200304075 A7 B7 五、發明説明（1 ) [發明所屬之技術領域] (請先閲讀背面之注意事項再填寫本頁) 本發明係關於數位濾波器之設計方法及設計裝置、數 位瀘波器設計用程式、以及數位濾波器，尤其是，具有由 複數延遲器構成之附有分接頭之延遲線，在使各分接頭之 信號分別成爲數倍後，實施加算並輸出之FIR濾波器的設 計方法相關。 [先前技術] . 應用於通信、計測、聲頻 影像信號處理、醫療、地 震學等之各種分野的各種電子機器中，通常在其內部會實 施某些數位信號處理。數位信號處理之最重要的基本操作 ，係從混合各種信號或雜訊之輸入信號當中只取出必要頻 帶之信號的濾波處理。因此，執行數位信號處理之電子機 器中，大多會使用數位濾波器。 經濟部智慧財產局員工消費合作社印製200304075 A7 B7 V. Description of the invention (1) [Technical field to which the invention belongs] (Please read the precautions on the back before filling out this page) The present invention relates to the design method and design device of digital filter, and the design of digital wave waver Programs, and digital filters, in particular, there are delay lines with taps composed of complex delayers, and the FIR filters are added and output after the signals of each tap are multiplied several times. . [Prior art]. Used in various electronic devices in various fields, such as communication, measurement, audio and video signal processing, medical treatment, and seismology, some digital signal processing is usually implemented inside. The most important basic operation of digital signal processing is the filtering process of extracting only the signals in the necessary frequency band from the input signal of mixing various signals or noise. Therefore, most electronic machines that perform digital signal processing use digital filters. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs
數位濾波器大多會採用IIR(Infinite Impulse Response: 無限脈衝響應）濾波器、及FIR(Finite Impulse Response:有限 脈衝響應）瀘波器。其中，FIR濾波器具有下述優點。第1， FIR濾波器之傳送函數之極只位於z平面之原點，電路會隨 時處於安定狀態。第2，可實現完全正確之直線相位特性。 若以通過域及阻止域之配置來實施濾波器之分類，則可分 爲低通濾波器、旁通濾波器、帶域通過濾波器、及帶域消 除濾波器之4種。IIR濾波器時，基本上爲低通濾波器，其 他之旁通濾波器、帶域通過濾波器、及帶域消除濾波器係 從低通濾波器發展至可執行頻率變換等之處理而實現。FIR -5- 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 200304075 Μ Β7_ 五、發明説明（2 ) 濾波器中，旁通濾波器等亦因低通濾波器而可實現。 例如，設計旁通濾波器時’首先’會設計基本之低通 濾波器，然後實施頻率變換。又’必要時’可利用重複實 施低通濾波器之設計及頻率變換’設計具有期望頻率特性 之旁通濾波器。此處之頻率變換處理’係以抽樣頻率及截 止頻率之比率爲基礎，執行使用窗函數或Chebyshev近似法 等之摺積演算等，求取濾波器之傳送函數’再將其置換成 頻率成分之處理。 然而，前述傳統濾波器設計法，需要頻率變換等之高 級專業知識，而有設計濾波器並不容易之問題。又，即使 勉強可以設計旁通濾波器、帶域通過濾波器、及帶域消除 濾波器等典型濾波器，卻很難實現具有類比式複雜波形之 頻率特性的濾波器設計。又，使用窗函數或Chebyshev近似 法等之頻率變換的計算非常複雜。因此，若以軟體實現， 將會形成很大之處理負荷，而以軟體實現則有電路規模變 大之問題。 爲了解決此問題，本發明的目的就是提供可簡易設計 具有任意頻率特性之FIR數位濾波器的方法。 又，本發明之另一目的，就是提供更易設計以較小電 路規模實現高精度之期望頻率特性的FIR數位濾波器之方 .法。 [發明內容] 爲了解決前述課題，本發明中，輸入代表期望頻率特 --------1 — 衣-- (請先閲讀背面之注意事項再填寫本頁) 訂 經濟部智慧財產局員工消費合作社印製 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -6 - 200304075 A7 B7 五、發明説明（3 ) ---------衣-- (請先閲讀背面之注意事項再填寫本頁) 性之數列或函數，再對該輸入之數列或函數實施逆傅立葉 轉換，析出其結果之實數項，對由該析出之實數項所構成 之數列，實施前半部及後半部之排序處理、以及將前述實 數項所構成之數列乘以2n(n爲自然數）並捨去小數點以下之 位數後再將其結果乘以1/2η之處理，將利用此方式所得之 數列當做濾波器係數群。 本發明之其他形態則係代表期望頻率特性之數列或函 數，輸入具有比數位濾波器之分接頭數多之資料點的數列 或函數，對該輸入之數列或函數實施逆傅立葉轉換，析出 其結果之實數項，對由該析出之實數項所構成之數列，實 施前半部及後半部之排序處理、以及對前述實數項所構成 之數列實施乘以特定窗函數之處理，將利用此方式所得之 數列當做濾波器係數群。 [實施方式] 以下爲本發明之良好實施形態。 以下，參照圖面說明本發明之一實施形態。 經濟部智慧財產局員工消費合作社印製 第1圖係本實施形態數位瀘波器之設計方法的處理順 序流程圖。此處設計之數位濾波器，係具有由複數延遲器 所構成之附有分接頭之延遲線，依據提供之濾波器係數群 使各分接頭之信號分別成爲數倍後，實施加算並執行輸出 之類型的FIR濾波器。 FIR濾波器會將以有限時間長度表示之脈衝響應直接當 做濾波器之係數。因此，FIR濾波器之設計係決定可得到期 本紙張尺度適用中國國家標準（CNS )八4規格（210X297公釐） 經濟部智慧財產局員工消費合作社印製 200304075 A7 _______B7 五、發明説明（4 ) 望頻率特性的濾波器係數群。因此，第1圖之流程圖就是 決定此種FIR濾波器之濾波器係數群的方法。 如第1圖所示，首先，輸入代表期望頻率特性之波形 的數列（步驟S 1)。此時，輸入之數列資料數愈多愈好。本 來’爲了要構成理想之濾波器，需要有無限個濾波器係數 ’故需要無限個濾波器之分接頭。因此，爲了降低和期望 頻率特性之誤差，應使頻率誤差爲必要範圍內之方式輸入 對應濾波器係數之數的資料數。至少輸入資料數多於欲求 取之濾波器係數之數（數位濾波器之分接頭數）的數列。 此資料輸入可直接輸入各個數値，亦可在以表示頻率 一增益特性之2次元輸入座標上描繪期望頻率特性之波形 ’然後將描繪之波形置換成和其對應之數値並輸入。使用 後者之輸入方法時，因可以一邊以影像確認期望頻率特性 一邊輸入資料，故很容易以直接感覺來輸入代表期望頻率 特性之資料。 有數種手段可實現後者之輸入方法。例如，將代表頻 率一增益特性之2次元平面顯示於電腦之顯示畫面，在此2 次兀平面上利用GUI(Graphical User Interface)等描繪期望頻 率特性之波形，然後將其數値資料化。又，以數化器或繪 圖器等指向裝置取代電腦畫面上之GUI亦可。此處列舉之 方法只是單純實例而已，亦可利用其他方法輸入數列。又 ，此處係以數列方式輸入期望頻率特性，然而，亦可以代 表該頻率特性之波形的函數來執行輸入。 其次，將以此方式輸入之頻率特性視爲傳送函數並實 I ： 訂 (請先閱讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -8- 200304075 經濟部智慧財產局員工消費合作社印製 A7 B7 五、發明説明（5 ) 施逆傅立葉轉換（反FFT)，析出其結果之實數項（步驟S2) 。如大家所知，對某數列實施傅立葉轉換（FFT)之處理， 可得到對應該數列之頻率一增益特性的波形。因此，輸入 代表期望頻率一增益特性之波形的數列或函數，對其實施 反FFT，並析出其實數項，則可得到以實現該頻率一增益特 性爲目的之必要基本數列。此數列相當於欲求取之濾波器 係數群。 但，以反FFT求取之數列本身，並未實施可直接當做 濾波器係數群使用之排序。亦即，任何類型之數位濾波器 ，其濾波器係數之數列具有對稱性，中央値爲最大，隨著 和中央之距離的加大，其値會以重複擺動方式逐漸變小。 相對於此，以反FFT求取之數列的中央値會最小，而兩端 之値爲最大。因此，以將利用反FFT求取之數列的中央値 移至兩的方式貫施即半部及後半部之排序》使其成爲中 央値爲最大値之前後對稱（步驟S3)。 利用此方式得到之數列可直接視爲濾波器係數群，然 而，本實施形態中會進一步對其實施幕演算（步驟S4)。如 上面所述，在步驟S1之資料輸入階段，應儘量增加輸入資 料之數，直到和期望頻率特性之誤差爲必要範圍內。此輸 入資料數係對應濾波器係數之數。因此，從此輸入資料利 用反FFT等處理求取之數列若直接當做濾波器係數群使用 ，則數位濾波器之分接頭數會極多，電路規模會變得很大 。因此，利用幕演算，將分接頭數減至必要數。 此時，使用之窗函數存在矩形窗、漢明窗、漢尼窗、 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -9 - —-ϋ —ϋ ϋϋ mi-''ν —ϋϋ ϋϋ ·ϋ· ι_ιϋ (請先閱讀背面之注意事項再填寫本頁) 200304075 Α7 Β7 五、發明説明（6 ) (請先閲讀背面之注意事項再填寫本頁) 八一卜lx y卜窗等之各種函數。可使用任何窗函數，但以 漢尼窗較佳。因爲漢尼窗之窗的兩端値爲〇，且數値會從中 央値朝兩端方向以緩和之方式遞減的函數。例如，使用矩 形窗時，會強制將分接頭數切除成有限個，而此會使濾波 器之特性上產生振鈴（漣波現象）。相對於此，因不會以有限 値切除濾波器係數，而以緩斜率變化成〇，故可抑制振鈴之 產生。 亦可直接將以此方式得到之數列直接當做濾波器係數 群使用。然而，利用反FFT及幕演算求取之濾波器係數群 ，小數點以下之位數極多，且爲複雜之隨機値的集合。因 此，若直接將此數列當做濾波器係數群使用，則數位瀘波 器需要相當多的乘法器，而不切實際。 經濟部智慧財產局員工消費合作社印製 因此，必須實施捨去數列之小數點以下之位數等，實 施瀘波器係數之捨去。然而，若只是單純捨去之捨去處理 ，其結果只是數列之位數減少而已，依然爲複雜之隨機値 ，而仍然需要眾多乘法器。又，單純捨去會降低濾波器係 數群之精度，而擴大和期望頻率特性之誤差。因此，本實 施形態實施如下所述之捨去演算處理（步驟S5)。亦即，將 前述步驟S4之幕處理後的數列乘以2η (η爲自然數）並實施 小數點以下之位數的捨去（整數化），再將其結果乘以1/2" 〇 利用此捨去演算，全部濾波器係數都爲1 /2η之整數倍 的値。因此，可對來自數位瀘波器之各分接頭的信號分別 乘以整數倍之部分，在實施全部乘法輸出之加算後，可使 10- 本紙張尺度適用中國國家標準（CNS ) Α4規格（210Χ297公釐） 200304075 A7 B7 五、發明説明（7 ) ---------衣-- (請先閲讀背面之注意事項再填寫本頁) 數位濾波器之構成上爲一致之1 /2n倍。而且整數倍之部分 可以如+…（i、j爲任意之整數）之2進位數的加法來表 現。利用此方式，可大幅銷減數位濾波器整體之乘法器的 使用數，而節化構成。又，因將以反FFT得到之數列乘以 2n倍後再進行捨去，和單純載割數列之小數點以下之位數 時相比，可降低捨去誤差。利用此方式，再在無損濾波器 特性之精度的情形下實現濾波器係數群之簡化。 本實施形態中，以經過此捨去演算求取之數列當做最 終之濾波器係數群。又，前述之步驟S 3〜S 5的處理並不一 定要依照此順序，只要在實施幕演算後再執行捨去演算即 可。例如，亦可在排序前實施幕演算。此時，實施漢尼窗 之乘算，使窗之兩端的係數値成爲"1”，而窗之中央部的係 數値成爲"0"。因爲在一連串步驟中之較早階段實施幕演算 ’故可減少以後之演算所使用之資料數，而可減輕執行演 算之處理負荷。 經濟部智慧財產局員工消費合作社印製 以下’以具體實例詳細說明以上説明之本實施形態的 瀘波器設計方法。如第2圖所示，步驟S1中會描繪以"1"基 準化之濾波器的頻率一增益特性，並將其數値資料化。輸 入資料會以抽樣頻率之中央爲軸而對稱。此時，輸入資料 長度（圖表之長度亦即數列之數）m爲頻率誤差位於必要範 圍內之値’且，爲了簡化步驟S2之反FFT處理而使其成爲 2k之形式。 例如，設計以抽樣頻率爲44.ΙΚΗζ之聲頻信號爲對象之 FIR濾波器時，輸入資料長度m及最大頻率誤差之關係如 -11 - 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 200304075 經濟部智慧財產局員工消費合作社印製 A7 B7 _五、發明説明（8 ) 第3圖所示。此處之最大頻率誤差係相當於圖表之1標尺 的頻率，利用44.1KHz/m之演算求取。聲頻處理時，10Hz 程度爲容許誤差範圍內，故輸入資料長度m使用4096。 第2圖所示之圖表實例，係相當於抽樣頻率爲44.1 KHz 、輸入資料長度m爲409 6、截止頻率爲8KHz、截止頻率之 增益下降量爲-60dB之低通濾波器的頻率特性。此時，圖表 之橫軸會等分成4096個標尺（時鐘）。若時鐘數爲CK，則該 時鐘數CK之頻率f爲 f = CK X (44·1/4096)(ΚΗζ” 因此，相當於8ΚΗζ之時鐘數CK1爲 CK1 = f X (4096/44.1K)与 743.04。 步驟S2時，將以第2圖所示方式輸入之低通瀘波器的 頻率特性視爲傳送函數，實施反FFT處理，並析出其結果 之實數項。又，在其次之步驟S3中，爲了將以反FFT求取 之數列變換成可當做瀘波器係數群使用之順序，如第4圖 所示，將數列分成前半部及後半部並實施排序。亦即，實 施將第0時鐘之數値更換成第2048時鐘之數値（以下，以 0 — 2048 表示）、1 + 2049、2->2050 ..... 2047 + 4095、 2048 + 0、2049 + 1 ..... 4095今2047 之排序。 又，步驟S4中，會以減少分接頭數爲目的而實施幕演 算。如上面所述，窗函數有矩形窗、漢明窗、漢尼窗、 hartlet窗等，此處使用兩端會平滑收斂於0之漢尼窗。第5 圖係受到窗函數之寬度限制的分接頭數及阻隔特性之關係 圖。由此可知，分接頭數愈多則截止頻率之特性的變化就 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -12 - (請先閱讀背面之注意事項再填寫本頁) 200304075 Α7 Β7 經濟部智慧財產局員工消費合作社印製 五、發明説明（9 ) 愈大。 此處之實例，係以數位濾波器之分接頭數爲1 27個之 方式來設定窗函數之寬度。第6圖係此時之漢尼窗的函數 値圖。以利用排序求取之數列（4096個資料列）之中央部分 乘以此第6圖所示之漢尼窗（1 27個資料列）。此時，漢尼窗 之範圍外的係數全部以0計算。其次，在最後之步驟S5中 ，將幕演算後之數列乘以2n並捨去小數點以下之位數，再 將其結果乘以l/2n (例如，2n =2048)。 第7圖係利用以上之計算求取之濾波器係數群（1 27個 濾波器係數）。第8圖係對以前述第7圖之方式求取之濾波 器係數群的數列實施FFT之結果的頻率一增益特性及頻率 一相位特性圖，頻率一增益特性係以對數標尺來表示增益 。第9圖係針對同一頻率一增益特性以直線標尺來表示增 益之圖，第10圖係z平面圖。從第8圖〜第1 〇圖可知，利 用本實施形態濾波器設計方法求取之濾波器係數群，大致 可正確實現截止頻率爲8KHz之低通濾波器特性。而且，截 止頻率之衰減量爲40 dB以上，而且，相位特性爲直線，實 現安定之特性。 第11圖係使用以本實施形態瀘波器設計方法求取之濾 波器係數群構成之低通濾波器的構成實例圖。此濾波器係 利用級聯連接之127個D型正反器1·!〜1·127以1時鐘CK 依序延遲輸入信號。其次，對從各D型正反器h〜iq27之 輸出分接頭取出之信號，將濾波器係數乘以2048之結果的 整數値以127個係數器2·!〜2·127分別實施乘算，並以127 (請先閲讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) Α4規格（210Χ297公釐） -13- 200304075 A7 B7 五、發明説明（1〇 ) 個加法器h〜1.⑴實施乘算結果之加算並輸出。 其次，設於最終段之加法器3.^27之輸出段的乘法器4， 會將加算輸出乘以1/2048使其回復原有擺動，並將其結果 暫存於D型正反器5後，執行輸出。又，此例中，係數器 及加法器各設有127個，然而，瀘波器係數値爲0之部分 ，可省略係數器及加法器。因此，實際上，可以少於第11 圖之數的乘法器及加法器來構成數位濾波器。如上所示， 本實施形態中，因求取濾波器係數時執行特殊之捨去演算 ’，而可簡化設計之數位濾波器的構成。 以上係以設計低通濾波器時爲例進行説明，然而，其 他數位濾波器亦可實施相同設計。帶通濾波器之設定實例 説明如下。此處，帶通濾波器的期望頻率特性係以第12圖 所示之頻率特性數列之方式輸入。第1 2圖所示期望頻率特 性係只有5〜8KHz之頻帶的信號可通過。又’此處之抽樣 頻率爲44.1 KHz、輸入資料長度爲4096。 對第1 2圖所示之輸入資料，和前述之低通濾波器相同 ，實施反FFT◊排序4幕演算（窗爲漢尼窗’寬度爲127) 4 捨去演算，可求取第Π圖所示之濾波器係數群。 ^ 第14圖係對如第13圖求取之濾波器係數群的數列實 施FFT之結果的頻率一增益特性及頻率一相位特性圖’頻 率一增益特性係以對數標尺表示增益。第1 5圖係針對相同 頻率一增益特性以直線標尺表示增益，第1 6圖係z平面圖 。由第14圖〜第1 6圖可知，利用本實施形態之濾波器設 計方法求取之濾波器係數群’大致可實現通過頻帶爲5〜 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -14 - ^^衣-- (請先閲讀背面之注意事項再填寫本頁) 訂 經濟部智慧財產局員工消費合作社印製 經濟部智慧財產局員工消費合作社印製 200304075 A7 B7 五、發明説明（11 ) 8KHz之帶通濾波器特性。而且，截止頻率之衰減量爲40dB 以上，相位特性爲直線而實現安定之特性。 第17圖係使用於助聽器或各種聲頻裝置等之音質調整 用低通瀘波器的期望頻率特性之輸入資料圖。此音質調整 用低通濾波器之頻率特性爲類比式連續變化。亦對第17圖 所示輸入資料實施相同之反FFT4排序+幕演算+捨去演算 ，並對以此方式得到之瀘波器係數群實施FFT，可得到第 1 8圖之頻率特性。由此可知，利用本實施形態濾波器設計 方法求取之濾波器係數群，可實現大致正確之音質調整用 低通濾波器的期望頻率特性。又，圖上雖然並未標示，然 而，相位特性亦呈直線，實現安定之特性。 第19圖係使用於助聽器或各種聲頻裝置等之音質調整 用旁通濾波器的期望頻率特性之輸入資料圖。此音質調整 用旁通濾波器之頻率特性爲類比式連續變化。亦對第19圖 所示輸入資料實施相同之反FFT +排序4幕演算+捨去演算 ，並對以此方式得到之濾波器係數群實施FFT，可得到第 20圖之頻率特性。由此可知，利用本實施形態瀘波器設計 方法求取之濾波器係數群，可實現大致正確之音質調整用 旁通濾波器之期望頻率特性。又，圖上雖然並未標示，然 而，相位特性亦呈直線，實現安定之特性。Most digital filters use IIR (Infinite Impulse Response :) and FIR (Finite Impulse Response :) impulse filters. Among them, the FIR filter has the following advantages. First, the pole of the transfer function of the FIR filter is only at the origin of the z-plane, and the circuit will be in a stable state at any time. Second, it is possible to achieve a completely correct linear phase characteristic. If the classification of the filters is implemented by the configuration of the pass domain and the block domain, they can be classified into four types: low-pass filters, bypass filters, band-pass filters, and band-elimination filters. The IIR filter is basically a low-pass filter. Other bypass filters, band-pass filters, and band-elimination filters are developed from low-pass filters to perform frequency conversion. FIR -5- This paper size applies Chinese National Standard (CNS) A4 specification (210X297 mm) 200304075 Μ B7_ V. Description of the invention (2) Bypass filters, etc. can also be realized by low-pass filters. For example, when designing a bypass filter, 'first', a basic low-pass filter is designed and then a frequency conversion is performed. If necessary, the design of the low-pass filter and the frequency conversion can be repeated to design a bypass filter having desired frequency characteristics. The frequency conversion process here is based on the ratio of the sampling frequency and the cut-off frequency, and performs a deconvolution calculation using a window function or Chebyshev approximation method to find the transfer function of the filter, and replaces it with the frequency component. deal with. However, the aforementioned conventional filter design method requires advanced expertise such as frequency conversion, and there is a problem that it is not easy to design a filter. In addition, even though typical filters such as a bypass filter, a band pass filter, and a band cancel filter can be designed, it is difficult to realize a filter design with a frequency characteristic of an analog complex waveform. The calculation of the frequency conversion using a window function or the Chebyshev approximation method is very complicated. Therefore, if it is implemented in software, a large processing load will be formed, and if it is implemented in software, there is a problem that the circuit scale becomes large. In order to solve this problem, an object of the present invention is to provide a method for easily designing an FIR digital filter having an arbitrary frequency characteristic. In addition, another object of the present invention is to provide a method for more easily designing a FIR digital filter that achieves a desired frequency characteristic with high accuracy in a small circuit scale. [Summary of the Invention] In order to solve the aforementioned problems, in the present invention, input represents the desired frequency characteristics -------- 1 — clothing-(Please read the notes on the back before filling this page) Order the Intellectual Property Bureau of the Ministry of Economic Affairs The paper size printed by the employee consumer cooperative is applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) -6-200304075 A7 B7 V. Description of the invention (3) --------- clothing-(please first (Read the notes on the back and fill in this page), and then perform the inverse Fourier transform on the input sequence or function to isolate the real number of the result, and implement the first half of the sequence composed of the separated real number. Sorting processing of the first half and the second half, and processing of multiplying the sequence of real numbers by 2n (n is a natural number) and rounding off the number of digits below the decimal point, and then multiplying the result by 1 / 2η will use The sequence obtained by this method is regarded as the filter coefficient group. Other forms of the present invention are sequences or functions that represent desired frequency characteristics. A sequence or function having more data points than the number of taps of a digital filter is input, and an inverse Fourier transform is performed on the input sequence or function, and the result is obtained. For real numbers, the first half and the second half are sorted for the sequence formed by the separated real number, and the sequence of the real number is multiplied by a specific window function. The result obtained by this method will be used. The sequence is treated as a filter coefficient group. [Embodiment] The following is a preferred embodiment of the present invention. Hereinafter, one embodiment of the present invention will be described with reference to the drawings. Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs. Figure 1 is a flowchart of the processing sequence of the design method of the digital wave waver in this embodiment. The digital filter designed here has a delay line with taps composed of a complex delayer. After the signal of each tap is several times according to the provided filter coefficient group, it is added and output is performed. Type of FIR filter. The FIR filter directly uses the impulse response expressed in a finite time length as the coefficient of the filter. Therefore, the design of the FIR filter was decided to obtain the paper size applicable to the Chinese National Standard (CNS) 8 4 specifications (210X297 mm) printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 200304075 A7 _______B7 V. Description of the invention (4) Filter coefficient group with desired frequency characteristics. Therefore, the flowchart in Fig. 1 is a method for determining the filter coefficient group of such an FIR filter. As shown in Fig. 1, first, a series of waveforms representing a desired frequency characteristic is input (step S1). At this time, the more data entered in the series, the better. Originally, 'in order to form an ideal filter, an infinite number of filter coefficients are needed', so taps of an infinite number of filters are required. Therefore, in order to reduce the error from the desired frequency characteristics, the number of data corresponding to the number of filter coefficients should be input in such a way that the frequency error is within the necessary range. Enter at least a series of more data than the number of filter coefficients (number of taps of the digital filter) to be obtained. This data input can be directly input each number, or you can draw the waveform of the desired frequency characteristic on the 2-dimensional input coordinates representing the frequency-gain characteristic, and then replace the drawn waveform with the corresponding number and input it. When using the latter input method, data can be input while confirming the desired frequency characteristics with an image, so it is easy to input the data representing the desired frequency characteristics with a direct feeling. There are several ways to implement the latter input method. For example, a two-dimensional plane representing a frequency-gain characteristic is displayed on a computer display screen, and a graphical user interface (GUI) or the like is used to draw a waveform of a desired frequency characteristic on the two-dimensional plane, and then the data is converted into data. It is also possible to replace the GUI on the computer screen with a pointing device such as a digitizer or a plotter. The methods listed here are just examples, and other methods can be used to enter the sequence. Here, the desired frequency characteristics are input in a series of numbers. However, the input may be performed as a function of the waveform of the frequency characteristics. Secondly, consider the frequency characteristics input in this way as a transfer function and implement I: Order (please read the precautions on the back before filling this page) This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm)- 8- 200304075 A7 B7 printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 5. Description of the invention (5) Inverse Fourier transform (inverse FFT) is performed, and the real number of the results is extracted (step S2). As everyone knows, by performing Fourier transform (FFT) processing on a certain sequence, a waveform corresponding to the frequency-gain characteristic of the sequence can be obtained. Therefore, by inputting a sequence or function of the waveform representing the desired frequency-gain characteristic, performing inverse FFT on it, and analyzing the actual terms, the necessary basic sequence can be obtained for the purpose of achieving the frequency-gain characteristic. This series is equivalent to the filter coefficient group to be obtained. However, the sequence itself obtained by the inverse FFT does not implement the sorting which can be directly used as the filter coefficient group. That is, any type of digital filter has a series of filter coefficients with symmetry, and the center 値 is the largest. As the distance from the center increases, its 値 will gradually decrease in a repeated swinging manner. In contrast, the center 値 of the sequence obtained by the inverse FFT will be the smallest, and the 値 at the two ends will be the largest. Therefore, the order of the half and the second half of the sequence obtained by using the inverse FFT is shifted to two, so that it becomes the center 値 as the largest 値 before and after symmetry (step S3). The sequence obtained in this way can be directly regarded as a filter coefficient group. However, in this embodiment, a curtain calculation is further performed on it (step S4). As described above, in the data input stage of step S1, the number of input data should be increased as much as possible until the error from the desired frequency characteristic is within the necessary range. The number of input data is the number of corresponding filter coefficients. Therefore, if the sequence obtained from the input data using inverse FFT processing is directly used as the filter coefficient group, the number of taps of the digital filter will be extremely large, and the circuit scale will become very large. Therefore, use curtain calculations to reduce the number of taps to the necessary number. At this time, the window functions used include rectangular windows, Hamming windows, Hani windows, and this paper size is applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) -9-—-ϋ —ϋ ϋϋ mi-'' ν —Ϋϋ ϋϋ · ϋ · ι_ιϋ (Please read the notes on the back before filling in this page) 200304075 Α7 Β7 V. Description of the invention (6) (Please read the notes on the back before filling in this page) Bayibu lx ybu window And other functions. Any window function can be used, but a Hanni window is preferred. Because the ends 汉 of the window of the Hanni window are zero, and the number 値 will be a function that decreases in a gradual manner from the center 値 toward the ends. For example, when using a rectangular window, the number of taps is forcibly cut to a limited number, and this will cause ringing (ripple phenomenon) in the characteristics of the filter. In contrast, since the filter coefficient is not cut off with a finite chirp, but changes to 0 with a gentle slope, the occurrence of ringing can be suppressed. The sequence obtained in this way can also be used directly as a filter coefficient group. However, the filter coefficient group obtained using inverse FFT and curtain calculations has many digits below the decimal point and is a complex set of random chirps. Therefore, if this sequence is used directly as a group of filter coefficients, a digital multiplier requires a considerable number of multipliers, which is impractical. Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs. Therefore, it is necessary to implement rounding down of the number of digits below the decimal point, etc., to implement the rounding wave coefficient. However, if it is simply discarded and processed, the result is only a reduction in the number of digits in the sequence, which is still a complex random 値, and still requires many multipliers. In addition, simply rounding down will reduce the accuracy of the filter coefficient group and increase the error with the desired frequency characteristics. Therefore, in this embodiment, a rounding calculation process is performed as described below (step S5). That is, multiply the sequence processed in the above step S4 by 2η (η is a natural number), round down (integer) the number of digits below the decimal point, and then multiply the result by 1/2 " In this rounding calculation, all filter coefficients are 値 which is an integer multiple of 1 / 2η. Therefore, the signals from the taps of the digital oscilloscope can be multiplied by integer multiples respectively. After the addition of all the multiplication outputs is implemented, the 10-paper size can be applied to the Chinese National Standard (CNS) A4 specification (210 × 297). (Mm) 200304075 A7 B7 V. Description of the invention (7) --------- Clothing-(Please read the precautions on the back before filling out this page) The structure of the digital filter is consistent 1 / 2n Times. In addition, the integral multiples can be expressed by the addition of binary digits such as + ... (i and j are arbitrary integers). With this method, the number of multipliers used in the entire digital filter can be significantly reduced, and the structure can be reduced. In addition, because the sequence obtained by the inverse FFT is multiplied by 2n times and then rounded down, the rounding error can be reduced compared with the case where the number of digits below the decimal point is simply carried out. In this way, simplification of the filter coefficient group is achieved with the accuracy of the lossless filter characteristics. In this embodiment, the series obtained by this rounding calculation is used as the final filter coefficient group. In addition, the processing of steps S 3 to S 5 described above does not necessarily follow this order, as long as the rounding calculation is performed after the curtain calculation is performed. For example, curtain calculations can also be performed before sorting. At this time, the multiplication of the Hanni window is implemented so that the coefficient 値 at both ends of the window becomes " 1, and the coefficient 値 at the center of the window becomes " 0 ". Because the curtain calculus is implemented at an earlier stage in a series of steps 'Therefore, the number of data used in subsequent calculations can be reduced, and the processing load for performing calculations can be reduced. The following is printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs. Method. As shown in Fig. 2, in step S1, the frequency-gain characteristic of the "1" referenced filter is plotted, and its data is converted into data. The input data is symmetrical with the center of the sampling frequency as the axis. At this time, the length of the input data (the length of the graph, that is, the number of the series) m is the frequency error within a necessary range 且 ', and in order to simplify the inverse FFT processing of step S2, it is made into a 2k form. For example, the design is When the FIR filter with the sampling frequency of 44.ΙΚΗζ is the target FIR filter, the relationship between the input data length m and the maximum frequency error is -11-This paper standard is applicable to Chinese national standards (CNS) A4 specification (210X297 mm) 200304075 Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs A7 B7 _V. Description of the invention (8) Shown in Figure 3. The maximum frequency error here is equivalent to 1 scale of the chart The frequency is calculated by 44.1KHz / m. During audio processing, the 10Hz degree is within the allowable error range, so the input data length m is 4096. The example of the chart shown in Figure 2 is equivalent to the sampling frequency of 44.1KHz. The input data length m is 409 6. The frequency characteristics of the low-pass filter with a cut-off frequency of 8KHz and a cut-off frequency gain of -60dB. At this time, the horizontal axis of the chart will be equally divided into 4096 scales (clock). The number of clocks is CK, then the frequency f of the number of clocks CK is f = CK X (44 · 1/4096) (ΚΗζ ”Therefore, the number of clocks CK1 equivalent to 8KΗζ is CK1 = f X (4096 / 44.1K) and 743.04 In step S2, the frequency characteristics of the low-pass chirped wave inputted in the manner shown in FIG. 2 are regarded as a transfer function, an inverse FFT process is performed, and a real number term of the result is analyzed. Also, in step S3, In order to transform the sequence obtained by the inverse FFT into As the order in which the waverifier coefficient group is used, as shown in Fig. 4, the sequence is divided into the first half and the second half and sorted. That is, the number 0 of the 0th clock is replaced with the number 2048 of the clock (hereinafter , Represented by 0 — 2048), 1 + 2049, 2-> 2050 ..... 2047 + 4095, 2048 + 0, 2049 + 1 ... .. 4095 to 2047. Also, in step S4, The curtain calculation will be implemented for the purpose of reducing the number of taps. As mentioned above, window functions include rectangular windows, Hamming windows, Hani windows, hartlet windows, etc. Here, Hani windows that will smoothly converge to 0 at both ends are used. Figure 5 is a graph showing the relationship between the number of taps and the barrier characteristics, which is limited by the width of the window function. It can be known that the more the number of taps, the more the cut-off frequency changes. The Chinese paper standard (CNS) A4 (210X297 mm) applies to this paper size. -12-(Please read the precautions on the back before filling this page) 200304075 Α7 Β7 Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 5. The description of the invention (9) is larger. The example here is to set the width of the window function in such a way that the number of taps of the digital filter is 1 to 27. Figure 6 is a function map of the Hanni window at this time. The central part of the sequence (4096 rows) obtained by sorting is multiplied by the Hanni window (127 rows) shown in Figure 6. At this time, all coefficients outside the range of the Hanni window are calculated as zero. Next, in the final step S5, multiply the sequence after the curtain calculation by 2n and round off the number of digits below the decimal point, and then multiply the result by 1 / 2n (for example, 2n = 2048). Fig. 7 shows the filter coefficient group (127 filter coefficients) obtained by the above calculation. Fig. 8 is a frequency-gain characteristic and a frequency-phase characteristic graph obtained by performing FFT on a series of filter coefficient groups obtained in the manner shown in Fig. 7 above. The frequency-gain characteristic represents a gain on a logarithmic scale. Fig. 9 is a graph showing gain with a linear scale for the same frequency-gain characteristic, and Fig. 10 is a plan view of z. As can be seen from Fig. 8 to Fig. 10, the filter coefficient group obtained by the filter design method of this embodiment can roughly realize the low-pass filter characteristic with a cutoff frequency of 8 kHz. In addition, the cut-off frequency has an attenuation of 40 dB or more, and the phase characteristics are linear, achieving stable characteristics. Fig. 11 is a diagram showing an example of the configuration of a low-pass filter using the filter coefficient group obtained by the design method of the wave filter of this embodiment. This filter uses 127 D-type flip-flops 1 ·! ~ 1 · 127 connected in cascade to sequentially delay the input signal by 1 clock CK. Next, for the signals taken from the output taps of each of the D-type flip-flops h ~ iq27, multiply the filter coefficient by an integer of 2048, and then multiply by 127 coefficients 2 ·! ~ 2 · 127, And 127 (Please read the precautions on the back before filling this page) This paper size is applicable to the Chinese National Standard (CNS) A4 specification (210 × 297 mm) -13- 200304075 A7 B7 V. Description of the invention (10) adders h ~ 1.⑴ Add and output the multiplication result. Secondly, the multiplier 4 of the output section of the adder 3. ^ 27 in the final section will multiply the added output by 1/2048 to restore the original swing, and temporarily store the result in the D-type flip-flop 5 After that, execute the output. In this example, there are 127 coefficient units and adders each. However, for the part where the coefficient 値 of the wave filter is 0, the coefficient units and the adders can be omitted. Therefore, in practice, a digital filter can be formed by a multiplier and an adder that are smaller than the numbers in FIG. 11. As shown above, in this embodiment, a special rounding calculation is performed when obtaining the filter coefficients, thereby simplifying the design of the digital filter structure. The above description is based on the case of designing a low-pass filter. However, other digital filters can also implement the same design. An example of setting the band-pass filter is described below. Here, the desired frequency characteristic of the band-pass filter is input as a frequency characteristic sequence shown in FIG. 12. The desired frequency characteristic shown in Figure 12 is that only signals in the frequency band of 5 to 8 kHz can pass. Here, the sampling frequency is 44.1 KHz, and the input data length is 4096. The input data shown in Figure 12 is the same as the above-mentioned low-pass filter, and the inverse FFT and sorting are performed in 4 scenes (the window is Hanni window, and the width is 127). Filter coefficient group shown. ^ Figure 14 shows the frequency-gain characteristics and frequency-phase characteristics of the FFT result of the series of filter coefficient groups obtained as shown in Figure 13. The frequency-gain characteristics show the gain on a logarithmic scale. Figure 15 shows the gain on a linear scale for the same frequency-gain characteristic. Figure 16 shows the z-plane. As can be seen from FIG. 14 to FIG. 16, the filter coefficient group 'obtained by using the filter design method of this embodiment can roughly realize a passing frequency band of 5 to this paper size. The Chinese National Standard (CNS) A4 specification (210X297) is applicable. (Mm) -14-^^ clothing-(Please read the notes on the back before filling out this page) Order printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs Printed by the Employee Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 200304075 A7 B7 V. Invention description (11) 8KHz bandpass filter characteristics. In addition, the cut-off frequency has an attenuation of 40 dB or more, and the phase characteristics are linear and stable. Fig. 17 is an input data diagram of a desired frequency characteristic of a low-pass chirped wave device for adjusting the sound quality of a hearing aid or various audio devices. The frequency characteristics of this sound quality adjustment low-pass filter are continuously changed by analogy. The same inverse FFT4 sorting + curtain calculus + rounding calculus is performed on the input data shown in Figure 17, and the FFT is performed on the wavelet coefficient group obtained in this way, and the frequency characteristics of Figure 18 can be obtained. From this, it can be seen that the filter coefficient group obtained by the filter design method according to this embodiment can realize a desired frequency characteristic of a low-pass filter for sound quality adjustment that is approximately accurate. In addition, although not shown on the figure, the phase characteristics are also linear, achieving stable characteristics. Fig. 19 is an input data diagram of desired frequency characteristics of a bypass filter used for sound quality adjustment of a hearing aid or various audio devices. The frequency characteristics of the bypass filter for sound quality adjustment are continuously changed by analogy. The same inverse FFT + sorting 4 scene calculus + rounding calculus is performed on the input data shown in Fig. 19, and the FFT is performed on the filter coefficient group obtained in this way to obtain the frequency characteristics of Fig. 20. From this, it can be seen that the filter coefficient group obtained by the design method of the chirped wave filter according to this embodiment can realize a desired frequency characteristic of the bypass filter for sound quality adjustment which is almost accurate. In addition, although not shown on the figure, the phase characteristics are also straight, achieving stable characteristics.
如上説明之本實施形態數位濾波器設計方法，可以軟 體構成、DSP、或軟體之其中任一種來實現。例如，利用軟 體來實現時，本實施形態之濾波器設計裝置係由電腦之 CPU或MPU、RAM、及ROM等所構成，可利用儲存於RAM I 衣 ： 訂 (請先閱讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -15- 200304075 A7 B7 五、發明説明（12 ) 、ROM、或硬碟等之程式的執行來實現。 (請先閲讀背面之注意事項再填寫本頁) 因此，係將可使電腦執行前述本實施形態之機能的程 式儲存於如CD-ROM之記錄媒體，將其讀取至電腦即可實 現。儲存前述程式之記錄媒體，除了 CD-ROM以外，尙可 使用軟碟、硬碟、磁帶、光磁、光磁碟、DVD、非揮發性 記憶卡等。又，亦可利用經由網際網路等網路下載前述程 式來實現。 又，不但可以利用電腦執行提供之程式來實現前述實 施形態之機能，此程式和電腦上啓動之OS (作業系統）或其 他應用軟體等共同實現前述實施形態之機能時、或提供之 程式的處理之全部或部分利用電腦之機能擴充板或機能擴 充單元實現前述實施形態之機能時，相關之程式亦包含於 本發明之實施形態內。 經濟部智慧財產局員工消費合作社印製 如以上之詳細説明所示，本實施形態中，因係以影像 方式輸入代表期望頻率特性之波形的數列，並利用對其實 施逆傅立葉轉換來求取濾波器係數群，即使無特殊之數學 知識或電子工程知識，亦可簡單地決定實現期望頻率特性 之FIR數位濾波器之係數。又，必須強調一點，就是不只 是低通濾波器而已，連旁通濾波器、帶通濾波器、 bandemilation濾波器、梳形濾波器、及類比之任意波形的 濾波器等都可以相同方法來簡單地進行設計。 又，本實施形態中，因對利用逆傅立葉轉換求取之數 列實施特殊之捨去演算，故可在不降低濾波器之精度的情 形下，簡化濾波器係數群，且可大幅削減瀘波器之構成要 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -16 - 200304075 A7 B7 經濟部智慧財產局員工消費合作社印製 五、發明説明（13 ) 素的乘法器（除法器）之使用數。又，本實施形態中，係對逆 傅立葉轉換之結果乘以必要長度之窗函數，可增加輸入資 料長度且將頻率誤差抑制於較小，同時，可減少濾波器係 數之數（數位濾波器之分接頭數）。利用此方式，除了可簡化 設計之數位濾波器構成，亦可以高精度實現期望頻率特性 〇 又，前述實施形態只是本發明之實施上的具體實例而 已，不能被視爲且用來限定本發明之技術範圍。亦即，只 要不背離本發明之精神或其主要特徴，可以各種形態實施 〇 依據以上説明之本發明，以數列或函數輸入期望頻率 特性之波形，並對其實施逆傅立葉轉換來求取濾波器係數 群，即使不具專業知識，亦很容易即可實施低通瀘波器、 旁通濾波器、帶通濾波器、bandemilation瀘波器、以及具 有任意頻率特性之FIR數位濾波器的設計。 又，依據本發明，對利用逆傅立葉轉換求取之數列實 施特殊之捨去演算，故可在不會降低濾波器特性之精度的 情形下，簡化求取之濾波器係數群，而可大幅減少瀘波器 構成要素之乘法器的使用數。利用此方式，很容易就可以 設計以小電路規模實現高精度之期望頻率特性的FIR數位 濾波器。 又，依據本發明，因對逆傅立葉轉換之結果實施幕演 算，除了可增加最先輸入之數列的長度且將頻率誤差抑制 於較小以外，尙可減少濾波器係數之數（數位濾波器之分 (請先閲讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 經濟部智慧財產局員工消費合作社印製 200304075 A7 B7 五、發明説明（14 ) 接頭數），而簡化設計之數位濾波器的構成。利用此方式’ 很容易就可以設計以小電路規模實現高精度之期望頻率特 性的FIR數位濾波器。 本發明在產業之利用上’具有下述優點。 本發明可以簡易方法設計具有任意頻率特性之FIR數 位濾波器。又，很容易就可以設計以小電路規模實現高精 度之期望頻率特性的FIR數位濾波器。 [圖式簡單說明] 第1圖係本實施形態數位濾波器之設計方法的處理順 序圖。 第2圖係在第1圖步驟S 1輸入之期望頻率特性的實例 〇 第3圖係輸入資料長度及最大頻率誤差之關係圖。 第4圖係第1圖步驟S3之排序處理的説明圖。 第5圖係因第1圖步驟S4使用之窗函數的寬度而受到 限制之分接頭數及阻隔特性之關係圖。 第6圖係第1圖步驟S4使用之漢尼窗的函數値圖。 第7圖係從第2圖所示之期望頻率特性數列以本實施 形態濾波器設計方法求取之濾波器係數群圖。 第8圖係對以本實施形態濾波器設計方法求取之第7 圖所示濾波器係數群數列實施FFT之結果的頻率一增益特 性（對數標尺）及頻率一相位特性圖。 第9圖係對以本實施形態濾波器設計方法求取之第7 ---------•裝----：---訂------ (請先閲讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -18- 200304075 經濟部智慧財產局員工消費合作社印製 A7 _____B7五、發明説明（15 ) 圖所示瀘波器係數群數列實施FFT之結果的頻率一增益特 性（直線標尺）圖。 第1 0圖係以本實施形態濾波器設計方法求取之第7圖 所示濾波器係數群數列實施FFT之結果的z平面圖。 第1 1圖係由以本實施形態濾波器設計方法求取之濾波 器係數群所構成之數位FIR濾波器的構成例圖。 第12圖係在第1圖步驟S1輸入之期望頻率特性的其 他實例圖。 第13圖係從第12圖所示之期望頻率特性數列以本實 施形態濾波器設計方法求取之濾波器係數群圖 第14圖係對以本實施形態瀘波器設計方法求取之第13 圖所示濾波器係數群數列實施FFT之結果的頻率一增益特 性（對數標尺）及頻率一相位特性圖。 第1 5圖係對以本實施形態濾波器設計方法求取之第1 3 圖所示濾波器係數群數列實施FFT之結果的頻率一增益特 性（直線標尺）圖。 第16圖係以本實施形態濾波器設計方法求取之第13 圖所示濾波器係數群數列實施FFT之結果的z平面圖。 第17圖係在第1圖步驟S1輸入之期望頻率特性的其 他實例圖。 第1 8圖係對從第17圖所示之期望頻率特性數列以本 實施形態濾波器設計方法求取之濾波器係數群實施FFT之 結果的頻率特性圖。 第19圖係在第1圖步驟S1輸入之期望頻率特性的其 (請先閲讀背面之注意事項再填寫本頁) 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） _ 19 200304075 A7 B7 、五、發明説明（16 ) 他實例圖。 第20圖係對從第19圖所示之期望頻率特性數列以本 實施形態濾波器設計方法求取之濾波器係數群實施FFT之 結果的頻率特性圖。 衣 ； 訂 (請先閱讀背面之注意事項再填寫本頁) 經濟部智慧財產局員工消費合作社印製 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -20-The method for designing the digital filter according to the embodiment described above can be implemented by any of a software configuration, a DSP, and software. For example, when implemented by software, the filter design device of this embodiment is composed of a computer's CPU or MPU, RAM, and ROM, and can be stored in the RAM. Clothes: Order (please read the precautions on the back before (Fill in this page) This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) -15- 200304075 A7 B7 V. Implementation of the program (12), ROM, or hard disk. (Please read the precautions on the back before filling this page) Therefore, the program that enables the computer to perform the functions of this embodiment described above is stored in a recording medium such as a CD-ROM and can be implemented by reading it to the computer. In addition to the CD-ROM, you can use floppy disks, hard disks, magnetic tapes, magneto-optical disks, magneto-optical disks, DVDs, and non-volatile memory cards. It can also be realized by downloading the aforementioned program via a network such as the Internet. In addition, not only can the program provided by the computer be used to implement the functions of the foregoing embodiment, but this program and the OS (operating system) or other application software launched on the computer can jointly implement the functions of the foregoing embodiment or the processing of the provided program When all or part of a computer's function expansion board or function expansion unit is used to implement the functions of the foregoing embodiments, the related programs are also included in the embodiments of the present invention. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs, as shown in the above detailed description. In this embodiment, because a series of waveforms representing the desired frequency characteristics are input in the form of images, and inverse Fourier transform is used to obtain filtering The filter coefficient group can easily determine the coefficients of the FIR digital filter to achieve the desired frequency characteristics even without special mathematical or electrical engineering knowledge. Also, it must be emphasized that it is not just a low-pass filter. Even bypass filters, band-pass filters, bandemilation filters, comb filters, and analog arbitrary waveform filters can be simplified in the same way. To design. In addition, in this embodiment, special rounding calculation is performed on the sequence obtained by inverse Fourier transform, so that the filter coefficient group can be simplified without reducing the accuracy of the filter, and the wave filter can be greatly reduced. The composition of this paper is based on the Chinese National Standard (CNS) A4 specification (210X297 mm) -16-200304075 A7 B7 Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 5. Description of the invention (13) Prime multiplier (divider) ) Of the number of uses. In addition, in this embodiment, the result of the inverse Fourier transform is multiplied by a window function of the necessary length, which can increase the length of the input data and suppress the frequency error to a small value. At the same time, the number of filter coefficients can be reduced. Number of taps). In this way, in addition to simplifying the design of the digital filter configuration, it is also possible to achieve the desired frequency characteristics with high accuracy. Moreover, the foregoing embodiment is only a specific example of the implementation of the present invention, and cannot be considered and used to limit the present invention. Technical scope. That is, as long as it does not deviate from the spirit of the present invention or its main features, it can be implemented in various forms. According to the present invention described above, a waveform of a desired frequency characteristic is input in a series or function, and the inverse Fourier transform is performed to obtain a filter. The coefficient group makes it easy to implement the design of low-pass chirpers, bypass filters, band-pass filters, bandemilation chirpers, and FIR digital filters with arbitrary frequency characteristics, even without professional knowledge. In addition, according to the present invention, a special rounding operation is performed on the sequence obtained by the inverse Fourier transform, so that the filter coefficient group obtained can be simplified without reducing the accuracy of the filter characteristics, and the number of filter coefficients can be greatly reduced. Number of multipliers used by the waver component. In this way, it is easy to design a FIR digital filter that achieves high-precision desired frequency characteristics on a small circuit scale. In addition, according to the present invention, because the curtain calculation is performed on the result of the inverse Fourier transform, in addition to increasing the length of the first input sequence and suppressing the frequency error, the number of filter coefficients (the number of digital filters can be reduced) (Please read the precautions on the back before filling this page) This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) Printed by the Intellectual Property Bureau Staff Consumer Cooperatives of the Ministry of Economic Affairs 200304075 A7 B7 V. Invention Description (14 ) Number of connectors) to simplify the design of the digital filter. In this way, it is easy to design a FIR digital filter that achieves the desired frequency characteristics with high accuracy in a small circuit scale. The present invention has the following advantages in industrial use. The present invention allows a simple method to design an FIR digital filter with arbitrary frequency characteristics. In addition, it is easy to design a FIR digital filter that achieves high-precision desired frequency characteristics on a small circuit scale. [Brief description of the drawing] Fig. 1 is a processing sequence diagram of the design method of the digital filter in this embodiment. Fig. 2 is an example of the desired frequency characteristics input in step S 1 of Fig. 1 ○ Fig. 3 is a relationship diagram between the input data length and the maximum frequency error. FIG. 4 is an explanatory diagram of the sorting process in step S3 of FIG. 1. FIG. Fig. 5 is a diagram showing the relationship between the number of taps and the barrier characteristics that are limited due to the width of the window function used in step S4 of Fig. 1. Fig. 6 is a function map of the Hanni window used in step S4 of Fig. 1. Fig. 7 is a graph of filter coefficient groups obtained from the desired frequency characteristic sequence shown in Fig. 2 by the filter design method of this embodiment. Fig. 8 is a graph of frequency-gain characteristics (logarithmic scale) and frequency-phase characteristics of the filter coefficient group sequence shown in Fig. 7 obtained by the filter design method of this embodiment, which is obtained by performing FFT. Fig. 9 is the 7th from the filter design method of this embodiment --------- • installation ----: --- Order ------ (Please read the first Note: Please fill in this page again.) This paper size is in accordance with Chinese National Standard (CNS) A4 specification (210X 297 mm) -18- 200304075. Printed by A7 _____B7 printed by the Consumers ’Cooperative of Intellectual Property Bureau of the Ministry of Economic Affairs. Frequency-gain characteristic (linear scale) of oscilloscope coefficient group sequence as a result of performing FFT. Fig. 10 is a z-plane diagram of the result of performing the FFT on the series of filter coefficient groups shown in Fig. 7 obtained by the filter design method of this embodiment. Fig. 11 is a diagram showing a configuration example of a digital FIR filter composed of a filter coefficient group obtained by the filter design method of this embodiment. Fig. 12 is a diagram showing another example of the desired frequency characteristic input in step S1 of Fig. 1. FIG. 13 is a graph of the filter coefficient group obtained from the desired frequency characteristic sequence shown in FIG. 12 by the filter design method of this embodiment. FIG. 14 is the thirteenth figure obtained by the design method of the wave filter of this embodiment. The figure shows the frequency-gain characteristics (logarithmic scale) and frequency-phase characteristics of the filter coefficient group sequence shown in the figure. Fig. 15 is a frequency-gain characteristic (linear scale) obtained by performing FFT on the series of filter coefficient groups shown in Fig. 13 obtained by the filter design method of this embodiment. FIG. 16 is a z-plane diagram of the result of performing the FFT on the filter coefficient group sequence shown in FIG. 13 obtained by the filter design method of this embodiment. Fig. 17 is a diagram showing another example of the desired frequency characteristic input in step S1 of Fig. 1. Fig. 18 is a frequency characteristic diagram obtained by performing FFT on the filter coefficient group obtained by the filter design method of this embodiment from the desired frequency characteristic sequence shown in Fig. 17. Figure 19 is the desired frequency characteristic entered in step S1 of Figure 1 (please read the precautions on the back before filling this page) This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) _ 19 200304075 A7, B7, V. Invention description (16) Other examples. Fig. 20 is a frequency characteristic diagram obtained by performing FFT on the filter coefficient group obtained by the filter design method of this embodiment from the desired frequency characteristic sequence shown in Fig. 19. (Please read the precautions on the back before filling this page) Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs This paper size applies to China National Standard (CNS) A4 (210X297 mm) -20-