolated signal is adjacent to the interpolated signal spectrum without any gap on the high frequency side. Therefore, the interpolated signal after the band is expanded is closer to the original signal before the band is limited.
[0015]
Obtaining the interpolated signal, specifying the upper limit of the spectrum distribution of the acquired interpolated signal, determining the upper and lower limits of the first to third bands based on the identified result, and the determination result Accordingly, if the upper and lower limits of the first to third bands are changed, the first to third bands are optimized.
[0016]
Envelope information representing an envelope of the spectrum of the interpolated signal is extracted, the component extracted by the third filter is acquired, and the acquired spectrum intensity is represented by the envelope indicated by the envelope information. Filtering the component to be substantially equal to the intensity being
An output signal representing the sum of the filtered component in the third band and the interpolated signal may be generated.
By doing so, the component to be added to the interpolated signal is added to the interpolated signal along the spectrum envelope of the interpolated signal. Therefore, the interpolated signal after the band is expanded is closer to the original signal before the band is limited.
[0017]
The interpolated signal is delayed so as to be substantially in phase with the component in the third band, and the output signal representing the sum of the component in the third band and the delayed interpolated signal is generated. By doing so, even if a signal delay occurs in the process of extracting the components in the first to third bands and mixing the components in the first and second bands, the signal to be interpolated The bandwidth is accurately expanded.
[0018]
A computer-readable recording medium according to the third aspect of the present invention is
Computer
A first filter for extracting a component in the first band from the interpolated signal to be interpolated;
A second filter for extracting a component in a second band from the interpolated signal;
By mixing the components extracted by the first and second filters , the product of the component in the first band or its harmonic and the component in the second band or its harmonic is represented. A mixing section for generating a signal ;
A third filter for extracting a component in a third band from the signal obtained by the mixing;
An adder for generating an output signal representing a sum of the component in the third band extracted by the third filter and the interpolated signal;
It is characterized by recording a program for making it function.
[0019]
A computer that executes a program recorded on such a recording medium adds a component constituting the interpolated signal or a component corresponding to the sum or difference of its harmonic components to the interpolated signal, and expands the band of the interpolated signal. To do. Since the added component can be regarded as a harmonic component of a part of the interpolated signal, when the interpolated signal is a band-limited signal, the interpolated signal after the band is expanded is band-limited. It is close to the original signal. Therefore, if the interpolated signal represents an audio signal, the audio signal is restored using the interpolated signal whose band has been expanded, thereby restoring the audio signal with high sound quality.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a frequency interpolation apparatus according to an embodiment of the present invention will be described with reference to the drawings, taking a frequency interpolator as an example.
[0021]
FIG. 1 is a diagram showing a configuration of a frequency interpolator according to an embodiment of the present invention.
As shown in the figure, this frequency interpolator includes BPFs (band pass filters) 1A, 1B, and 4, a delay unit 2, a mixing unit 3, and an adding unit 5.
[0022]
Both BPFs 1A and 1B are simultaneously supplied with signals (input signals) to be subjected to frequency interpolation by this frequency interpolator. Then, among the signals supplied to each of them, the components in the passbands specific to each of them are passed and supplied to the mixing unit 3, and the other components are substantially cut off.
[0023]
The input signal is a signal representing voice or the like. The spectrum distribution of the voice or the like represented by the input signal corresponds to, for example, the original voice or the like from which a frequency component of a certain value or higher (for example, 14 kHz or higher) has been removed.
[0024]
The passband range of BPF 1A and 1B is as shown in FIG.
(1) The upper limit frequency of the pass band of BPF 1A (band indicated as “BA” in FIG. 2) is substantially equal to the lower limit frequency of the pass band of BPF 1B (band indicated as “BB” in FIG. 2).
(2) The width of the pass band of BPF 1A is approximately equal to one half of the bandwidth of the band (band indicated as “Badd” in FIG. 2) occupied by the component added to the input signal by performing frequency interpolation. ,
(3) The upper limit frequency of the pass band of the BPF 1B is approximately equal to the upper limit frequency of the band occupied by the input signal (the band indicated as “Bin” in FIG. 2).
(4) The width of the passband of BPF1B is substantially equal to the width of the passband of BPF1A.
There is a relationship.
[0025]
That is, the frequency of the lower limit of the passband of BPF1A f AL, the frequency upper limit f AH of the passband of BPF1A, frequency f BL of the lower limit of the passband of BPF1B, the frequency of the upper limit of the passband of BPF1B f BH, up to f iN of the band where the input signal occupies, when the bandwidth occupied by the components to be added to the input signal by interpolation of the frequency and w, f AL, f AH, each of f BL, f BH, f iN , and w There is a relationship shown in Equations 1 to 3 between the values.
[0026]
[Expression 1]
f AH = f BL
[Expression 2]
f BH = f IN
[Equation 3]
(F AH −f AL ) = (f BH −f BL ) = (w / 2)
[0027]
The delay unit 2 is supplied with the same input signal as that supplied to the BPFs 1A and 1B simultaneously with the BPFs 1A and 1B. Then, the signal supplied to itself is delayed and supplied to the adder 5.
The length of time for which the delay unit 2 delays the signal is substantially equal to the length of time that elapses until the signal components supplied to the BPFs 1A and 1B are supplied to the addition unit 5 via the mixing unit 3 and the BPF 4. Is equal to
The phase of the delayed input signal supplied from the delay unit 2 to the adder 5 and the phase of the signal supplied from the BPF 4 to the adder 5 are between those supplied to the adder 5 at the same time. , Substantially in phase.
[0028]
The mixing unit 3 mixes the components supplied from the BPF 1A and 1B with each other, thereby generating a signal representing the product of the component that has passed through the BPF 1A or its harmonic and the component that has passed through the BPF 1B or its harmonic. The signal is supplied to the BPF 4.
[0029]
Of the components supplied from the mixing unit 3, the BPF 4 passes a component occupying a band having a lower frequency limit of fIN and an upper frequency limit of ( fIN + w), and supplies it to the adding unit 5 to supply other components. Substantially cut off.
[0030]
The adder 5 generates a signal representing the sum of the delayed input signal supplied to the delay unit 2 and the component supplied from the BPF 4 and outputs the signal as an output signal of the frequency interpolator.
[0031]
The input signal (ie, output signal) after frequency interpolation is the product of the component of the input signal passing through BPF 1A or its harmonic and the component of the input signal passing through BPF 1B or its harmonic. Is composed of a signal obtained by adding to the input signal a component that occupies a band whose lower limit is f IN and whose upper limit is (f IN + w).
Since the component added to the input signal is composed of some harmonic components of the input signal, if the input signal is a band-limited signal, the output signal is the input signal before the band is limited. It will be close to.
[0032]
Note that the configuration of the frequency interpolator is not limited to that described above.
For example, some or all of the functions of BPF 1A, BPF 1B, delay unit 2, mixing unit 3, BPF 4 and addition unit 5 may be performed by a DSP (Digital Signal Processor) or a CPU (Central Processing Unit).
[0033]
Further, the values of f AL , f AH , f BL , f BH , f IN , and w are not necessarily required to have the relationships shown in Formulas 1 to 3.
However, when these values have the relationships shown in Equations 1 to 3, there is a high possibility that the components of the input signal passing through the BPFs 1A and 1B can be regarded as harmonic components of a part of the input signal itself. Further, the spectrum of the component passing through the BPF 4 is adjacent to the spectrum of the input signal without a gap on the high frequency side. Therefore, when the input signal represents an audio signal with a band limited, the output signal is closer to the input signal before the band is limited.
[0034]
Further, each of the BPFs 1A, 1B, and 4 may change its pass band by a known method in accordance with an instruction supplied to each of the BPFs 1A, 1B, and 4. And this frequency interpolator may be provided with the control part which supplies the instruction | indication which changes each pass band to BPF1A, 1B and 4. FIG.
[0035]
This control unit is composed of, for example, a Fourier transform unit and an analysis unit, both of which are composed of, for example, a DSP or a CPU.
The Fourier transform unit acquires an input signal, performs Fourier transform, and generates a signal representing a spectrum obtained as a result of the Fourier transform. The analysis unit specifies a component having the highest frequency among the components of the spectrum indicated by the signal generated by the Fourier transform unit, and determines the frequency of the specified spectrum as the value of f IN described above. Next, the analysis unit compares the value of the determined f IN, based on the predetermined value indicating the upper limit of the frequency components to be added to the input signal, determines the value of the above w, determined values of f IN and w Further, the values of f AL , f AH , f BL and f BH are determined. Then, an instruction to change the pass band is supplied to the BPF 1A so that the determined values of f AL and f AH become the lower limit and the upper limit of the pass band of the BPF 1A. The BPF 1B is supplied with an instruction to change the pass band so that the determined values of f BL and f BH become the lower limit and the upper limit of the pass band of the BPF 1B. The BPF 4 is supplied with an instruction to change the pass band so that the determined values f IN and (f IN + w) become the lower limit and the upper limit of the pass band of the BPF 4.
[0036]
Further, the frequency interpolator may determine the intensity of the spectrum of the component added to the input signal by extrapolating it to the envelope of the spectrum of the input signal.
Specifically, for example, the frequency interpolator includes an equalizer, and the equalizer filters components to be supplied to the adder 5 by the BPF 4 so as to match the frequency characteristics indicated by the signal supplied to the equalizer. To the adder 5. On the other hand, the analysis unit described above identifies a function that forms an envelope of the spectrum of the input signal by performing a regression calculation process based on the signal generated by the above-described Fourier transform unit, and based on the specified function, The frequency characteristic of the output signal in the band where the frequency is f IN and the upper limit frequency is (f IN + w) is determined. And the signal which shows a determination result shall be supplied to the above-mentioned equalizer.
[0037]
Although the embodiments of the present invention have been described above, the frequency interpolating apparatus according to the present invention can be realized using a normal computer system, not a dedicated system.
For example, a medium in which a program for executing the operations of the above-described BPF 1A, 1B and 4, the delay unit 2, the mixing unit 3, the adding unit 5, the control unit, and the equalizer is stored in a personal computer or microcomputer ( By installing the program from a CD-ROM, MO, floppy disk or the like, a frequency interpolator that executes the above-described processing can be configured.
[0038]
Further, for example, the program may be posted on a bulletin board (BBS) of a communication line and distributed via the communication line. Also, a carrier wave is modulated by a signal representing the program, and the obtained modulated wave is An apparatus that transmits and receives the modulated wave may demodulate the modulated wave to restore the program.
The above-described processing can be executed by starting this program and executing it under the control of the OS in the same manner as other application programs.
[0039]
When the OS shares a part of processing, or when the OS constitutes a part of one component of the present invention, a program excluding the part is stored in the recording medium. May be. Also in this case, in the present invention, it is assumed that the recording medium stores a program for executing each function or step executed by the computer.
[0040]
【The invention's effect】
As described above, according to the present invention, there is provided a frequency interpolation device and a frequency interpolation method for restoring a signal close to an original signal from a modulated wave obtained using a signal in which the band of the original signal is limited. Realized.
Further, according to the present invention, a frequency interpolation device and a frequency interpolation method for restoring an audio signal with high sound quality are realized.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration of a frequency interpolator according to an embodiment of the present invention.
FIG. 2 is a graph showing a band occupied by an input signal and components added to the input signal, and a pass band of the BPF.
[Explanation of symbols]
1A, 1B, 4 BPF
2 delay unit 3 mixing unit 5 addition unit

Claims (11)

補間される対象である被補間信号のうち第1の帯域内の成分を抽出する第1のフィルタと、
前記被補間信号のうち第2の帯域内の成分を抽出する第2のフィルタと、
前記第1及び第2のフィルタが抽出した各前記成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成する混合部と、
前記混合により得られる信号のうち第3の帯域内の成分を抽出する第3のフィルタと、
前記第3のフィルタが抽出した前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する加算部と、を備える、
ことを特徴とする周波数補間装置。
A first filter for extracting a component in the first band from the interpolated signal to be interpolated;
A second filter for extracting a component in a second band from the interpolated signal;
By mixing the components extracted by the first and second filters , the product of the component in the first band or its harmonic and the component in the second band or its harmonic is represented. A mixing section for generating a signal ;
A third filter for extracting a component in a third band from the signal obtained by the mixing;
An adder that generates an output signal representing a sum of the component in the third band extracted by the third filter and the interpolated signal;
A frequency interpolation device characterized by the above.
前記第1の帯域が占める帯域幅は、前記第2の帯域が占める帯域幅に実質的に等しく、
前記第1の帯域の上限は前記第2の帯域の下限に実質的に等しく、
前記第2の帯域の上限は被補間信号のスペクトルの分布の上限に実質的に等しく、
前記第3の帯域の下限は前記第2の帯域の上限に実質的に等しく、
前記第3の帯域が占める帯域幅は、前記第1の帯域が占める帯域幅の2倍に実質的に等しい、
ことを特徴とする請求項1に記載の周波数補間装置。
The bandwidth occupied by the first band is substantially equal to the bandwidth occupied by the second band;
The upper limit of the first band is substantially equal to the lower limit of the second band;
The upper limit of the second band is substantially equal to the upper limit of the spectrum distribution of the interpolated signal,
The lower limit of the third band is substantially equal to the upper limit of the second band;
The bandwidth occupied by the third band is substantially equal to twice the bandwidth occupied by the first band;
The frequency interpolating apparatus according to claim 1.
前記第1のフィルタは、自己に供給される指示に応答して、前記第1の帯域の上限及び下限を変化させる手段を備え、
前記第2のフィルタは、自己に供給される指示に応答して、前記第2の帯域の上限及び下限を変化させる手段を備え、
前記第3のフィルタは、自己に供給される指示に応答して、前記第3の帯域の上限及び下限を変化させる手段を備え、
前記被補間信号を取得して、取得した当該被補間信号のスペクトルの分布の上限を特定し、特定した結果に基づいて、前記第1乃至第3の帯域の上限及び下限を決定し、前記第1のフィルタに、前記第1の帯域の上限及び下限を自己が決定した値とする指示を供給し、前記第2のフィルタに、前記第2の帯域の上限及び下限を自己が決定した値とする指示を供給し、前記第3のフィルタに、前記第3の帯域の上限及び下限を自己が決定した値とする指示を供給する解析手段を備える、
ことを特徴とする請求項2に記載の周波数補間装置。
The first filter includes means for changing an upper limit and a lower limit of the first band in response to an instruction supplied to the first filter,
The second filter comprises means for changing the upper and lower limits of the second band in response to an instruction supplied to the second filter;
The third filter comprises means for changing the upper and lower limits of the third band in response to an instruction supplied to the third filter;
Acquiring the interpolated signal, specifying an upper limit of the spectrum distribution of the acquired interpolated signal, determining upper and lower limits of the first to third bands based on the specified result, The first filter is supplied with an instruction to set the upper limit and the lower limit of the first band as determined by the self, and the second filter is provided with the value determined by the self as the upper limit and the lower limit of the second band. Analyzing means for supplying an instruction to supply, to the third filter, an instruction to set an upper limit and a lower limit of the third band to values determined by the self,
The frequency interpolation apparatus according to claim 2, wherein
前記被補間信号のスペクトルの包絡線を表す包絡線情報を抽出し、前記第3のフィルタが抽出した成分を取得し、取得した当該成分のスペクトルの強度が前記包絡線情報が示す包絡線により表される強度に実質的に等しくなるように当該成分をフィルタリングして前記加算部に供給するイコライズ手段を備え、
前記加算部は、前記イコライズ手段がフィルタリングした前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成するものである、
ことを特徴とする請求項1、2又は3に記載の周波数補間装置。
Envelope information representing an envelope of the spectrum of the interpolated signal is extracted, the component extracted by the third filter is acquired, and the acquired spectrum intensity is represented by the envelope indicated by the envelope information. An equalizing means for filtering the component to be substantially equal to the intensity to be supplied and supplying the filtered component to the adding unit;
The adding unit is configured to generate an output signal representing a sum of the component in the third band filtered by the equalizing unit and the interpolated signal.
The frequency interpolation apparatus according to claim 1, 2, or 3.
前記加算部は、前記第3の帯域内の成分と実質的に同相になるように前記被補間信号を遅延させる遅延部を備え、前記第3の帯域内の成分及び前記遅延部が遅延させた前記被補間信号の和を表す前記出力信号を生成する、
ことを特徴とする請求項1乃至4のいずれか1項に記載の周波数補間装置。
The adding unit includes a delay unit that delays the interpolated signal so as to be substantially in phase with the component in the third band, and the component in the third band and the delay unit are delayed. Generating the output signal representing the sum of the interpolated signals;
The frequency interpolation device according to claim 1, wherein the frequency interpolation device is a frequency interpolation device.
補間される対象である被補間信号のうち第1の帯域内の成分を抽出し、
前記被補間信号のうち第2の帯域内の成分を抽出し、
抽出された前記第1及び第2の帯域内の各成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成し、
前記混合により得られる信号のうち第3の帯域内の成分を抽出し、
抽出された前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する、
ことを特徴とする周波数補間方法。
Extracting the component in the first band from the interpolated signal to be interpolated,
Extracting a component in a second band from the interpolated signal;
By mixing the extracted components in the first band and the second band, the product of the component in the first band or its harmonic and the component in the second band or its harmonic is obtained. Generates a signal that represents
Extracting a component in the third band from the signal obtained by the mixing;
Generating an output signal representing a sum of the extracted component in the third band and the interpolated signal;
A frequency interpolation method characterized by that.
前記第1の帯域が占める帯域幅は、前記第2の帯域が占める帯域幅に実質的に等しく、
前記第1の帯域の上限は前記第2の帯域の下限に実質的に等しく、
前記第2の帯域の上限は被補間信号のスペクトルの分布の上限に実質的に等しく、
前記第3の帯域の下限は前記第2の帯域の上限に実質的に等しく、
前記第3の帯域が占める帯域幅は、前記第1の帯域が占める帯域幅の2倍に実質的に等しい、
ことを特徴とする請求項6に記載の周波数補間方法。
The bandwidth occupied by the first band is substantially equal to the bandwidth occupied by the second band;
The upper limit of the first band is substantially equal to the lower limit of the second band;
The upper limit of the second band is substantially equal to the upper limit of the spectrum distribution of the interpolated signal,
The lower limit of the third band is substantially equal to the upper limit of the second band;
The bandwidth occupied by the third band is substantially equal to twice the bandwidth occupied by the first band;
The frequency interpolation method according to claim 6.
前記被補間信号を取得して、取得した当該被補間信号のスペクトルの分布の上限を特定し、特定した結果に基づいて、前記第1乃至第3の帯域の上限及び下限を決定し、決定結果に従って、前記第1乃至第3の帯域の上限及び下限を変化させる、
ことを特徴とする請求項7に記載の周波数補間方法。
Obtaining the interpolated signal, specifying the upper limit of the spectrum distribution of the acquired interpolated signal, determining the upper and lower limits of the first to third bands based on the identified result, and the determination result To change the upper and lower limits of the first to third bands,
The frequency interpolation method according to claim 7.
前記被補間信号のスペクトルの包絡線を表す包絡線情報を抽出し、前記第3のフィルタが抽出した成分を取得し、取得した当該成分のスペクトルの強度が前記包絡線情報が示す包絡線により表される強度に実質的に等しくなるように当該成分をフィルタリングし、
フィルタリングした前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する、
ことを特徴とする請求項6、7又は8に記載の周波数補間方法。
Envelope information representing an envelope of the spectrum of the interpolated signal is extracted, the component extracted by the third filter is acquired, and the acquired spectrum intensity is represented by the envelope indicated by the envelope information. Filtering the component to be substantially equal to the intensity being
Generating an output signal representing the sum of the filtered component in the third band and the interpolated signal;
The frequency interpolation method according to claim 6, 7 or 8.
前記第3の帯域内の成分と実質的に同相になるように前記被補間信号を遅延させ、前記第3の帯域内の成分及び遅延させた前記被補間信号の和を表す前記出力信号を生成する、
ことを特徴とする請求項6乃至9のいずれか1項に記載の周波数補間方法。
The interpolated signal is delayed so as to be substantially in phase with the component in the third band, and the output signal representing the sum of the component in the third band and the delayed interpolated signal is generated. To
The frequency interpolation method according to claim 6, wherein:
コンピュータを、
補間される対象である被補間信号のうち第1の帯域内の成分を抽出する第1のフィルタと、
前記被補間信号のうち第2の帯域内の成分を抽出する第2のフィルタと、
前記第1及び第2のフィルタが抽出した各前記成分を混合することにより、前記第1の帯域内の成分又はその高調波と前記第2の帯域内の成分又はその高調波との積を表す信号を生成する混合部と、
前記混合により得られる信号のうち第3の帯域内の成分を抽出する第3のフィルタと、
前記第3のフィルタが抽出した前記第3の帯域内の成分及び前記被補間信号の和を表す出力信号を生成する加算部と、
して機能させるためのプログラムを記録したコンピュータ読み取り可能な記録媒体。
Computer
A first filter for extracting a component in the first band from the interpolated signal to be interpolated;
A second filter for extracting a component in a second band from the interpolated signal;
By mixing the components extracted by the first and second filters , the product of the component in the first band or its harmonic and the component in the second band or its harmonic is represented. A mixing section for generating a signal ;
A third filter for extracting a component in a third band from the signal obtained by the mixing;
An adder for generating an output signal representing a sum of the component in the third band extracted by the third filter and the interpolated signal;
The computer-readable recording medium which recorded the program for making it function.
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