JP2004150825A - Spectral analysis apparatus and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce frequency-dependent interpolation errors and to reduce S/N-ratio-dependent interpolation errors in a spectral analysis apparatus. <P>SOLUTION: The spectral analysis apparatus is provided with an A/D converter 1 for converting an input continuous-time signal 100 into a discrete-time signal 101; a fast Fourier transform (FFT) device 2 for converting the discrete-time signal 101 into a discrete spectrum 102; an interpolator 3 for acquiring the amount p<SB>1</SB>of frequency interpolation to the discrete spectrum 102 of a peak point through the use of intensity ratios between the peak point of the discrete spectrum 102 and two of its adjacent points; and, additionally, a corrector 4 for correcting the discrete spectrum of the peak point outputted from the FFT device 2 on the basis of the amount p<SB>1</SB>of interpolation. The corrector 4 is made to correct the discrete spectrum of the peak point through the use of the amount p<SB>1</SB>of interpolation and interpolation errors of the interpolator 3 corresponding to a frequency indicated by the amount p<SB>1</SB>of interpolation. <P>COPYRIGHT: (C)2004,JPO

Description

【００３５】
次に、ＦＦＴ演算器２は、入力された離散時間信号１０１をＦＦＴによってスペクトラム１０２に変換し、補間器３および補正器４に出力する。
【００３６】
次に、補間器３は、入力されたスペクトラム１０２のピークおよびその両隣のサンプル点を検出し、上述した第１の補間法に従って、入力されたスペクトラム１０２のピーク点でのスペクトルに対する補間量ｐ_１を計算し、補正器４に出力する。ここで、補間量ｐ_１は、次式（数２）で表される。
【００３７】
【数２】

【００３８】
ここで、ｒ_０は、ＦＦＴ演算器２より出力された周波数スペクトラム１０２のピーク点を挟んだ両隣の２サンプル点でのスペクトル強度比である。ＦＦＴ演算器２において、数１で表される離散時間信号１０１に、ハニング窓を施したフーリエ変換スペクトラムをＤ（ｍ）とし、第ｋ番目のサンプル点でのスペクトルＤ（ｋ）にピークが現れたとする。この場合、スペクトル強度比ｒ_０は、次式（数３）で表される。
【００３９】
【数３】

【００４０】
なお、上述の第１の補間法は、実際には、｜Ｄ（ｋ＋１）｜／｜Ｄ（ｋ）｜および｜Ｄ（ｋ−１）｜／｜Ｄ（ｋ）｜の２種類のスペクトル強度比を用いている。しかし、ここでは原理説明のため、数３で示される１種類のスペクトル強度比ｒ_０を用いて、補間量ｐ_１を求めるようにしている。
【００４１】
次に、補正器４において、記憶器４４は、ＦＦＴ演算器２より出力されたスペクトラム１０２を記憶する。
【００４２】
また、周波数補正器４１は、補間器３より出力された補間量ｐ_１と、この補間量ｐ_１に応じて定まる補正量δｐとを用いて、次式（数４）により、補正されたサンプリング番号小数部ｐを求める。
【００４３】
【数４】

【００４４】
ここで、δｐは、補間量ｐ_１が示す周波数に応じて定まる補間器３の補間誤差に応じた補正量である。この補正量δｐは、次式（数５）示すように、補間器３での補間量ｐ_１の多項式で表される。
【００４５】
【数５】

【００４６】
ここで、ｐ_１の範囲は、−０．５≦ｐ_１≦０．５であるから、数５の各項の最大寄与は、ｐ_１＝±０．５のときに現れる。このとき、各項の値は、第１項の値を１．０とおくと、第１項から順に１．０、０．００７１６、‐０．１２９１０、０．０３０３２、…となり、第１項の寄与が最大である。
【００４７】
なお、上述の数５は、次のようにして導くことができる。すなわち、ＦＦＴ演算器２から出力されたスペクトラムのピーク点の両隣サンプリング点ｋ±１におけるスペクトル強度の理論値は、フーリエ変換理論を用いて、次式（数６）のように定義する。
【００４８】
【数６】

【００４９】
ここで、ｋ＋ｐはピーク位置のサンプリング番号を実数表現した変数である。ｋはサンプリング番号整数部であり、スペクトラムのピーク点に一致する。また、上述したように、ｐはサンプリング番号小数部であり、信号周波数がＦＦＴ周波数分解能の整数倍でない場合の端数であって、スペクトラムのピーク点でのスペクトルが示す周波数と、前記ピーク点とその隣接点との間に存在する真のピーク位置での周波数との差分（誤差）を示す。
【００５０】
一般に、ＦＦＴのサンプリング数Ｎは大きい数であるから、サンプリング番号小数部ｐは、その近似値である補間量ｐ_１からごくわずかの範囲内にある。そこで、数４を数６に代入し、次式（数７）により、スペクトラムのピーク点の両隣サンプリング点ｋ±１におけるスペクトル強度の理論値の比ｒを求める。
【００５１】
【数７】

【００５２】
このスペクトル強度理論値比ｒが数３で示したスペクトル強度比ｒ_０に一致するように補正量δｐを定める。ここで、補間量ｐ_１の補正が正しく行なわれた場合、すなわち、サンプリング番号小数部ｐが正しく求められた場合、図１３に示した周波数誤差は全ての周波数においてゼロになる。この場合、補正量δｐは、図１３に示す周波数誤差特性の符号を反転したものとなる。したがって、図１３に示す周波数誤差特性を最小自乗法によって多項式近似することにより、補正量δｐとして、（数５）で示す多項式を導くことができる。
【００５３】
さて、補正器４は、以上のようにして周波数補正器４１によりサンプリング番号小数部ｐを求めたならば、このサンプリング番号小数部ｐを用いて、記憶部４４に記憶されている周波数スペクトラム１０２のピーク点（サンプル点ｋ）でのスペクトルを補正する。
【００５４】
具体的には、周波数補正器４１は、ピーク点でのスペクトルが表す周波数を次式（数８）により補正し、その結果である周波数ｆを、周波数補正結果１０４として出力して、記憶器４５に記憶する。
【００５５】
【数８】

【００５６】
また、振幅補正器４２は、ピーク点でのスペクトルが表わす振幅を次式（数９）により補正し、その結果である振幅Ａを、振幅補正結果１０５として出力して、記憶器４５に記憶する。
【００５７】
【数９】

【００５８】
また、位相補正器４３は、ピーク点でのスペクトルが表わす位相を次式（数１０）により補正し、その結果である振幅φを、位相補正結果１０６として出力して、記憶器４５に記憶する。
【００５９】
【数１０】

【００６０】
以上のようにして記憶器４５に記憶された周波数補正結果１０４、振幅補正結果１０５および位相補正結果１０６を、ＦＦＴ演算器２より出力された周波数スペクトラム１０２のピーク点でのスペクトル補正結果１０７として、必要なタイミングで出力する。
【００６１】
次に、本実施形態のスペクトル分析装置による補正結果について説明する。
【００６２】
図２に、入力信号１００が図１１（ａ）に示す諸元を持つ正弦波信号であり、６４個のサンプル点（Ｎ＝６４）からなるＦＦＴ演算器２を用いた場合の補正結果の一例を示す。
【００６３】
図示するように、図１１（ａ）に示す信号諸元（周波数、振幅、および位相）と補正された信号諸元との誤差は、周波数誤差が約０．００００６Ｈｚ、振幅誤差が、約０．００００２、そして、位相誤差が約０．０１度である。同条件の従来例である図１１（ｂ）および図１１（ｃ）と比較して、周波数誤差、振幅誤差および位相誤差がおよそ１００分の１程度であり、著しく改善されたことが分かる。
【００６４】
図３に、離散時間信号の周波数を変化させた場合に、補正結果に含まれる周波数誤差の一例を示す。同条件の従来例である図１３と比較して、周波数誤差がいずれの周波数でも、およそ１００分の１程度に改善されたことが分かる。
【００６５】
図３は、補間量ｐ_１に含まれる周波数誤差量を示している。図３にみられる周波数誤差量は、正弦波成分を含むので、更なる改善のためには正弦波を含む補正関係を適用する必要がある。しかし、正弦波計算は回路数が増加するので実現が容易ではない。このため、最小回路数で誤差の最大改善効果を得るために、上述の数５すなわち周波数誤差が周波数の多項式で表わされる関係を用いて、補正量δｐを計算している。
【００６６】
なお、図３は、ＦＦＴ周波数分解能ｆｒｅｓ＝１Ｈｚとした場合の例である。この場合の周波数誤差の最大値は０．０００１Ｈｚであった。周波数誤差とＦＦＴ周波数分解能とは比例関係にある。したがって、このことは、いかなる周波数分解能のＦＦＴ演算器を用いても、ＦＦＴ周波数分解能の１／１００００の誤差で周波数を測定できることを意味する。
【００６７】
以上、本発明の第１実施形態について説明した。
【００６８】
次に、本発明の第２実施形態について説明する。
【００６９】
図４は、本発明の第２実施形態が適用されたスペクトル分析装置の概略構成図である。
【００７０】
図示するように、本実施形態のスペクトル分析装置は、Ａ／Ｄ変換器１と、入力がＡ／Ｄ変換器１の出力側に接続されるＦＦＴ演算器２と、入力がＦＦＴ演算器２の出力側に接続される補間器３と、二つの入力がそれぞれ補間器３およびＦＦＴ演算器２の出力側に接続される補正器４と、二つの入力がそれぞれＡ／Ｄ変換器１および補正器４の出力側に接続される時間基準補正器５とを、有する。
【００７１】
以上のような構成において、先ず、Ａ／Ｄ変換器１は、入力信号１００をＡ／Ｄ変換により離散時間信号１０１へと変換する。次に、ＦＦＴ演算器２は、離散時間信号１０１を周波数スペクトラム１０２へと変換し、補間器３および補正器４に出力する。さらに、補間器３は、入力された周波数スペクトラム１０２を上述した第１の補間法に従って補間し、スペクトル補間結果１０３を得、補正器４へと出力する。そして、補正器４は、入力されたスペクトル補間結果１０３とＦＦＴ演算器２から出力された周波数スペクトラム１０２とをスペクトル補正し、スペクトル補正結果１０７を出力する。
【００７２】
本実施形態では、図１に示す構成に対して、さらに、時間基準補正器５を加えている。時間基準補正器５は、補正器４の出力を記憶する記憶器５４と、入力が補正器４の出力である再生器５１と、Ａ／Ｄ変換器１の出力を記憶する記憶器５３と、２つの入力が再生器５１および記憶器５３の出力に接続された残差計算機５２と、２つの入力が残差計算機５２および記憶器５４の出力に接続された補正量算出器５５と、２つの入力が記憶器５４および補正量算出器５５の出力に接続された加算器５６と、を有する。
【００７３】
再生器５１は、スペクトル補正結果１０７の中の周波数、振幅及び位相データを用いて、上記（数１）により、時間領域の再生信号１０８を生成する。該再生信号１０８は残差計算器５２に入力される。
【００７４】
残差計算器５２は、入力された再生器５１からの再生信号１０８と記憶器５３からの離散時間信号１１０との残差１０９を求め、補正量算出器５５に送る。
記憶器５３は、Ａ／Ｄ変換器１の出力である離散時間信号１０１を格納し、残差計算器５２に離散時間信号１１０として、必要なタイミングで出力する。
【００７５】
記憶器５４は、スペクトル補正器４の出力１０７を格納し、補正量算出器５５及び加算器５６に必要なタイミングで出力する。
【００７６】
補正量算出器５５は、残差１０９と、記憶器５４から読み出された補正結果１１１とを用いて、残差１０９が最小となるような振幅Ａ、周波数のサンプル番号の小数部ｐ、および位相φの補正量（△Ａ，△ｐおよび△φ）を求める。演算結果１１２すなわち補正量△Ａ， △ｐおよび△φは、加算器５６に送られる。補正量△ｐ， △Ａおよび △φは、最小自乗法を用いて（数１１）の解として求められる。
【００７７】
【数１１】

【００７８】
加算器５６は、前記補正量および記憶器５４に格納されているスペクトル補正結果１１１を用いて（数１２）に示す加算を行い、補正結果１１３を出力する。ここに、近似値Ａ_２， ｐ_２， φ_２は前記スペクトル補正すなわち、ｐ_２＝ｐ_１＋δｐ、及び該ｐ_２を（数９）および（数１０）に代入して求めた補正量である。周波数は更に（数８）に代入し、周波数、振幅および位相が決定される。
【００７９】
【数１２】

【００８０】
時間基準補正器５の機能は、周波数領域での補間結果１０３を時間領域へと変換し、その変換信号を、基準となる離散時間信号１０１にできる限り一致させる周波数、振幅、位相の変化量を求めるものである。
【００８１】
次に、本実施形態のスペクトル分析装置による時間補正結果について説明する。図５は、時間基準補正の結果を時間軸上に示している。黒丸２００は離散時間信号１０１をグラフ上にプロットしたものである。点線２０１は前記スペクトル補間法によって求められた周波数ｆ、振幅Ａおよび位相φを（数１）に代入して再生した離散時間信号（以下、「再生信号２０１」と言う）である。信号２０２は時間基準補正を経た最終結果である。離散時間信号２００と時間基準補正量２０２との差は、離散時間信号２００と再生信号２０１との差よりも小さくなり、この補正の妥当性を示している。
【００８２】
図６に、（数１）で示される信号にランダム雑音を加え、本実施例に入力した場合の、時間基準補正結果の一例を示す。図６における周波数誤差は、各Ｓ／Ｎについて１０００回の周波数誤差測定を行なった、その代表値である。特性２０３（点線）はスペクトル補間のみの場合であって、図１４と同一である。特性２０４は時間基準補正をした場合である。誤差改善量は、Ｓ／Ｎが８０ｄＢの場合は０．００７Ｈｚ、Ｓ／Ｎが２０ｄＢの場合は０．０１４Ｈｚと、Ｓ／Ｎ全域に亘って周波数誤差が改善されていることが明らかである。
【００８３】
なお、本実施形態において図７（ａ）に示すように、補正器４をもたない構成も考えられる。時間基準補正器５の２つの入力のうち補正器４の出力１０７は、該出力１０７に近いものであれば、出力１０７に限らない。元来、補間器３の出力１０３と補正器４の出力１０７は非常に近い値であるから、補間器３の出力１０３は、補正器５にとっての入力信号となりうる。
【００８４】
また、本実施形態において図７（ｂ）に示すように、補間器３及び補正器４ともに省略してよい場合がある。上述した図７（ａ）の場合と同じ理由により、ＦＦＴ演算器２の出力１０２は補正器４の出力１０７にある程度の誤差の範囲内にあるから、ＦＦＴ演算器２の出力１０２は、補正器５にとっての入力信号となりうる。この場合、ＦＦＴ演算器２の出力１０２のピークを検出するためのピーク検出器６を付加することにより、時間基準補正器５の入力信号となりうる。該ピーク検出器６の動作を図１２によって説明する。ピーク検出器６への入力は、ＦＦＴ演算器２からの離散信号スペクトラム１０２である。図１２におけるピーク位置は、信号周波数ｆ ＝ ８ Ｈｚ、ピークスペクトル強度 ｜Ｄ（ｋ）｜ ＝ １５．６５であるから、これらをもとに（数１３）を用いて信号の周波数、振幅および位相の近似値を計算する。該結果はピーク検出器出力１１４として出力され、時間基準補正器５に入力される。
【００８５】
【数１３】

【００８６】
図８は、図４、図７（ａ）および（ｂ）、図１０の構成を持つスペクトル分析装置の分析結果が持つ周波数誤差と、離散時間信号１０１のＳ／Ｎとの関係を表示したものである。図８において、特性２０３は、従来技術で説明した図１０における補間のみで時間基準補正をしない場合の、周波数誤差とＳ／Ｎとの関係を現わしている。特性２０６は、図７（ｂ）が示すピーク検出器６を持つ場合の周波数誤差であり，補間のみの特性２０３と比較すると、時間基準補正による誤差改善効果が大きいことが示されている。特性２０４は、図４が示す補間器３と補正器４と時間基準補正器５とを持つ場合の周波数誤差である。特性２０５（点線）は、図７（ａ）が示す補間器３と時間基準補正器５とを持つ場合の周波数誤差である。 また、特性２０４および２０５との間に殆ど差がないのは、補間器３の出力１０３と、補正器４の出力１０７が極めて近いからである。これに対し、特性２０６と特性２０４および２０５との間の差が大きいのは、ＦＦＴ演算器２の出力のピーク分析のみでは真値からの差が大きいからである。
【００８７】
以上述べた如く、周波数の時間基準補正効果は、時間基準補正器５への入力として補正器４の出力 または 補間器３の出力いずれを用いる場合も同程度の効果である。また、時間基準補正器５への入力としてＦＦＴ演算器２の出力を用いる場合は、僅かに誤差が増加するものの補間器３および補正器４を不要とする点で有利である。これら補正方法は希望する補正誤差の大きさにより選択することができる。
【００８８】
次に、上記時間基準補正器５を有する実施形態の具体的な適用例として、上記実施形態のいずれか（図１、図４、図７（ａ）、図７（ｂ））を搭載した水中音響信号を解析するソナー装置を図９に示す。
【００８９】
ソナー装置７の構成は、ソナー制御器７１とその入力が前記ソナー制御器７１の出力側に接続されたソナー送信機７２と、ソナー受信機７３と入力が前記ソナー制御器７１と前記ソナー送信機７２の出力側に接続されたソナー信号解析器７４を有する。
【００９０】
前記ソナー制御器７１は、ソナー制御信号７００を前記ソナー送信機７２と前記ソナー信号解析器７４とに出力する。
【００９１】
前記ソナー送信機７２は、入力された前記ソナー制御信号７００に基づいて、ソナー送信信号７０１を水中へ出力し、また前記ソナー送信信号の理論値７０２を前記ソナー信号解析器７４へと出力する。
【００９２】
前記ソナー受信機７３は、水中からソナー信号７０３を受信し、受信した該ソナー信号７０３の一部をソナー受信信号７０４として前記ソナー信号解析器７４に出力する。
【００９３】
前記ソナー信号解析器７４は、スペクトル分析器７４１と信号処理器７４２とから構成される。
【００９４】
前記スペクトル分析器７４１は、第二の実施形態の構成（図１、図４、図７（ａ）、図７（ｂ））のいずれかを持ち、その構成に基づく処理を行なう。前記スペクトル分析器７４１への入力は、前記ソナー受信信号７０４であり、そのソナースペクトル解析結果７０５を前記信号処理器７４２に出力する。
【００９５】
前記信号処理機７４２は、前記ソナー制御信号７００と、前記ソナー送信信号の理論値７０２と、前記ソナースペクトル解析結果７０５を入力とする。それらの信号を比較することにより、目的に応じた処理を行い、ソナー信号処理結果７０６として、前記ソナー装置７の外部へ出力する。
【００９６】
このソナー装置は、水中の対象物へ前記ソナー送信信号７０１を送信し、その反射波として前記ソナー信号７０３を使う場合は、アクティブソナー装置となる。一方、水中，水底或いは水上の物体から放射される信号を前記ソナー信号７０３とする場合は、前記ソナー受信器７３と前記信号解析器７４とを用いて、パッシブソナー装置となる。
【００９７】
いずれの場合においても、その解析結果の周波数誤差は、入力信号周波数への依存性が低く、また、低Ｓ／Ｎ下の信号の解析においても周波数誤差が低減される。
【００９８】
尚、本発明は、上記の実施形態に限定されるものではない。その要旨の範囲内で数々の変形が可能である。例えば、上記の第１，２の実施形態において、補間器３に第二の補間例を用いる場合でも、第一の補間例を利用する場合と、同様の効果が期待できる。
【００９９】
【発明の効果】
以上説明したように本発明によれば、補間誤差が持つ入力信号周波数への依存性を改善し、低Ｓ／Ｎ下の信号において、周波数に対するスペクトル補間誤差を減少させることが可能となる。
【図面の簡単な説明】
【図１】本発明の第一の実施形態を説明するブロック図である。
【図２】本発明の第一の実施形態によるスペクトル補正結果の一例を説明する図である。
【図３】本発明の第一の実施形態によるスペクトル補正において、周波数誤差の周波数依存性を説明する図である。
【図４】本発明の第二の実施形態を説明するブロック図である。
【図５】時間基準補正器の原理を説明する図である。
【図６】本発明の第二の実施形態による時間基準補正において、改善された周波数誤差のＳ／Ｎへの依存性を説明する図である。
【図７】スペクトル補正がない場合の実施例を説明するブロック図である。
【図８】スペクトル補間、スペクトル補正、時間基準補正の組み合わせにおいて、周波数誤差のＳ／Ｎ依存性を説明する図である。
【図９】スペクトル解析装置を搭載したソナー装置のブロック図である。
【図１０】従来技術によるスペクトル分析装置を説明するブロック図である。
【図１１】（ａ）離散時間信号諸元と、（ｂ）および（ｃ）従来技術によるスペクトル補間結果の一例を説明する図である。
【図１２】ＦＦＴ演算器の出力を説明する図である。
【図１３】従来技術によるスペクトル補間の周波数依存性を説明する図である。
【図１４】従来技術によるスペクトル補間のＳ／Ｎ依存性を説明する図である。
【符号の説明】
１…Ａ／Ｄ変換器、２…ＦＦＴ演算器、３…補間器、４…補正器、５…時間基準補正器、６…ピーク検出器、７…ソナー装置、４１…周波数補正器、４２…振幅補正器、４３…位相補正器、４４，４５…記憶器、５１…再生器、５２…残差計算器、５３，５４…記憶器、５５…補正量算出器、５６…加算器、７１…ソナー制御器、７２…ソナー送信機、７３…ソナー受信機、７４…ソナー信号解析器、７４１…スペクトル分析器、７４２…信号処理機。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a technique for spectral analysis of a signal.
[0002]
[Prior art]
Spectral analysis is a basic measurement technique used in various fields including the electric and mechanical fields. Examples include voice analysis, modulation / demodulation signal analysis, radar / sonar signal analysis, mechanical vibration analysis, and the like.
[0003]
An excellent method used at that time is a method using a fast Fourier transform (hereinafter, referred to as “FFT”). The FFT is a method of digitizing an analog signal, performing a Fourier transform on data of a fixed sampling number, converting the data into a spectrum, and calculating a frequency and an amplitude included in the analog signal from the spectrum. The FFT can calculate the correct frequency and amplitude only when the signal frequency is an integer multiple of the FFT resolution (ie, a numerical value obtained by dividing the sampling frequency by the number of FFT samples). This means that when the signal frequency is other than an integer multiple of the FFT resolution, leakage occurs near the original frequency. That is, in this case, the FFT cannot obtain the peak spectrum at the original signal frequency, and gives a spectrum at a frequency sample point (an integral multiple of the FFT resolution) in the vicinity, that is, a calculated value close to the peak spectrum. Will be. Therefore, the correct frequency and amplitude cannot be calculated.
[0004]
As described above, in the measurement apparatus using the FFT, the measurement result includes the above-described error due to the FFT. For this reason, a spectrum interpolation method has been proposed that reduces the error due to FFT as much as possible.
[0005]
There are two examples of conventional spectral interpolation.
[0006]
The first interpolation method is a method of analytically calculating the frequency, amplitude, and phase of an input signal using an intensity ratio of three sample points of a peak point of a spectrum output from the FFT and two adjacent points thereof (for example, Non-Patent Document 1).
[0007]
In the second interpolation method, a spectrum approximation formula is prepared in advance, and the intensities of the three peaks of the spectrum output from the FFT and its three neighboring points are applied to this approximation formula to obtain the frequency and frequency of the input signal. This is a method of calculating the amplitude and the phase (for example, see Patent Document 1).
[0008]
FIG. 10 is a schematic configuration diagram of a spectrum analyzer using a conventional spectrum interpolation method. In this spectrum analyzer, an A / D converter 1, an FFT operator 2 whose input is connected to the output of the A / D converter 1, and a spectrum interpolator 3 whose input is connected to the output of the FFT operator 2 And
[0009]
The A / D converter 1 converts an input signal 100, which is a continuous time signal (analog signal), into a discrete time signal 101 by A / D conversion, and outputs the signal to the FFT calculator 2.
[0010]
The FFT calculator 2 converts the input discrete-time signal 101 into a frequency spectrum 102 by FFT, and outputs the frequency spectrum 102 to the interpolator 3.
[0011]
Then, the interpolator 3 performs interpolation on the spectrum at the peak point of the input frequency spectrum 102 and outputs the result (frequency, amplitude, and phase) as an interpolation result 103.
[0012]
An example of the spectrum interpolation operation by the interpolator 3 will be described below.
[0013]
Here, as the input signal 100, a sine wave signal having the frequency, amplitude, and phase shown in FIG. 11A, that is, a frequency of 8.1 (Hz), an amplitude of 1.000, and a phase of 10.000 (degrees) Is used. FIG. 12 shows the frequency spectrum 102 converted by the FFT calculator 2 consisting of 64 sample points. It is immediately apparent from the frequency spectrum 102 shown in FIG. 12 that the frequency of the input signal will be about 8 (Hz). Since the spectrum is not symmetric, it is estimated that the frequency will not be exactly 8 (Hz) but will be about 8 (Hz).
[0014]
FIGS. 11B and 11C show the results of interpolating the spectrum at the peak point of the frequency spectrum 102 by the interpolator 3. Here, FIG. 11B corresponds to the above-described first interpolation method (for example, see Non-Patent Document 1), and FIG. 11C shows the above-described second interpolation method (for example, see Patent Document 1). It corresponds to.
[0015]
As shown in FIG. 11B, the result of the first interpolation method has a frequency error of about 0.004 Hz, an amplitude error of about 0.015, and a phase error of about 0.6 degrees. As shown in FIG. 11C, the result of the second interpolation method has a frequency error of about 0.008 Hz, an amplitude error of about 0.008, and a phase error of about 1.4 degrees. Both values are close to the specifications shown in FIG. Note that the frequency error is the difference between the frequency of the input signal 100 and the interpolated frequency, the amplitude error is the difference between the amplitude of the input signal 100 and the interpolated amplitude, and the phase error is This is the difference between the phase of the input signal 100 and the interpolated phase.
[0016]
As described above, the spectrum interpolation method is an effective means for obtaining the frequency, amplitude, and phase of a signal with higher accuracy than the conventional FFT alone.
[0017]
[Non-patent document 1]
Makoto Tabei, Mitsuhiro Ueda “High-precision frequency determination method using FFT” IEICE Transactions A, Vol. J70-A, No. 5, pp. 798-805 (1987)
[Patent Document 1]
JP-A-6-160445, "High-resolution frequency analyzer, hologram observing apparatus and vector spectrum analyzer using this apparatus"
[0018]
[Problems to be solved by the invention]
However, the present inventors have confirmed that the following problems occur when the first and second interpolation methods described above are applied to the FFT spectrum analysis technique.
[0019]
That is, the first problem is that a frequency-dependent interpolation error occurs. FIG. 13 shows a frequency error (difference between the frequency of the input signal 100 and the interpolated frequency) when the frequency of the input signal 100 is continuously changed in the first interpolation method described above. As shown, when the frequency of the input signal 100 changes, the frequency error changes periodically. In the example shown in FIG. 13, the amount of change is in the range of about 0 to 0.02 (Hz). Thus, the fact that the error depends on the frequency of the input signal is detrimental for high-precision frequency measurement.
[0020]
A second problem is that the signal-to-noise ratio (hereinafter, referred to as S / N (unit: dB)) is reduced and the frequency error is increased. In fact, the Fourier transform of temporally random noise randomly changes the spectral intensity over all frequencies. In the above-described first and second interpolation methods, the noise component is superimposed on the peak point of the frequency spectrum 102 and the three sample points on both sides thereof, so that the interpolation result 103 is affected by the noise. FIG. 14 is a graph showing the relationship between S / N and frequency error. In the figure, as shown by the characteristic curve 203, when the noise increases (that is, the S / N decreases), the frequency error increases. Generally, the S / N that can be realized by measuring physical phenomena and electric circuits is at most about 100 dB. Therefore, in most cases, the interpolation result 103 contains a considerable error.
[0021]
The present invention has been made in view of the above circumstances, and an object of the present invention is to reduce an interpolation error that occurs when the first and second interpolation methods described above are applied to an FFT spectrum analysis technique. Specifically, it is to reduce the interpolation error depending on the frequency. Another object is to reduce an interpolation error depending on S / N.
[0022]
[Means for Solving the Problems]
In order to solve the above problems, a first aspect of the present invention is an A / D converter for converting an input continuous-time signal into a discrete-time signal, and the discrete-time signal output from the A / D converter. To a discrete spectrum, a fast Fourier transform (FFT) unit, and an intensity ratio of the peak point of the discrete spectrum output from the FFT unit and its neighboring points, or the peak point and its neighboring points are used. By applying the intensity to the approximation formula, in addition to the interpolator for obtaining the frequency interpolation amount for the discrete spectrum of the peak point, the peak point output from the FFT unit based on the interpolation amount obtained by the interpolator. Is further provided.
[0023]
Then, the corrector corrects the discrete spectrum of the peak point output from the FFT unit using the interpolation amount and a correction amount determined according to a frequency indicated by the interpolation amount.
[0024]
According to a second aspect of the present invention, there is provided an A / D converter for converting an input continuous-time signal into a discrete-time signal, and converting the discrete-time signal output from the A / D converter into a discrete spectrum. Using the fast Fourier transform (FFT) unit and the intensity ratio between the peak point of the discrete spectrum output from the FFT unit and its neighboring points, or applying the intensity of the peak point and its neighboring points to an approximate expression Accordingly, in addition to the interpolator for interpolating the discrete spectrum of the peak point, a time reference corrector for correcting the interpolation result in the interpolator is further provided.
[0025]
Then, the time reference corrector includes a reproduction signal reproduced from the signal specifications (frequency, amplitude, and phase) interpolated by the interpolator, and the discrete time signal output from the A / D converter. The signal specifications interpolated by the interpolator are corrected so that the difference becomes small.
[0026]
In this embodiment, a peak detector that outputs a frequency, an amplitude and a phase at a peak point of the discrete spectrum output from the FFT unit may be provided instead of the interpolator. In this case, the time base corrector is configured to reduce the difference between the reproduced signal reproduced from the output result of the peak detector and the discrete time signal output from the A / D converter so as to reduce the difference. Correct the output result of the detector.
[0027]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described.
[0028]
First, a first embodiment of the present invention will be described.
[0029]
FIG. 1 is a schematic configuration diagram of a spectrum analyzer to which the first embodiment of the present invention is applied.
[0030]
As shown in the figure, the spectrum analyzer of the present embodiment has an A / D converter 1, an FFT operator 2 whose input is connected to the output of the A / D converter 1, and an input which is an output of the FFT operator 2. , And a corrector 4 whose two inputs are connected to the output of the interpolator 3 and the output of the FFT calculator 2, respectively.
[0031]
The compensator 4 includes a memory 44 for storing the output of the FFT calculator 2, a frequency compensator 41 whose input is connected to the output of the interpolator 3, and two inputs for the frequency compensator 41 and the memory 44. The phase corrector 43 whose two inputs are connected to the outputs of the frequency corrector 41 and the memory 44, the output of the frequency corrector 41, the output of the amplitude corrector 42, And a storage unit 45 for storing the output of the phase corrector 43.
[0032]
In the above configuration, first, the A / D converter 1 converts the input signal 100, which is a continuous time signal (analog signal), into a discrete time signal 101 by A / D conversion, and outputs the signal to the FFT calculator 2. .
[0033]
This discrete time signal 101 is represented by the following equation (Equation 1).
[0034]
(Equation 1)

[0035]
Next, the FFT calculator 2 converts the input discrete-time signal 101 into a spectrum 102 by FFT, and outputs the spectrum 102 to the interpolator 3 and the corrector 4.
[0036]
Next, the interpolator 3 detects the peak of the input spectrum 102 and sample points on both sides thereof, and according to the first interpolation method described above, the interpolation amount p for the spectrum at the peak point of the input spectrum 102. ₁ Is calculated and output to the corrector 4. Here, the interpolation amount p ₁ Is represented by the following equation (Equation 2).
[0037]
(Equation 2)

[0038]
Where r ₀ Is the spectral intensity ratio at two sample points on both sides of the peak point of the frequency spectrum 102 output from the FFT calculator 2. In the FFT calculator 2, the Fourier transform spectrum obtained by applying a Hanning window to the discrete-time signal 101 represented by Equation 1 is D (m), and a peak appears in the spectrum D (k) at the k-th sample point. Suppose. In this case, the spectral intensity ratio r ₀ Is represented by the following equation (Equation 3).
[0039]
[Equation 3]

[0040]
Note that the first interpolation method described above actually uses two types of spectral intensities of | D (k + 1) | / | D (k) | and | D (k-1) | / | D (k) | The ratio is used. However, here, for the sake of explanation of the principle, one kind of spectrum intensity ratio r shown in Expression 3 ₀ , The interpolation amount p ₁ I want to ask.
[0041]
Next, in the corrector 4, the storage unit 44 stores the spectrum 102 output from the FFT operation unit 2.
[0042]
Further, the frequency corrector 41 calculates the interpolation amount p output from the interpolator 3. ₁ And the interpolation amount p ₁ The corrected sampling number decimal part p is obtained by the following equation (Equation 4) using the correction amount δp determined according to
[0043]
(Equation 4)

[0044]
Here, δp is the interpolation amount p ₁ Is a correction amount according to the interpolation error of the interpolator 3 determined according to the frequency indicated by. This correction amount δp is calculated by the interpolation amount p in the interpolator 3 as shown in the following equation (Equation 5). ₁ Is represented by the following polynomial.
[0045]
(Equation 5)

[0046]
Where p ₁ Range is -0.5 ≦ p ₁ Since ≦ 0.5, the maximum contribution of each term in Equation 5 is p ₁ = Appears when ± 0.5. At this time, assuming that the value of the first term is 1.0, the value of each term is 1.0, 0.00716, -0.12910, 0.03032,... Is the largest contribution.
[0047]
Note that the above Equation 5 can be derived as follows. That is, the theoretical value of the spectrum intensity at the sampling points k ± 1 on both sides of the peak point of the spectrum output from the FFT calculator 2 is defined by the following equation (Equation 6) using Fourier transform theory.
[0048]
(Equation 6)

[0049]
Here, k + p is a variable expressing the sampling number of the peak position in a real number. k is an integer part of the sampling number, which coincides with the peak point of the spectrum. Further, as described above, p is a sampling number decimal part, which is a fraction when the signal frequency is not an integral multiple of the FFT frequency resolution, and the frequency indicated by the spectrum at the peak point of the spectrum, and the peak point and its peak point. The difference (error) from the frequency at the true peak position existing between the adjacent points is shown.
[0050]
In general, the sampling number N of the FFT is a large number, so the sampling number decimal part p is an interpolation amount p which is an approximate value thereof. ₁ Within a very small range. Therefore, the equation (4) is substituted into the equation (6), and the ratio r of the theoretical value of the spectrum intensity at the sampling points k ± 1 on both sides of the peak point of the spectrum is obtained by the following equation (equation 7).
[0051]
(Equation 7)

[0052]
This spectrum intensity ratio r is the spectrum intensity ratio r shown in Expression 3. ₀ The correction amount δp is determined so as to coincide with. Here, the interpolation amount p ₁ Is correctly performed, that is, when the sampling number decimal part p is correctly obtained, the frequency error shown in FIG. 13 becomes zero at all frequencies. In this case, the correction amount δp is obtained by inverting the sign of the frequency error characteristic shown in FIG. Therefore, by approximating the frequency error characteristic shown in FIG. 13 with a polynomial using the least squares method, a polynomial represented by (Equation 5) can be derived as the correction amount δp.
[0053]
Now, when the frequency corrector 41 obtains the sampling number decimal part p as described above, the corrector 4 uses the sampling number decimal part p to calculate the frequency spectrum 102 of the frequency spectrum 102 stored in the storage unit 44. The spectrum at the peak point (sample point k) is corrected.
[0054]
Specifically, the frequency corrector 41 corrects the frequency represented by the spectrum at the peak point by the following equation (Equation 8), outputs the resulting frequency f as a frequency correction result 104, and To memorize.
[0055]
(Equation 8)

[0056]
Further, the amplitude corrector 42 corrects the amplitude represented by the spectrum at the peak point by the following equation (Equation 9), outputs the resultant amplitude A as an amplitude correction result 105, and stores the result in the storage unit 45. .
[0057]
(Equation 9)

[0058]
Further, the phase corrector 43 corrects the phase represented by the spectrum at the peak point by the following equation (Equation 10), outputs the resultant amplitude φ as the phase correction result 106, and stores the result in the storage unit 45. .
[0059]
(Equation 10)

[0060]
The frequency correction result 104, the amplitude correction result 105, and the phase correction result 106 stored in the storage device 45 as described above are used as a spectrum correction result 107 at the peak point of the frequency spectrum 102 output from the FFT calculator 2. Output at the required timing.
[0061]
Next, a correction result by the spectrum analyzer of the present embodiment will be described.
[0062]
FIG. 2 shows an example of a correction result when the input signal 100 is a sine wave signal having the specifications shown in FIG. 11A and the FFT calculator 2 including 64 sample points (N = 64) is used. Is shown.
[0063]
As shown, the error between the signal specifications (frequency, amplitude, and phase) shown in FIG. 11A and the corrected signal specifications has a frequency error of about 0.00006 Hz and an amplitude error of about 0. 00002, and the phase error is about 0.01 degrees. 11B and 11C, which are conventional examples under the same conditions, the frequency error, the amplitude error, and the phase error are about 1/100, which means that the frequency error, the amplitude error, and the phase error are significantly improved.
[0064]
FIG. 3 shows an example of a frequency error included in the correction result when the frequency of the discrete time signal is changed. It can be seen that the frequency error is improved to about 1/100 at any frequency as compared with FIG. 13 which is a conventional example under the same condition.
[0065]
FIG. 3 shows the interpolation amount p. ₁ Shows the amount of frequency error included in. Since the frequency error amount shown in FIG. 3 includes a sine wave component, it is necessary to apply a correction relation including a sine wave for further improvement. However, sine wave calculation is not easy to realize because the number of circuits increases. For this reason, in order to obtain the effect of maximizing the error with the minimum number of circuits, the correction amount δp is calculated using the above-described equation 5, that is, the relationship in which the frequency error is represented by a frequency polynomial.
[0066]
FIG. 3 shows an example in which the FFT frequency resolution fres = 1 Hz. The maximum value of the frequency error in this case was 0.0001 Hz. The frequency error is proportional to the FFT frequency resolution. Therefore, this means that the frequency can be measured with an error of 1/10000 of the FFT frequency resolution using an FFT calculator having any frequency resolution.
[0067]
The first embodiment of the present invention has been described above.
[0068]
Next, a second embodiment of the present invention will be described.
[0069]
FIG. 4 is a schematic configuration diagram of a spectrum analyzer to which the second embodiment of the present invention is applied.
[0070]
As shown in the figure, the spectrum analyzer of the present embodiment includes an A / D converter 1, an FFT operator 2 whose input is connected to the output side of the A / D converter 1, and an input of the FFT operator 2. An interpolator 3 connected to the output side, a corrector 4 whose two inputs are connected to the output side of the interpolator 3 and an output side of the FFT operation unit 2, respectively, and two inputs each of which is an A / D converter 1 and a corrector 4 and a time reference corrector 5 connected to the output side.
[0071]
In the above configuration, first, the A / D converter 1 converts the input signal 100 into a discrete-time signal 101 by A / D conversion. Next, the FFT calculator 2 converts the discrete-time signal 101 into a frequency spectrum 102, and outputs it to the interpolator 3 and the corrector 4. Further, the interpolator 3 interpolates the input frequency spectrum 102 according to the first interpolation method described above, obtains a spectrum interpolation result 103, and outputs the result to the corrector 4. Then, the corrector 4 corrects the spectrum of the input spectrum interpolation result 103 and the frequency spectrum 102 output from the FFT calculator 2, and outputs a spectrum correction result 107.
[0072]
In the present embodiment, a time reference corrector 5 is further added to the configuration shown in FIG. The time reference corrector 5 includes a storage device 54 that stores the output of the corrector 4, a regenerator 51 whose input is the output of the corrector 4, a storage device 53 that stores the output of the A / D converter 1, A residual calculator 52 having two inputs connected to the outputs of the regenerator 51 and the storage unit 53; a correction amount calculator 55 having two inputs connected to the outputs of the residual calculator 52 and the storage unit 54; And an adder 56 whose input is connected to the output of the memory 54 and the correction amount calculator 55.
[0073]
The reproducer 51 uses the frequency, amplitude, and phase data in the spectrum correction result 107 to generate a time-domain reproduced signal 108 by the above (Equation 1). The reproduced signal 108 is input to the residual calculator 52.
[0074]
The residual calculator 52 obtains a residual 109 between the input reproduced signal 108 from the reproducer 51 and the discrete time signal 110 from the storage 53 and sends the residual 109 to the correction amount calculator 55.
The storage unit 53 stores the discrete time signal 101 output from the A / D converter 1 and outputs it to the residual calculator 52 as a discrete time signal 110 at a required timing.
[0075]
The storage unit 54 stores the output 107 of the spectrum corrector 4 and outputs it to the correction amount calculator 55 and the adder 56 at necessary timing.
[0076]
The correction amount calculator 55 uses the residual 109 and the correction result 111 read from the storage unit 54 to make the amplitude A such that the residual 109 is minimized, the decimal part p of the frequency sample number, and The correction amount (△ A, △ p, and △ φ) of the phase φ is obtained. The calculation result 112, that is, the correction amounts ΔA, Δp and Δφ are sent to the adder 56. The correction amounts Δp, ΔA, and Δφ are obtained as solutions of (Equation 11) using the least squares method.
[0077]
[Equation 11]

[0078]
The adder 56 performs addition shown in (Equation 12) using the correction amount and the spectrum correction result 111 stored in the storage unit 54, and outputs a correction result 113. Where the approximate value A ₂ , P ₂ , Φ ₂ Is the spectral correction, ie p ₂ = P ₁ + Δp, and the p ₂ Is substituted into (Equation 9) and (Equation 10). The frequency is further substituted into (Equation 8), and the frequency, amplitude and phase are determined.
[0079]
(Equation 12)

[0080]
The function of the time reference corrector 5 is to convert the interpolation result 103 in the frequency domain into the time domain, and change the frequency, amplitude, and phase of the converted signal to match the discrete time signal 101 as a reference as much as possible. Is what you want.
[0081]
Next, the result of time correction by the spectrum analyzer of the present embodiment will be described. FIG. 5 shows the result of the time reference correction on the time axis. A black circle 200 is a plot of the discrete time signal 101 on a graph. A dotted line 201 is a discrete-time signal (hereinafter, referred to as a “reproduced signal 201”) reproduced by substituting the frequency f, the amplitude A, and the phase φ obtained by the spectrum interpolation method into (Equation 1). Signal 202 is the final result after time base correction. The difference between the discrete time signal 200 and the time reference correction amount 202 is smaller than the difference between the discrete time signal 200 and the reproduced signal 201, indicating the validity of this correction.
[0082]
FIG. 6 shows an example of a time-base correction result when random noise is added to the signal shown in (Equation 1) and the signal is input to the present embodiment. The frequency error in FIG. 6 is a representative value obtained by performing 1000 frequency error measurements for each S / N. A characteristic 203 (dotted line) is a case where only spectrum interpolation is performed, and is the same as FIG. A characteristic 204 is obtained when the time reference is corrected. The error improvement amount is 0.007 Hz when the S / N is 80 dB, and 0.014 Hz when the S / N is 20 dB. It is clear that the frequency error is improved over the entire S / N range.
[0083]
In this embodiment, as shown in FIG. 7A, a configuration without the corrector 4 is also conceivable. Of the two inputs of the time reference corrector 5, the output 107 of the corrector 4 is not limited to the output 107 as long as it is close to the output 107. Originally, the output 103 of the interpolator 3 and the output 107 of the corrector 4 are very close values, so that the output 103 of the interpolator 3 can be an input signal for the corrector 5.
[0084]
In this embodiment, as shown in FIG. 7B, there is a case where both the interpolator 3 and the corrector 4 may be omitted. For the same reason as in FIG. 7A described above, the output 102 of the FFT calculator 2 is within a certain error range with respect to the output 107 of the corrector 4, so the output 102 of the FFT calculator 2 is 5 can be an input signal. In this case, by adding the peak detector 6 for detecting the peak of the output 102 of the FFT calculator 2, the signal can be an input signal of the time reference corrector 5. The operation of the peak detector 6 will be described with reference to FIG. The input to the peak detector 6 is the discrete signal spectrum 102 from the FFT calculator 2. Since the peak position in FIG. 12 has the signal frequency f = 8 Hz and the peak spectrum intensity | D (k) | = 15.65, the frequency, amplitude, and phase of the signal are calculated using (Expression 13) based on these. Calculate the approximate value of. The result is output as a peak detector output 114 and input to the time reference corrector 5.
[0085]
(Equation 13)

[0086]
FIG. 8 shows the relationship between the frequency error of the analysis result of the spectrum analyzer having the configuration shown in FIGS. 4, 7A and 7B and FIG. 10 and the S / N of the discrete time signal 101. It is. 8, a characteristic 203 represents the relationship between the frequency error and the S / N when the time reference correction is not performed only by the interpolation in FIG. 10 described in the related art. The characteristic 206 is a frequency error when the peak detector 6 shown in FIG. 7B is provided, and shows that the error improvement effect by the time-base correction is large as compared with the characteristic 203 of only interpolation. A characteristic 204 is a frequency error when the interpolator 3, the corrector 4, and the time reference corrector 5 shown in FIG. 4 are provided. A characteristic 205 (dotted line) is a frequency error when the interpolator 3 and the time reference corrector 5 shown in FIG. Also, there is almost no difference between the characteristics 204 and 205 because the output 103 of the interpolator 3 and the output 107 of the corrector 4 are very close. On the other hand, the difference between the characteristic 206 and the characteristics 204 and 205 is large because only the peak analysis of the output of the FFT calculator 2 has a large difference from the true value.
[0087]
As described above, the time-based correction effect of the frequency is substantially the same regardless of whether the output of the corrector 4 or the output of the interpolator 3 is used as an input to the time-based corrector 5. Further, when the output of the FFT calculator 2 is used as an input to the time reference corrector 5, although the error slightly increases, it is advantageous in that the interpolator 3 and the corrector 4 are not required. These correction methods can be selected according to the magnitude of a desired correction error.
[0088]
Next, as a specific application example of the embodiment having the time reference corrector 5, an underwater equipped with any of the above-described embodiments (FIGS. 1, 4, 7A, and 7B). FIG. 9 shows a sonar device for analyzing an acoustic signal.
[0089]
The configuration of the sonar device 7 includes a sonar controller 71, a sonar transmitter 72 whose input is connected to an output side of the sonar controller 71, a sonar receiver 73, and an input which is the sonar controller 71 and the sonar transmitter. It has a sonar signal analyzer 74 connected to the output of 72.
[0090]
The sonar controller 71 outputs a sonar control signal 700 to the sonar transmitter 72 and the sonar signal analyzer 74.
[0091]
The sonar transmitter 72 outputs a sonar transmission signal 701 underwater based on the input sonar control signal 700, and outputs a theoretical value 702 of the sonar transmission signal to the sonar signal analyzer 74.
[0092]
The sonar receiver 73 receives the sonar signal 703 from underwater and outputs a part of the received sonar signal 703 to the sonar signal analyzer 74 as a sonar reception signal 704.
[0093]
The sonar signal analyzer 74 includes a spectrum analyzer 741 and a signal processor 742.
[0094]
The spectrum analyzer 741 has one of the configurations (FIGS. 1, 4, 7A, and 7B) of the second embodiment, and performs processing based on the configuration. The input to the spectrum analyzer 741 is the sonar reception signal 704, and outputs the sonar spectrum analysis result 705 to the signal processor 742.
[0095]
The signal processor 742 receives the sonar control signal 700, the theoretical value 702 of the sonar transmission signal, and the sonar spectrum analysis result 705 as inputs. By comparing these signals, processing according to the purpose is performed, and the result is output to the outside of the sonar device 7 as a sonar signal processing result 706.
[0096]
This sonar device is an active sonar device when transmitting the sonar transmission signal 701 to an underwater object and using the sonar signal 703 as a reflected wave thereof. On the other hand, when a signal radiated from an object underwater, underwater or on the water is used as the sonar signal 703, a passive sonar device is formed using the sonar receiver 73 and the signal analyzer 74.
[0097]
In any case, the frequency error of the analysis result has low dependency on the input signal frequency, and the frequency error is reduced even in the analysis of the signal under low S / N.
[0098]
Note that the present invention is not limited to the above embodiment. Many modifications are possible within the scope of the gist. For example, in the first and second embodiments described above, even when the second interpolation example is used for the interpolator 3, the same effect can be expected as when the first interpolation example is used.
[0099]
【The invention's effect】
As described above, according to the present invention, it is possible to improve the dependency of the interpolation error on the input signal frequency, and to reduce the frequency-based spectral interpolation error in a signal with low S / N.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating a first embodiment of the present invention.
FIG. 2 is a diagram illustrating an example of a spectrum correction result according to the first embodiment of the present invention.
FIG. 3 is a diagram illustrating frequency dependence of a frequency error in spectrum correction according to the first embodiment of the present invention.
FIG. 4 is a block diagram illustrating a second embodiment of the present invention.
FIG. 5 is a diagram illustrating the principle of a time reference corrector.
FIG. 6 is a diagram illustrating the dependence of the improved frequency error on S / N in the time reference correction according to the second embodiment of the present invention.
FIG. 7 is a block diagram illustrating an embodiment when there is no spectrum correction.
FIG. 8 is a diagram illustrating the S / N dependency of a frequency error in a combination of spectrum interpolation, spectrum correction, and time reference correction.
FIG. 9 is a block diagram of a sonar device equipped with a spectrum analyzer.
FIG. 10 is a block diagram illustrating a spectrum analyzer according to the related art.
11A is a diagram illustrating an example of discrete-time signal specifications, and FIG. 11B is a diagram illustrating an example of a result of spectrum interpolation according to the related art.
FIG. 12 is a diagram illustrating an output of the FFT calculator.
FIG. 13 is a diagram illustrating the frequency dependence of spectrum interpolation according to the related art.
FIG. 14 is a diagram illustrating the S / N dependency of spectrum interpolation according to the related art.
[Explanation of symbols]
REFERENCE SIGNS LIST 1 A / D converter, 2 FFT calculator, 3 interpolator, 4 corrector, 5 time reference corrector, 6 peak detector, 7 sonar device, 41 frequency corrector, 42 Amplitude corrector, 43: phase corrector, 44, 45 ... storage, 51 ... regenerator, 52: residual calculator, 53, 54 ... storage, 55 ... correction amount calculator, 56: adder, 71 ... Sonar controller, 72: sonar transmitter, 73: sonar receiver, 74: sonar signal analyzer, 741: spectrum analyzer, 742: signal processor.

Claims (7)

An A / D converter for converting an input continuous-time signal into a discrete-time signal;
A fast Fourier transform (FFT) unit for converting the discrete-time signal output from the A / D converter into a discrete spectrum;
Using the intensity ratio of the peak point of the discrete spectrum output from the FFT unit and its neighboring points, or by applying the intensity of the peak point and its neighboring points to an approximate expression, the discrete spectrum of the peak point is calculated. An interpolator for obtaining a frequency interpolation amount,
A corrector that corrects the discrete spectrum of the peak point output from the FFT unit based on the interpolation amount obtained by the interpolator,
The corrector is
A spectrum analyzer, wherein the discrete spectrum of the peak point output from the FFT unit is corrected using the interpolation amount and a correction amount determined according to a frequency indicated by the interpolation amount. The spectrum analyzer according to claim 1,
The spectrum analyzer according to claim 1, wherein a correction amount of the corrector is substantially proportional to a frequency indicated by the interpolation amount. An A / D converter for converting an input continuous-time signal into a discrete-time signal;
A fast Fourier transform (FFT) unit for converting the discrete-time signal output from the A / D converter into a discrete spectrum;
The discrete spectrum of the peak point is obtained by using the intensity ratio of the peak point of the discrete spectrum output from the FFT unit and its neighboring points, or by applying the intensity of the peak point and its neighboring points to an approximate expression. An interpolator for interpolating,
A time reference corrector for correcting the interpolation result in the interpolator,
The time base corrector includes:
The interpolation is performed so that the difference between the reproduction signal reproduced from the signal specifications (frequency, amplitude, and phase) interpolated by the interpolator and the discrete time signal output from the A / D converter is reduced. A spectrum analyzer that corrects the signal data interpolated by the analyzer. An A / D converter for converting an input continuous-time signal into a discrete-time signal;
A fast Fourier transform (FFT) unit for converting the discrete-time signal output from the A / D converter into a discrete spectrum;
A peak detector that outputs a frequency, an amplitude and a phase at a peak point of the discrete spectrum output from the FFT unit;
A time reference corrector that corrects the output result of the peak detector,
The time base corrector includes:
Correcting the output result of the peak detector so that the difference between the reproduction signal reproduced from the output result of the peak detector and the discrete time signal output from the A / D converter is reduced. Characteristic spectrum analyzer. An A / D conversion step of converting the input continuous time signal into a discrete time signal;
A fast Fourier transform (FFT) step of converting the discrete time signal obtained by the A / D conversion step into a discrete spectrum;
By using the intensity ratio of the peak point of the discrete spectrum obtained from the FFT step and its adjacent points, or by applying the intensity of the peak point and its adjacent points to an approximate expression, the frequency of the peak point with respect to the discrete spectrum is obtained. An interpolation step for obtaining an interpolation amount of
Correcting the discrete spectrum of the peak point obtained by the FFT step based on the interpolation amount obtained in the interpolation step,
The correcting step includes:
A spectrum analysis method, wherein a discrete spectrum of the peak point obtained in the FFT step is corrected using the interpolation amount and a correction amount determined according to a frequency indicated by the interpolation amount. An A / D conversion step of converting the input continuous time signal into a discrete time signal;
A fast Fourier transform (FFT) step of converting the discrete time signal obtained by the A / D conversion step into a discrete spectrum;
The discrete spectrum of the peak point is interpolated by using the intensity ratio of the peak point of the discrete spectrum obtained from the FFT step and its neighboring points, or by applying the intensity of the peak point and the neighboring points to an approximate expression. Interpolation step
A time reference correction step of correcting the interpolation result in the interpolation step,
The time reference correction step includes:
The interpolation is performed so that the difference between the reproduction signal reproduced from the signal specifications (frequency, amplitude and phase) interpolated in the interpolation step and the discrete time signal obtained in the A / D conversion step becomes small. A spectrum analysis method, wherein the signal data interpolated by the step is corrected. An A / D conversion step of converting the input continuous time signal into a discrete time signal;
A fast Fourier transform (FFT) step of converting the discrete time signal obtained by the A / D conversion step into a discrete spectrum;
A peak detecting step of outputting a frequency, an amplitude and a phase at a peak point of the discrete spectrum obtained by the FFT step;
A time reference correction step of correcting the output result of the peak detection step,
The time reference correction step includes:
Correcting the output result of the peak detection step so that the difference between the reproduction signal reproduced from the output result of the peak detection step and the discrete time signal obtained by the A / D conversion step is reduced. Characteristic spectrum analysis method.

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