200303648 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的設計方法及設計裝置、數 位濾波器設計用程式、數位濾波器之發明，特別是關於具 備由複數之延遲器所構成的具有分線之延遲線，將各分線 之訊號分別放大數倍後加總而輸出之FIR濾波器的設計法 先前技術 在通訊、測量、聲音/影像訊號處理、醫療、地震學 等各種領域所提供的種種電子機器，在其內部通常進行某 種的數位訊號處理。數位訊號處理之最重要的基本操作， 在於從混有各種訊號或雜音的輸入訊號中，僅取出必要的 頻率帶域的訊號的濾波處理。因此，在進行數位訊號處理 的電子機器，多使用數位濾波器。 經濟部智慧財產局員工消費合作社印製 數位濾波器，多使用 IIR ( Infinite Impulse Response: 無限長脈衝應答）濾波器或FIR (Finit Impulse Response: 有限長脈衝應答）濾波器。其中FIR濾波器係具備由複數 延遲線所構成之具有分線之延遲線，將各分線之訊號分別 放大數倍後加總計算而輸出之形式的濾波器。具有以下的 優點。首先，FIR濾波器之傳達函數之極僅有Z平面之原 點而已，電路常保安定。其次，可以實現完全正確的直線 相位特性。 由通過帶域與阻止區域之配置來分類濾波器的話’主 要有低通濾波器、高通濾波器、帶域通過濾波器、帶域除 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -5- 200303648 A 7 B7 五、發明説明（2 ) 去濾波器等4種。IIR濾波器或FIR濾波器基本上爲低通 濾波器，其他的高通濾波器、帶域通過濾波器、帶域除去 (請先閱讀背面之注意事項再填寫本頁) 濾波器，係藉由從低通濾波器進行頻率變換等處理來實現 〇 從前，在設計基本的低通濾波器時’以採樣頻率與截 止（cut-off )頻率之比率爲根據，藉由進行使用窗函數或 者禁比雪夫近似法之套疊演算，求出FIR濾波器之對各分 線的係數。接著藉由使用所求得的濾波器係數進行模擬以 確認其頻率特性，同時適當修正係數値，得到所要特性的 低通濾波器。 此外，高通濾波器、帶域通過濾波器 '帶域除去濾波 器等其他濾波器在設計時，首先依照前述的手續設計複數 個作爲基本之低通濾波器。接著藉由將其組合進行頻率變 換等操作，設計具有所要的頻率特性之FIR濾波器。 然而，前述從前的濾波器設計法，必須要熟練的技術 人員耗費時間以及來精力進行設計，有著不容易設計所要 特性的FIR濾波器的問題。 經濟部智惡財產局員工消費合作社印製 此外，即使可以設計接近所要特性的FIR濾波器，設 計的濾波器的分線數也相當龐大，而且其係數値非常複雜 且爲無秩序之値。因此，亦有爲了實現該分線數以及係數 値必須要有大規模的電路構成（加法器、乘法器）的問題 。此外，實際使用所設計的FIr濾波器時，其演算量非常 多，有著處理負荷變重的問題。 本發明係爲了解決此一問題而完成者，目的在於達成 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -6 - 200303648 A7 B7 ___ 五、發明説明（3 ) (請先閲讀背面之注意事項再填寫本頁) 可以簡易地設計具有所要的頻率特性的FIR數位濾波器° 此外，本發明之目的在於可以簡易地設計可以小β足各 規模高精度地實現所要的頻率特性之FIR數位濾波器° 發明之揭示 爲解決前述課題，本發明將複數延遲器所構成的具# 線（Up )之延遲線的各分線的訊號，藉由指定的基本數 値列所構成的濾波器係數而分別放大數倍後，將這些乘算 結果相加而輸出的方式所構成的基本單元濾波器，作成1 個以上的單元濾波器，藉由任意組和前述1個以上的單元 濾波器進行濾波器設計。 前述基本單元濾波器的濾波器係數，例如係由絕對値 爲1，1，8, 8，1，1之比率的數値列所構成的。 此外，前述1個以上之單元濾波器，例如係藉由對前 述基本單元濾波器的輸出進行移動平均演算，或者藉由複 數縱向接續前述基本單元濾波器來作成的。 經濟部智慧財產苟員工消費合作社印製 在本發明的其他樣態，調整前述基本單元濾波器具有 的濾波器係數的分線間隔，而藉由任意組合調整後的前述 1個以上的單元濾波器以進行濾波器設計。 在本發明的其他樣態，複數縱向接續前述基本單元濾 波器，把藉此縱向接續所得到之濾波器係數變換其頻率一 增益（gain )特性成爲以增益的中心値爲軸而成線對稱的 狀態，複數縱向接續變換後的濾波器，使藉此縱向接續而 得之濾波器係數再次變換其頻率一增益特性成爲以增益的 本紙張尺度適用中國國家標準（CNS ) A4規格（21〇X；297公釐） 200303648 A7 B7 五、發明説明（4 ) 中心値爲軸而成線對稱的狀態，藉此調整前述單元濾波器 的頻率一增益特性的傾斜（梯度）部的傾斜程度。 (請先閱讀背面之注意事項再填寫本頁) 圖面之簡單說明 第1圖係顯示本實施型態的濾波器設計法之最基本的 4種基本單元濾波器F0〜F3之電路構成。 第2圖顯示第1圖所示之4種基本單元濾波器F0〜 F 3所使用的濾波器係數數値列。 第3圖顯不第1基本單元濾波器F0之頻率-增益（ g a i η )特性。 第4圖顯示第2基本單元濾波器F 1之頻率-增益特性 〇 第5圖顯示第3基本單元濾波器F2之頻率-增益特性 〇 第6圖顯示第4基本單元濾波器F3之頻率-增益特性 〇 第7圖顯示低通單元濾波器L10的產生演算法。 經濟部智慧財產局員工消費合作社印製 第8圖顯示低通單元濾波器L10的電路構成。 第9圖顯示低通單元濾波器L 1 1的產生演算法。 第1 0圖顯示低通單元濾波器L 11的電路構成。 第1 1圖顯示低通單元濾波器L 1 0、L 11之頻率-增益 特性。 第12圖顯示低通單元濾波器（L10) m之頻率-增益特 性0 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -8- 200303648 經濟部智慧財產局，-貝工消費合作社印製 A7 B7五、發明説明（5 ) 第Π圖顯示低通單元2次濾波器L20的產生演算法 〇 第1 4圖顯示低通單元2次濾波器L20的電路構成。 第15圖顯示低通單元2次濾波器L20的頻率-增益特 性。 第1 6圖顯示高通單元濾波器Η 1 0的產生演算法。 第1 7圖顯示高通單元濾波器Η 1 0的電路構成。 第1 8圖顯示高通單元濾波器Η 1 0、Η 1 1之頻率-增益 特性。 第19圖顯示高通單元濾波器（Η10) m之頻率-增益特 性。 第20圖顯示高通單元2次濾波器H20的產生演算法 〇 第21圖顯示高通單元2次濾波器H20的電路構成。 第22圖顯示高通單元2次濾波器H20的頻率-增益特 性。 第23圖顯示低通單元濾波器（Lln) 4之頻率—增益特 性。 第24圖顯示彙總第23圖所示之4個低通單元濾波器 (Lin) 4之頻率-增益特性。 第25圖顯示去除頻率帶域之一例之頻率-增益特性。 第26圖顯示去除頻率帶域之另一例之頻率-增益特性 〇 第27圖係供說明固定-6dB位置的斜坡變換之用的頻 (請先閲讀背面之注意事項再填寫本頁) 裝· 訂200303648 A7 _ B7_ V. Description of the invention (1) The technical field to which the invention belongs (please read the precautions on the back before filling this page) The present invention relates to the design method and design device of digital filters, programs for digital filter design, The invention of the digital filter, especially the design method of the FIR filter which has a delay line with a branch line composed of a complex delayer, and amplifies the signals of each branch line several times and then adds up the output Various electronic devices provided in various fields such as communication, measurement, audio / video signal processing, medical treatment, and seismology usually perform some kind of digital signal processing inside. The most important basic operation of digital signal processing is to filter out only the necessary frequency band signals from the input signals mixed with various signals or noise. Therefore, in electronic devices that perform digital signal processing, digital filters are often used. Digital filters are printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs, and most of them use IIR (Infinite Impulse Response) filters or FIR (Finit Impulse Response) filters. Among them, the FIR filter is a filter having a delay line composed of a plurality of delay lines and having sub-lines, and amplifying the signals of the sub-lines several times and then adding and calculating the output. It has the following advantages. First, the pole of the transfer function of the FIR filter is only the origin of the Z-plane, and the circuit is often fixed. Secondly, it is possible to achieve perfectly correct linear phase characteristics. The filters are classified by the configuration of the band region and the blocking region. There are mainly low-pass filters, high-pass filters, band-pass filters, and band-domain divisions. This paper is applicable to China National Standard (CNS) A4 specifications (210X297). 5) 200303648 A 7 B7 5. Description of the Invention (2) Four types of filters. The IIR filter or FIR filter is basically a low-pass filter. The other high-pass filters, band-pass filters, and band-removals are removed (please read the precautions on the back before filling this page). The low-pass filter implements frequency conversion and other processes. 从 In the past, when designing a basic low-pass filter, 'the sampling frequency and the cut-off frequency were used as the basis. The nesting algorithm of the approximation method is used to obtain the coefficients of the FIR filter on each branch line. Then, a simulation is performed using the obtained filter coefficients to confirm the frequency characteristics, and the coefficient 値 is appropriately modified to obtain a low-pass filter with the desired characteristics. In addition, when designing other filters such as a high-pass filter, a band-pass filter, and a band-removal filter, first, a plurality of basic low-pass filters are designed according to the aforementioned procedures. Then, the FIR filter having a desired frequency characteristic is designed by performing a combination such as frequency conversion. However, the aforementioned previous filter design method requires that skilled technicians take time and energy to design, and there is a problem that it is not easy to design a FIR filter with a desired characteristic. Printed by the Consumer Cooperatives of the Intellectual Property Office of the Ministry of Economic Affairs In addition, even if FIR filters close to the required characteristics can be designed, the number of divided lines of the designed filters is quite large, and their coefficients are very complex and disorderly. Therefore, there is also a problem that a large-scale circuit configuration (adder, multiplier) is required to realize the number of branch lines and the coefficient 値. In addition, when the designed FIr filter is actually used, its calculation amount is very large, and there is a problem that the processing load becomes heavy. The present invention was completed in order to solve this problem, and the purpose is to achieve the paper size and apply the Chinese National Standard (CNS) A4 specification (210X 297 mm) -6-200303648 A7 B7 ___ V. Description of the invention (3) (please first (Please read the notes on the back and fill in this page again.) FIR digital filters with desired frequency characteristics can be easily designed. In addition, the purpose of the present invention is to easily design the required frequency characteristics with small β and sufficient scale to achieve the required frequency characteristics with high accuracy. FIR digital filter ° Disclosure of the invention In order to solve the above-mentioned problem, the present invention uses the signal of each branch line of the delay line with # line (Up) formed by a complex delayer to form a specified basic number queue. The filter coefficients are amplified by several times, and the basic unit filter constructed by adding these multiplication results and outputting is made into one or more unit filters, which are filtered by an arbitrary group and the aforementioned one or more units. Filter design. The filter coefficients of the basic unit filter are, for example, constituted by a sequence of absolute 値 which is a ratio of 1,1,8,8,1,1. In addition, the one or more unit filters are made by, for example, performing a moving average calculation on the output of the basic unit filter, or by vertically connecting the basic unit filters in a complex direction. The Intellectual Property of the Ministry of Economic Affairs and the Consumer Consumption Cooperative printed other aspects of the present invention to adjust the line break interval of the filter coefficients of the basic unit filter, and adjust the above one or more unit filters by any combination. For filter design. In other aspects of the present invention, a complex number is vertically connected to the aforementioned basic unit filter, and the filter coefficient obtained by the vertical connection is used to transform its frequency-gain characteristic into a line symmetry with the center 値 of the gain as the axis. State, the filter after complex vertical conversion, so that the filter coefficients obtained by this vertical conversion again transform its frequency-gain characteristics to the Chinese paper standard (CNS) A4 specification (21〇X; 297 mm) 200303648 A7 B7 V. Description of the invention (4) The center 値 is an axis and is in a state of line symmetry, thereby adjusting the inclination of the inclination (gradient) portion of the frequency-gain characteristic of the aforementioned unit filter. (Please read the precautions on the back before filling in this page) Brief description of the drawing Figure 1 shows the circuit structure of the four basic unit filters F0 to F3, which are the most basic filter design method of this embodiment. Fig. 2 shows a series of filter coefficients used by the four basic unit filters F0 to F 3 shown in Fig. 1. Figure 3 shows the frequency-gain (g a i η) characteristic of the first basic unit filter F0. Figure 4 shows the frequency-gain characteristic of the second basic unit filter F1. Figure 5 shows the frequency-gain characteristic of the third basic unit filter F2. Figure 6 shows the frequency-gain of the fourth basic unit filter F3. Characteristics. Figure 7 shows the algorithm for generating the low-pass element filter L10. Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs Figure 8 shows the circuit configuration of the low-pass unit filter L10. Figure 9 shows the algorithm for generating the low-pass element filter L 1 1. FIG. 10 shows a circuit configuration of the low-pass unit filter L 11. Figure 11 shows the frequency-gain characteristics of the low-pass element filters L 1 0, L 11. Figure 12 shows the frequency-gain characteristics of the low-pass element filter (L10) m. 0 This paper size applies to the Chinese National Standard (CNS) A4 specification (210X 297 mm) -8- 200303648 Intellectual Property Bureau of the Ministry of Economic Affairs, -Beigong Printed by the consumer cooperative A7 B7 V. Description of the invention (5) Figure II shows the algorithm for generating the low-pass unit secondary filter L20. Figure 14 shows the circuit configuration of the low-pass unit secondary filter L20. Figure 15 shows the frequency-gain characteristics of the low-pass unit secondary filter L20. Figure 16 shows the algorithm for generating a high-pass element filter Η 10. Figure 17 shows the circuit configuration of the high-pass unit filter Η 10. Figure 18 shows the frequency-gain characteristics of the high-pass element filters Η 1 0, Η 1 1. Figure 19 shows the frequency-gain characteristics of the high-pass element filter (Η10) m. Figure 20 shows the algorithm for generating the high-pass unit secondary filter H20. Figure 21 shows the circuit configuration of the high-pass unit secondary filter H20. Figure 22 shows the frequency-gain characteristics of the high-pass unit secondary filter H20. Figure 23 shows the frequency-gain characteristics of the low-pass element filter (Lln) 4. Figure 24 shows the frequency-gain characteristics of the four low-pass unit filters (Lin) 4 shown in Figure 23. FIG. 25 shows the frequency-gain characteristics of an example of removing the frequency band. Figure 26 shows the frequency-gain characteristic of another example of removing the frequency band. Figure 27 is the frequency used to explain the slope conversion at a fixed -6dB position (please read the precautions on the back before filling this page).
.P 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -9- 200303648 A7 B7 五、發明説明（6 ) 率-增益特性。 第2 8圖係顯示所設計的濾波器電路的目標規格範例 (請先閱讀背面之注意事項再填寫本頁) 〇 第29圖顯示實現第28圖所示的目標規格之低通濾波 器的電路例。 第30圖顯示第29圖所示的低通濾波器的頻率-增益 特性。 第31圖擴大顯示第30圖所示的頻率-增益特性之通 過區域的部分。 第32圖顯示FM用帶域通過濾波器的設計範例。 第33圖顯示第32圖所示之FM用帶域通過濾波器的 頻率特性。 第34圖顯示AM用帶域通過濾波器的設計範例。 第35圖顯示第34圖所示之AM用帶域通過濾波器的 頻率特性。 第3 6圖顯示FM用帶域通過濾波器的其他設計範例 〇 經濟部智慧財產局員工消費合作社印製 第37圖顯示第36圖所示之FM用帶域通過濾波器的 頻率特性。 圖號說明 F0、Fl、F2、F3 基本單元濾波器 1-1、1.2、1·3、1.4、1·5 D 型正反器 2·1、2·2、2·3、2·4、2·5、2·6 計數器 本紙張尺度適用中國國家標準（CNS ) Α4規格（210Χ297公釐) -10- 200303648 經濟部智慧財產局員工消費合作社印製 A7 __ B7五、發明説明（7 ) 3-t. 3-2. 3-3. 3-4. 3〇- 加法器 4 乘法器 供實施發明之最佳型態 以下，根據圖面說明本發明之一實施型態。本實施型 態之濾波器設計法，係從根本重新審視以濾波器係數的計 算爲出發點的從前的設計法，而改用可藉以下所述之簡單 的單元濾波器的組合來設計所要特性的FIR濾波器。 亦即，使用以下說明的4種基本單元濾波器FOn、 Fin、F2n、F3n製作 4種單元濾波器Lin、L2n、Hln、 H2n，使用此4種單元濾波器Lin、L2n、Hln、H2n並藉 由這些的組合設計具有所要的頻率特性的FIR濾波器。 (1 )基本單元濾波器 第1圖係最基本的4種基本單元濾波器F〇、Fl、F2 、F 3的電路構成圖。此外，第2圖顯示在這4種基本單 元濾波器F0〜F3所使用的濾波器係數之數値列。又’表 示基本單元濾波器的符號F0〜F3之後所註記之” η”代表在 各濾波器係數之間所插入的”0”的數目（詳如後述）’ F0 〜F 3代表完全未插入” 0 ”。 在第1圖所示的基本單元濾波器F0〜F3 ’藉由縱向 接續的5個D型正反器1.1〜1·5使輸入訊號分別依序延遲 1時脈CK。接著，對各D型正反器1.1〜1·5之輸出輸入分 線所取出的訊號，以6個計數器2·!〜2.6分別乘算出濾波 (請先閱讀背面之注意事項再填寫本頁) •裝· 訂 % 本紙張尺度適用中國國家標準（CNS ) Α4規格（210Χ297公釐） -11 - 200303648 A7 B7 五、發明説明（8 ) (請先閲讀背面之注意事項再填寫本頁) 器係數放大1 6倍後的結果整數値h 1〜h 6，將這些乘算，結 果全部以5個加法窃3 · 1〜3 ·5累加。進而以設於最終段的 加法器3 · 5的輸出段之乘法器4，把加算輸出縮小爲1 /1 6 倍，還原振幅後輸出。 在本實施型態所使用的4種基本單元濾波器F0〜F3 ，電路構成均如第1圖所示，僅有濾波器係數（計數器2-!〜2.6之乘數値hi〜h6 )相異。由第2圖可知，基本單元 濾波器F0〜F3之濾波器係數，使用其絕對値僅有「1」或 者「8」之極爲單純的數値列所構成，加上正或者負之符 號而使其配列不同。其中，無論那個基本單元濾波器F0 〜F3之係數，對中央附近的分線之乘數値h3、h4其絕對 値爲「8」，對其兩側的分線之乘數値h 1、h 2、h 5、h 6絕 對値爲「1」。 經濟部智慧財產局員工消費合作社印製 (1-1 )第1基本單元濾波器F0 第1基本單元濾波器F0，係最基本的濾波器，爲例 如低通濾波器L 1 η或者低通單元2次濾波器L2n之構成要 素。第3圖顯示第1基本單元濾波器F0的頻率-增益（ gain )特性（將濾波器係數之數値列經由快速傅立葉轉換 FFT後之結果），（a )係以直線座標軸表示增益，（b ) 係以對數座標軸表示增益。在此第3圖，增益及頻率均以 1來基準化。 (1-2)第2基本單元濾波器F1 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -12- 200303648 A7 ___ B7_ 五、發明説明（9 ) (請先閲讀背面之注意事項再填寫本頁) 第2基本單元濾波器F1，爲例如高通單元2次濾波 器Η2n之構成要素。第4圖顯示第2基本單元濾波器fi 的頻率-增益（gain )特性，（a )係以直線座標軸表示增 益，（b )係以對數座標軸表示增益。在此第4圖，增益 及頻率也都是以1來基準化。 (1-3 )第3及第4基本單元濾波器F2、F3 第3及第4基本單元濾波器F2、F3，爲例如組合這 些而成爲高通單元濾波器Hln之構成要素。第5圖及第6 圖分別顯示第3及第4基本單元濾波器F2、F3的頻率-增 益（gain )特性，（a )係以直線座標軸表示增益，（b ) 係以對數座標軸表示增益。在此第5、6圖，增益及頻率 也都是以1來基準化。 (2 )單元濾波器 單元濾波器Lln，L2n，Hln，H2n係由上述之基本單元 濾波器FOn，Fln，F2n，F3n所產生的。 經濟部智慧財產局員工消費合作社印製 (2-1 )低通單元濾波器Lin 例如低通單元濾波器L 1 0的濾波器係數’如第7圖所 示，係藉由對基本單元濾波器F0的濾波器係數進行1次 移動平均演算而產生。 第8圖顯示低通單元濾波器L 1 0的電路構成。如第8 圖所示，在低通單元濾波器L 1 0，藉由被接續於基本單元 -13- 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） 200303648 A7 B7 五、發明説明（1〇) (請先閲讀背面之注意事項再填寫本頁) 濾波器（F0 ) 1 1的後段之D型正反器（flip-flop ) 12，使 基本單元濾波器1 1的輸出訊號僅延遲1時脈CK。接著將 藉由D型正反器1 2使受到延遲的前後訊號以加法器1 3 累加，而將該加算輸出以乘法器14縮小1 /2倍，而使振 福回到原來大小而輸出。 此外，低通單元濾波器L 1 1的濾波器係數，係藉由在 上述低通單元濾波器L 1 0的各濾波器係數之間分別插入1 個「0」而產生的。亦即，低通單元濾波器L 1 1的濾波器 係數，如第9圖所示，藉由對基本單元濾波器F01的濾波 器係數進行1次移動平均演算而產生。 第1 0圖顯示低通單元濾波器L 1 1的電路構成。如第 1 0圖所示，在低通單元濾波器L 1 1，藉由被縱向接續於基 本單元濾波器（F01) 21的後段之2個D型正反器22-!、 22-i，使基本單元濾波器21的輸出訊號僅延遲1時脈CK 。接著將藉由2個D型正反器2 2。' 2 2.!而受到延遲的前 後訊號以加法器23累加，而將該加算輸出以乘法器24縮 小1/2倍，而使振福回到原來大小而輸出。 經濟部智慧財產局員工消費合作社印製 同樣地，低通單元濾波器Lin ( n = 2,3，....）之濾波器 係數，係藉由在低通單元濾波器L 1 0之各濾波器係數之間 分別插入η個「〇」而產生的。 第1 1圖顯示低通單元濾波器L 1 0以及在各濾波器係 數之間分別插入1個「0」而產生的低通單元濾波器L 1 1 的頻率-增益特性，（a )係以直線座標軸表示增益，（b )係以對數座標軸表示增益。在此第1 1圖，增益及頻率 $紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -14- 200303648 A7 B7 五、發明説明（11 ) (請先閱讀背面之注意事項再填寫本頁) 均以1來基準化。由此第1 1圖可知，在濾波器係數間插 入的「0」的數目爲η的話，其頻率-增益特性之頻率軸（ 對平率方向之週期）成爲l/η。 (2-2)低通單元濾波器Lin的串聯接續 藉由串聯接續單元濾波器，使各單元濾波器之係數彼 此被乘算/加算而作出新的濾波器係數。以下，例如低通 單元濾波器L 10的串聯數爲m時，將此記載爲（L10 ) m 〇 第1 2圖顯示低通單元濾波器L 1 0、（ L 1 0 ) 2、（ L 1 0 )4、（ L 1 0 ) 8的頻率-增益特性，（a )係以直線座標軸 表示增益，（b )係以對數座標軸表示增益。在此第1 2圖 ，增益及頻率均以1來基準化。低通單元濾波器L 1 0僅有 1個的場合，振幅爲0.5的位置之時脈爲0.25。對此串聯 數變多的話，濾波器的通過頻帶幅變窄。例如m = 8的場 合，振幅成爲0.5的位置之時脈爲0.1 2 5。 經濟部智慧財產局員工消費合作社印製 由上述第12圖可知，低通單兀濾波器L10，具有頻 率特性的截止（cut-off )頻率部分的傾斜非常險峻的特徵 ，可得106dB/倍頻以上的特性。關於此低通單元濾波器 L 1 0，可得與基本單元濾波器F0 1同等的特性。針對基本 單元濾波器F0 1的頻率-增益特性雖未特別圖示，但特性 之肩部（通過區域）稍微升高，所以上述之串聯接續的使 用稍有困難存在。此點，基本單元濾波器F 1丨是較理想的 。低通單元濾波器（L 1 0 ) m，於低頻區域也可得極深的直 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -15- 200303648 A7 B7 五、發明説明（12) 接的降下特性。 (請先閲讀背面之注意事項再填寫本頁) (2-3 )低通單元2次濾波器L2n 低通單元2次濾波器L2n被要求要有險峻的截止特性 ’適於使用在被串聯接續的濾波器的最終段。例如低通單 元2次濾波器L20，如第13圖所示，藉由將基本單元濾 波器F0兩個縱向串聯接續而產生。 第14圖顯示低通單元2次濾波器L20的電路構成。 如第14圖所示，低通單元2次濾波器L20將2個基本單 元濾波器（F0 ) 31」、32·!縱向接續而構成。 第15圖顯示低通單元2次濾波器L20的頻率-增益特 性，（a )係以直線座標軸表示增益，（b )係以對數座標 軸表示增益。在此第15圖，增益及頻率也是以1來基準 化。由此第15圖可知，截止特性很急峻，肩部（通過區 域）升高的緣故，此低通單元2次濾波器L20最適於用在 濾波器區塊的最終段。 經濟部智慧財產局員工消費合作社印製 與低通單元濾波器L 1 η的場合同樣，低通單元2次濾 波器L2n ( η 2 1 )的濾波器係數係藉由在低通單元2次濾 波器L20的各濾波器係數之間分別插入η個「0」而產生 的。此外，藉由串聯接續m個低通單元2次濾波器L2n， 可以作出新的濾波器係數。低通單元2次濾波器（L2n ) π 之頻率-增益特性在串聯數m越多的情況下通過頻帶寬幅 越窄，即使於低頻也可得極深的直接的落下特性。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -16- 200303648 Α7 Β7 五、發明説明（13 ) (2-4)高通單元濾波器Hln (請先閲讀背面之注意事項再填寫本頁) 高通單元濾波器Η 1 0之濾波器係數，如第1 6圖所示 ，係藉由對基本單元濾波器F2、F 3之濾波器係數進行1 次移動平均演算而產生。 第1 7圖顯示高通單元濾波器Η 1 0之電路構成。如第 1 7圖所示，在高通單元濾波器Η 1 0，輸入訊號通過2個基 本單元濾波器（F2 ) 41、（ F3 ) 42，一方之基本單元濾波 器42的輸出訊號藉由被接續於其後段的D型正反器43 而僅延遲1時脈CK。接著，以加法器44來加算基本單元 濾波器41的輸出訊號，與D型正反器43所延遲1時脈的 基本單元濾波器42的輸出訊號，將該加算輸出以乘法器 45縮小1/2倍使振幅還原而輸出。 經濟部智慧財產局員工消骨合作社印製 與低通單元濾波器L 1 η的場合相同，高通單元濾波器 Η 1 η ( η - 1 )的濾波器係數係藉由在高通單元濾波器Η 1 Ο 的各濾波器係數之間分別插入η個「Ο」而產生的。此外 ，藉由串聯接續m個高通單元濾波器Η 1 η，可以作出新的 濾波器係數。高通單元濾波器（Hln) m之頻率-增益特性 在串聯數m越多的情況下通過頻帶寬幅越窄，即使於高 頻也可得極深的直接落下特性。 第1 8圖顯示高通單元濾波器Η 1 0以及在各濾波器係 數之間分別插入1個^ 0」而產生的高通單元濾波器Η 1 1 的頻率-增益特性。由此第1 8圖可知，即使在高通單元濾 波器的場合，在濾波器係數間插入η個^ 0」，可以使其 頻率-增益特性之頻率軸（對平率方向之週期）成爲1/η。 本纸張尺度適用中國國家標準（CNS ) Α4規格（210X297公釐） -17- 200303648 A7 _ B7 五、發明説明（14 ) (請先閲讀背面之注意事項再填寫本頁) 此外，第1 9圖顯示高通單元濾波器Η 1 0、（ Η 1 0 ) 2 、（Η 1 0 ) 4、（ Η 1 0 ) 8的頻率-增益特性，（a )係以直線 座標軸表示增益，（b )係以對數座標軸表示增益。在此 第19圖，增益及頻率也是以1來基準化。高通單元濾波 器H10僅有1個的場合，振幅爲0.5的位置之時脈爲0.25 。對此串聯數變多的話，濾波器的通過頻帶幅變窄。例如 8的場合，振幅成爲0.5的位置之時脈爲0.375。 由上述第19圖可知，高通單元濾波器H10，具有頻 率特性的截止（cut-off)頻率部分的傾斜非常險峻的特徵 ，可得106dB/倍頻以上的特性。關於高通單元濾波器（ Η 1 0 ) m，於高頻區域也可得極深的直接降下特性。 比較上述第18及第19圖，與先前顯示的第11及第 1 2圖可知，高通單元濾波器（Η 1 0 ) m，與低通單元濾波 器（L10) ”爲特性對稱之濾波器。 (2-5 )高通單元2次濾波器H2n 經濟部智慧財產局8工消費合作社印製 高通單元2次濾波器H2n被要求要有險峻的截止特 性，適於使用在被串聯接續的濾波器的最終段。例如高通 單元2次濾波器H20，如第20圖所示，藉由將基本單元 濾波器F 1兩個縱向串聯接續而產生。 第21圖顯示高通單元2次濾波器H20的電路構成。 如第21圖所示，高通單元2次濾波器H20將2個基本單 元濾波器（F1 ) 51」、51」縱向接續而構成。 第22圖顯示高通單元2次濾波器H20的頻率-增益特 性，（a )係以直線座標軸表示增益，（b )係以對數座標 本纸張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -18- 200303648 A7 B7 五、發明説明（15 ) (請先閱讀背面之注意事項再填寫本頁) 軸表示增益。在此第22圖，增益及頻率也是以^ 1」來基 準化。由此第22圖可知，截止特性很急峻，肩部（通過 區域）升高的緣故，此高通單元2次濾波器H20最適於 用在濾波器區塊的最終段。 與低通單元濾波器L 1 η的場合同樣，高通單元2次濾 波器Η2η ( η - 1 )的瀘波器係數係藉由在高通單元2次濾 波器Η20的各濾波器係數之間分別插入η個「0」而產生 的。此外，藉由串聯接續m個高通單元2次濾波器Η2η， 可以作出新的濾波器係數。高通單元2次濾波器（H2n ) m 之頻率-增益特性在串聯數m越多的情況下通過頻帶寬幅 越窄，即使於高頻也可得極深的直接的落下特性。 (3 )頻率帶域之穿透 經濟部智慧財產局8工消費合作社印製 頻率帶域之穿透，使用將單元濾波器4個以上串聯接 續者。第23圖顯示低通單元濾波器（L 1 0 ) 4、（ L 1 1 ) 4 、（L13 ) 4、（ L17 ) 4的頻率-增益特性。此外，第24圖 顯示將此4個頻率-增益特性整合於1個圖表之圖。此第 23圖與第24圖之增益及頻率也是以「1」來基準化。 第25圖顯示適當組合具有上述第23圖以及第24圖 所示之頻率特性的低通單元濾波器（L 1 0 ) 4、（ L 1 1 ) 4、 (L 1 3 ) 4、（ L 1 7 ) 4而進行頻率帶域之穿透之一例。如第 24圖所示，適當組合低通單元濾波器（L 1 0 ) 4、（ L 1 1 ) 4 、（L Π ) 4、（ L 1 7 ) 4的話，各特性値彼此相互抵銷而進 行頻率帶域之穿透。此外，以這些波形爲基本進行組合， 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -19- 200303648 A7 B7_ 五、發明説明（16 ) 應需要而進行往反轉頻率軸方向之移動，可以作出僅使所 要的頻率帶域通過之濾波器。 (請先閲讀背面之注意事項再填寫本頁) 第25圖（a )係組合4個低通單元濾波器（L 10 ) 4、 (L 1 1 ) 4、（ L Π ) 4、（ L 1 7 ) 4而將這些串聯接續時所得 到的頻率特性。據此，可得極爲低頻的區域成爲通過域之 低通濾波器，但有稍微的洩漏發生（但是此洩漏產生在落 下超過-106dB的部分，幾乎可以忽視）。 第25圖（b )係除了 4個低通單元濾波器（L10 ) 4、 (L 1 1 ) 4、（ L 1 3 ) 4、（ L 1 7 ) 4以外，還加入組合低通單 元2次濾波器（L27 ) 8而將這些串聯接續時所得之頻率特 性。根據此結果，低頻之極爲狹窄的區域成爲通過區域， 而且可得落入量在200dB以上之低通濾波器。而且完全不 會發生洩漏。 又，在第25圖，說明藉由低通單元濾波器（L 1 n ) 經濟部智慧財產局員工消費合作社印製 (m ^ 4 )或者低通單元二次濾波器（L2n ) m ( m - 4 )之 組合進行頻率帶域的穿透之例，但是藉由高通單元濾波器 (Hln ) m ( mg 4 )或者高通單元二次濾波器（H2n ) m ( m -4 )之組合進行頻率帶域的穿透也是可能的。此外，藉 由這些各種單元濾波器（Lin ) m、（ L2n ) m、 （ Hln ) m、 (lihi ) m之複數組合來進行頻率帶域的穿透也是可會g的 。第26圖顯示頻率帶域之其他的穿透例。 (4 )傾斜之調整（斜率變換） 藉由固定成爲-6dB之時脈位置，且加上使頻率特性 本紙張尺度適用中國國家標準（CNS )八4規格（210X297公釐） -20- 200303648 A7 B7 五、發明説明（17 ) 之波形的梯度成爲急峻的手法，使得必要的頻率特性更容 易實現。亦即’爲了要把特性收容於所要的頻率範圍內， 如果可以調整頻率特性的波形的傾斜程度的話將會很便利 〇 第2 7圖係供說明固定-6 d B位置的斜率變換的手法之 用的頻率-增益特性圖’ （a )係以直線座標軸表示增益， (b )係以對數座標軸表示增益。在此第27圖，增益及頻 率也都是以1來基準化。在此，原有資料使用低通單元濾 波器L10的頻率-增益特性（①）說明在固定-6dB位置的 情況下使傾斜急峻的場合。 如上所述，將2個低通單元濾波器l 1 0串聯接續的話 ，可以使傾斜急峻化，但成爲-6 d B的時脈位置往左側（ 低頻側）移動（②）。此處，進行以下所述之操作。首先 以增益的中心値（=0 _ 5 )爲軸，使②所示之低通單元濾 波器（L 1 0 ) 2之頻率-增益特性反轉（③）。此係藉由配 合延遲而由基準增益値「1」之單元脈衝（相當於中心値 1而其他全爲0之濾波器係數）減去低通單元濾波器（ L 1 0 ) 2的濾波器係數而求得。此③之頻率-增益特性，顯 示局通濾波器的特性（此處將此稱爲反轉高通濾波器）。 其次’將③所示之反轉高通濾波器串聯接續2個。藉 此所得之頻率-增益特性的傾斜變得更爲急峻，成爲-6dB 的時脈位置往右側（高頻側）移動（④）。此時，藉由使 串聯接續的反轉高通濾波器的個數與②的場合相同（2個 )’可以使往高頻側之移動量與先前之往低頻側的移動量 本紙張尺度適用中國國家標準（CNS ) A4規格（21〇X297公釐） I--------_裝-- (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 -21 - 200303648 A7 B7 五、發明説明（18 ) (請先閱讀背面之注意事項再填寫本頁) 成爲相同程度。最後，以增益的中心値（=〇· 5 )爲軸 使④所示之頻率-增益特性反轉（⑤）。此係藉由配合延 遲而由基準增益値「1」之單元脈衝減去④的濾波器係數 而求得。 觀察輸入資料①的頻率特性，與輸出資料⑤的頻率特 性的話，其在-6dB的時脈位置交差，輸出資料⑤的頻率 特性的傾斜比輸入資料①的還要急峻。 (5 )電路例 其次，顯示實際的電路例。目標規格如第2 8圖所示 。亦即，此處以衰減量爲l〇6dB/倍頻以上的低通濾波器 的設計爲目標。第29圖顯示實現此目標規格之低通濾波 器的電路例。衰減値依存於串聯接續的濾波器的個數，串 聯接續4個的場合的衰減量約爲40dB/倍頻。此次必須要 有106dB以上的衰減量，原則上串聯接續的濾波器個數爲 8個。 經濟部智慧財產局員工消費合作社印製 第29圖所示的電路，顯示以低通單元濾波器L 1 0有 8個，低通單元濾波器L 1 1有8個，低通單元濾波器L1 3 有8個，低通單元濾波器L 1 7有4個，低通單元2次濾波 器L27有8個並以此順序串聯接續而構成。由此第29圖 可知，根據本實施型態的濾波器設計法，由相同的單元濾 波器反復構成的極爲單純之構成可以得到所要特性的低通 濾波器。 此外，各單元濾波器的內部構成如上所述，全體必要 本紙張尺度適用中國國家標準（CNS )八4規格（210X29*7公釐） -22- 200303648 A7 B7 五、發明説明（19) 之分線數，如以下所述只需要相當少的量。 L108........6x 8= 48 個 (請先閲讀背面之注意事項再填寫本頁) L118........6x 8= 48 個 L138........ 6x 8=48 個 L174........6x 4 二 24 個 L278 ........ 1 2x 8 = 96 個 合計........264個 進而，對各分線輸出所必要的濾波器係數僅有、1/16, 1/16，-8/16，8/16 等 4 種。特別是 _8/16 = -1/2，8/16=1/2 所 以可以使演算電路大幅簡化。 經濟部智慧財產局員工消費合作社印製 第3 0圖，顯不第2 9圖所示之低通濾波器的頻率-增 益特性，（a )係以直線座標軸表示增益，（b )係以對數 座標軸表示增益。此外’第3 1圖係擴大顯示第3 0圖所示 的頻率-增益特性的通過區域的部分，（a )係以直線座標 軸表示增益，（b )係以對數座標軸表示增益。由第3 0圖 以及第31圖可知，第29圖的低通濾波器，滿足第2 8圖 所示的目標規格。又，通過區域的部分僅有些許（3 d B以 內）的超過（〇 v e r s h ο 〇 t )，想要將此平坦化的場合，進行 上述之斜率變換即可。 其次，說明藉由頻率帶域的穿透構成FM/AM廣播用 的帶通濾波器之例。使用本實施型態的濾波器設計法的話 ’可以自由決定帶通濾波器的中心頻率Fc或者訊號的採 樣頻率Fs之任一樣時，藉由最佳化頻率穿透的條件，可 以更簡化濾波器的構成。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -23- 200303648 A7 _____ B7_ 五、發明説明（2〇 ) (請先閲讀背面之注意事項再填寫本頁) 現在假設帶通濾波器的中心頻率Fc與訊號的採樣頻 率 Fs 的關係爲 Fs = 4*Fc。在 Fc = 450KHz 時，Fs=1.8MHz。 在這樣的設定的場合，可以不必組合低通濾波器與高通濾 波器藉由特性値彼此之抵銷來使必要的頻率帶域成爲穿透 ，而可以僅藉由高通濾波器的串聯接續就直接設計帶通濾 波器。 例如，僅藉由高通單元濾波器Η 1 1的串聯接續可以 構成FM用的帶通濾波器，藉由其接續數目m調整頻帶寬 幅（通過帶域寬度）。進而，藉由在此高通單元濾波器（ Hll ) m的後段接續高通單元濾波器（H2n ) m，可以調整 頻率特性的傾斜。 第32圖顯示中心頻率Fc爲450kHz的FM用帶通濾 波器的設計例。在第32圖之例，藉由串聯接續複數之高 通單元濾波器（H11 ) 12、（ H21 ) 5構成帶通濾波器。第 3 3圖顯示此第3 2圖所示之FM用帶通濾波器的頻率特性 ，第33圖（a)顯示全體之頻率-增益特性，第33圖（b )也合倂顯示頻率-相位特性。 經濟部智慧財產局員工消費合作社印製 如第33圖（a)所示，中心頻率Fc爲450kHz，-80dB 的部分的頻帶寬幅約爲400kHz可得極爲良好的帶通濾波 器。稍微發生一些洩漏，但此洩漏發生在- 80dB以上之落 入部分，幾乎可以忽視。此外，如第3 3圖（b )所示，在 通過帶域內實現相位的直線性。 根據如此構成的帶通濾波器的話，全體必要之分線數 ，如以下所述只需要相當少的量。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -24- 200303648 A 7 B7 五、發明説明（21 ) HI 1 ......12x 12= 144 個 H215........12x 5 = 60 個 (請先閱讀背面之注意事項再填寫本頁) 合計........204個 進而，對各分線輸出所必要的濾波器係數僅有-1Π 6, 1/16, -8/16，8/16等4種。可以使演算電路大幅簡化。 第34圖顯示中心頻率Fc爲450kHz的AM用帶通濾 波器的設計例。在第34圖之例，在第32圖所示之FM用 帶通濾波器的後段，進而串聯接續複數之低通單元濾波器 (L13)4、（L17)5、（L115)4、（L131)12 構成帶通濾 波器。第35圖顯示此第34圖所示之AM用帶通濾波器的 頻率特性，第3 5圖（a )顯示全體之頻率-增益特性，第 33圖（b )也合倂顯示頻率-相位特性。 如第35圖（a )所示，中心頻率Fc爲450kHz，-80dB 的部分的頻帶寬幅約爲20kHz可得極爲良好的帶通濾波器 。此場合也發生洩漏，但此洩漏發生在-80dB以上之落入 部分，幾乎可以忽視。此外，如第3 5圖（b )所示，在通 過帶域內實現相位的直線性。 經濟部智慧財產局8工消費合作社印製 第36圖係中心頻率Fc爲450kHz，-80dB的部分的頻 帶寬幅約爲400kHz的FM用帶通濾波器的其他設計例。 在第36圖之例，藉由串聯接續高通單元濾波器（H21 ) 4 與低通單元濾波器（L23 )構成帶通濾波器。根據此第36 圖之例，全體全體必要之分線數如以下所述，與第3 2圖 所示之例相比可以更簡單的構成得到具有相同頻率特性的 帶通濾波器。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -25- 200303648 A7 B7 五、發明説明（22 ) H214......12x 4= 48 個 L231......12x 1 = 12 個 C請先閱讀背面之注意事項存填寫本貢) 合計........60個 第3 7圖顯示此第3 6圖所示之FM (調頻）用帶通濾 波器的頻率特性，第37圖（a)顯示全體之頻率-增益特 性，第3 7圖（b )也合倂顯示頻率-相位特性。如第3 7圖 (a )所示，可得具有上述特性之極爲良好的帶通濾波器 。此場合發生的洩漏產生在-80dB以上之落入部分，幾乎 可以忽視。此外，如第37圖（b )所示，在通過帶域內實 現相位的直線性。 供實現以上所說明的本實施型態之數位濾波器的設計 方法之用的裝置，可以透過硬體構成、DSP、軟體等方式 來實現。例如透過軟體方式實現的場合，本實施型態的濾 波器設計裝置，實際上以電腦的CPU或MPU、RAM、 ROM等所構成，藉由被記憶於RAM或ROM或者硬碟等 之程式的動作而得以實現。 經濟部智慧財產局員工消費合作社印製 亦即，把以使電腦可以發揮上述本實施型態的機能的 方式使其動作之電腦程式紀錄於例如CD — ROM之類的記 錄媒體，並藉由將此讀入電腦而得以實現。作爲記錄上述 電腦程式的記錄媒體，除了 CD-ROM以外，可以使用軟碟 、硬碟、磁帶、光碟、M〇、DVD、非易失性記憶卡等。 此外，透過網際網路等網路把上述電腦程式下載至電腦也 可以實現。 亦即，把關於各種單元濾波器Lln，L2n，Hln，H2n的 本紙張尺度適用中國國家標準（CNS ) A4規格（210X 297公釐） -26- 200303648 A 7 B7 五、發明説明（23 ) 濾波器係數作爲資訊預先保持於RAM或者R〇M等記憶體 ，使用者指示關於單元濾波器Lln，L2n，Hln，H2n的任意 組合時，CPU使用被保持於上述記憶體的濾波器係數的資 訊，演算出被指示的組合所對應的濾波器係數而可以求得 α 例如，將各種單元濾波器Lln，L2n，Hln，H2n預先化 爲圖標（icon )(對應於各圖標把濾波器係數作爲資訊來 保存），使用者藉由在顯示器畫面上任意組合配置這些圖 標，使CPU自動計算出對應於該配列的濾波器係數而求 得之方法亦佳。此外，把所求得之濾波器係數自動進行快 速傅立葉變換（FFT )，將其結果作爲頻率-增益特性圖來 表示的話，可以確認所設計的濾波器的特性，可以更容易 地進行濾波器設計。 又，不僅是藉由電腦執行被供給的電腦程式而實現上 述實施型態的機能而已，該程式與電腦之操作系統（OS )或者與其他應用軟體等共同實現上述實施型態的機能的 場合，或者被供給之電腦程式的所有處理或者一部份處理 藉由電腦的擴張界面卡或功能擴充單元來進行而實現上述 實施型態的功能的場合，相關的電腦程式也都包含於本發 明的實施型態。 如以上所詳細說明的，在本實施型態，使用把指定的 基本數値列作爲濾波器係數的基本單元濾波器作爲基礎使 用1個以上的單元濾波器，藉由將其任意組合而設計具有 所要的頻率特性之FIR濾波器，因此可以僅藉由單元濾波 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） I-------裝-- (請先閱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骨合作社印製 -27- 200303648 A7 B7 五、發明説明（24 ) (請先閱讀背面之注意事項再填寫本頁) 器的組合自動產生複雜的濾波器係數。亦即’濾波器設計 法變得非常單純而且容易，即使非熟練的技術人員也可以 極爲簡便地進行濾波器設計。 此外，使用本實施型態所設計的濾波器電路所必要的 分線數目僅需非常少數，而且對各分線輸出所必要的濾波 器係數，僅有-1/16，1/16，-8/16，8/16等4種。可以使演 算電路大幅簡化。亦即，可以大幅削減電路元件數（特別 是乘法器）縮小濾波器電路規模，同時可以謀求耗電量的 降低，與演算負擔的減輕。 此外適用本實施型態所設計的濾波器電路，因爲係反 覆同一模式而成之極爲單純的構成，在積體化時可以縮短 工數，具有可以容易1C化的優點。此外，可得在特性面 上遮斷特性具有極大的改善可能，相位特性也成直線之極 爲優異的濾波器特性。 經濟部智慧財產局8工消費合作社印製 此外，在以上的說明僅顯示低通濾波器或帶通濾波器 的設計例，但藉由改變單元濾波器的組合方式，可以簡單 地以同一手法設計高通濾波器或頻帶消除濾波器、com濾、 波器、進而包括類比的任意波形的濾波器等。 又，在上述實施型態，作爲基本單元濾波器之例顯示 LOn〜L3n但並不以此爲限。亦即，使用絕對値「1」與「 8」之數値，把與第2圖不同的數値列作爲基本單元濾波 器的濾、波器係數亦可。此外，在上述實施型態，做爲單兀 濾波器之例顯示Lln，L2n，Hln，H2n等4種，但並不以此 爲限。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -28- 200303648 A7 ___B7_ 五、發明説明（25 ) (請先閱讀背面之注意事項再填寫本頁) 其他方面，上述之實施型態僅爲實施本發明之具體化 的一個範例而已，並不能夠據此限定解釋本發明的技術範 圍。亦即，本發明在不逸脫其精神以及不逸脫其主要特徵 的情況下，可以實施種種變形。 根據以上所說明之本發明，藉由任意組合把指定的基 本數値列作爲濾波器係數的基本單元濾波器所作成的1個 以上的單元濾波器而設計數位濾波器，可僅藉由組合單元 濾波器而得複雜的濾波器係數，即使非熟練技術人員也可 以極爲簡單地進行濾波器設計。 . 此外，根據本發明，所設計的數位濾波器電路所必要 的分線數目僅需非常少數，而且對各分線輸出所必要的濾 波器係數的種類也只需要非常少，可以使數位濾波器的構 成變得極爲簡單。亦即，可以大幅削減電路元件數（特別 是乘法器）縮小濾波器電路規模，同時可以謀求耗電量的 降低，與演算負擔的減輕。此外，所設計的濾波器電路， 因爲係反覆同一模式而成之極爲單純的構成，在積體化時 可以縮短工數，可以容易1C化。 經濟部智慧財產局員工消費合作社印製 產業上之利用可能性 本發明在可以簡易地設計具有所要的頻率特性的FIR 數位濾波器這方面相當有用。此外，本發明在可以簡易地 設計可以小電路規模高精度實現所要的頻率特性之FIR數 位濾波器這方面也相當有用。 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） -29-. P This paper size applies to China National Standard (CNS) A4 specification (210X297 mm) -9-200303648 A7 B7 V. Description of the invention (6) Rate-gain characteristics. Figure 28 shows an example of the target specification of the designed filter circuit (please read the precautions on the back before filling out this page). Figure 29 shows the circuit of a low-pass filter that achieves the target specification shown in Figure 28. example. Figure 30 shows the frequency-gain characteristics of the low-pass filter shown in Figure 29. Fig. 31 is an enlarged view showing a passage area of the frequency-gain characteristic shown in Fig. 30. Figure 32 shows a design example of a bandpass filter for FM. Fig. 33 shows the frequency characteristics of the FM band-pass filter shown in Fig. 32. Figure 34 shows a design example of a band pass filter for AM. Fig. 35 shows the frequency characteristics of the band pass filter for AM shown in Fig. 34. Figures 3 and 6 show other design examples of band pass filters for FM. Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs. Figure 37 shows the frequency characteristics of the band pass filters for FM shown in Figure 36. The figure numbers explain F0, Fl, F2, F3 basic unit filters 1-1, 1. 2.1.3, 1. 4, 1 · 5 D-type flip-flops 2.1, 2 · 2, 2 · 3, 2 · 4, 2 · 5, 2 · 6 Counters This paper size applies to China National Standard (CNS) Α4 specification (210 × 297 mm) ) -10- 200303648 A7 __ B7 printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs 5. Description of Invention (7) 3-t. 3-2. 3-3. 3-4. 30- Adder 4 Multiplier Best Mode for Implementing the Invention An embodiment of the present invention will be described below with reference to the drawings. The filter design method of this embodiment is a radical reexamination of the previous design method based on the calculation of filter coefficients. Instead, it uses a simple combination of unit filters described below to design the desired characteristics. FIR filter. That is, four types of element filters Lin, L2n, Hln, and H2n are made using the four types of elementary filters Fon, Fin, F2n, and F3n described below, and these four types of element filters Lin, L2n, Hln, and H2n are used and An FIR filter having a desired frequency characteristic is designed from a combination of these. (1) Basic unit filter Fig. 1 is a circuit configuration diagram of the most basic four types of basic unit filters F0, F1, F2, and F3. In addition, Fig. 2 shows a series of filter coefficients used in the four basic unit filters F0 to F3. Also "" η "after the symbols F0 to F3 of the basic unit filter represents the number of" 0 "inserted between the filter coefficients (see details below). F0 to F3 represents no insertion at all." 0 ". The basic unit filters F0 to F3 shown in Fig. 1 are connected to five D-type flip-flops 1. 1 ~ 1 · 5 delay the input signal in sequence by 1 clock CK. Next, for each D-type flip-flop 1. The signals taken from the output and input branches of 1 ~ 1 · 5 are counted by 6 counters 2 ~! ~ 2. 6 Multiply the filter separately (please read the notes on the back before filling in this page) • Binding and Binding% This paper size applies the Chinese National Standard (CNS) A4 specification (210 × 297 mm) -11-200303648 A7 B7 V. Description of the invention (8) (Please read the precautions on the back before filling in this page.) The result is an integer 値 h 1 ~ h 6 after multiplying the coefficient by 16 times. Multiply these results, and all the results are stolen by 5 additions. 3 · 1 ~ 3 5 cumulative. Furthermore, the multiplier 4 of the output stage of the adder 3 · 5 provided in the final stage reduces the addition output to 1/16 times, and restores the amplitude to output. In this embodiment, the four basic unit filters F0 ~ F3 are used, and the circuit configuration is as shown in Figure 1. Only the filter coefficients (counters 2-! To 2. The multipliers 値 hi ~ h6) of 6 are different. As can be seen from Fig. 2, the filter coefficients of the basic unit filters F0 to F3 are composed of extremely simple sequence numbers whose absolute values are only "1" or "8". The arrangement is different. Among them, regardless of the coefficients of the basic unit filters F0 to F3, the absolute multipliers 値 h3 and h4 of the line near the center are "8", and the multipliers 对其 h 1, and h of the line on both sides of the line 2. h 5 and h 6 are absolutely "1". Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs of the Consumer Cooperative (1-1) The first basic unit filter F0 The first basic unit filter F0 is the most basic filter, such as a low-pass filter L 1 η or a low-pass unit Components of the secondary filter L2n. Fig. 3 shows the frequency-gain characteristic of the first basic unit filter F0 (the result of FFT of the coefficients of the filter coefficients after fast Fourier transform FFT), (a) represents the gain on a linear coordinate axis, ) The gain is shown on a logarithmic axis. Here in Figure 3, the gain and frequency are both referenced at 1. (1-2) The second basic unit filter F1 This paper size is applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) -12- 200303648 A7 ___ B7_ V. Description of the invention (9) (Please read the note on the back first Please fill in this page again.) The second basic unit filter F1 is a component of the high-pass unit secondary filter Η2n, for example. Fig. 4 shows the frequency-gain characteristics of the second basic unit filter fi. (A) represents the gain on a linear axis, and (b) represents the gain on a log axis. In this figure, the gain and frequency are also referenced by 1. (1-3) The third and fourth basic unit filters F2 and F3 The third and fourth basic unit filters F2 and F3 are, for example, a combination of these to form a high-pass unit filter Hln. Figures 5 and 6 show the frequency-gain characteristics of the third and fourth basic unit filters F2 and F3, respectively. (A) represents the gain on a straight axis and (b) represents the gain on a logarithmic axis. In Figures 5 and 6, the gain and frequency are also referenced at 1. (2) Unit filters The unit filters Lln, L2n, Hln, H2n are generated by the above-mentioned basic unit filters FOn, Fln, F2n, F3n. Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs, Consumer Cooperative (2-1) Low-pass unit filter Lin, for example, the filter coefficient of low-pass unit filter L 1 0 is shown in Figure 7, which is based on the basic unit filter. The filter coefficient of F0 is generated by performing a moving average calculation. FIG. 8 shows a circuit configuration of the low-pass unit filter L 1 0. As shown in Figure 8, the low-pass element filter L 1 0 is connected to the basic unit -13- This paper size applies the Chinese National Standard (CNS) A4 specification (210X 297 mm) 200303648 A7 B7 V. Description of the Invention (1〇) (Please read the precautions on the back before filling this page) Filter (F0) 1 The D-flip (flip-flop) 12 in the latter stage makes the output of the basic unit filter 1 1 The signal is delayed by only 1 clock CK. Next, the delayed forward and backward signals are accumulated by the adder 1 3 by the D-type flip-flop 1 2, and the addition output is reduced by 1/2 times by the multiplier 14 to return the vibration to the original size and output. The filter coefficients of the low-pass unit filter L 1 1 are generated by inserting a "0" between each filter coefficient of the low-pass unit filter L 1 0 described above. That is, as shown in Fig. 9, the filter coefficients of the low-pass unit filter L 1 1 are generated by performing a moving average calculation on the filter coefficients of the basic unit filter F01. FIG. 10 shows a circuit configuration of the low-pass unit filter L 1 1. As shown in FIG. 10, the low-pass unit filter L 1 1 is connected to the two D-type flip-flops 22-! And 22-i in the rear stage of the basic unit filter (F01) 21 in the longitudinal direction. The output signal of the basic unit filter 21 is delayed by only 1 clock CK. Next, two D-type flip-flops 22 will be used. ' twenty two. The delayed signals are accumulated by the adder 23, and the added output is reduced by a factor of 1/2 by the multiplier 24, so that Zhenfu returns to the original size and is output. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. Similarly, the low-pass unit filter Lin (n = 2,3 ,. . . . ) Filter coefficients are generated by inserting n "0" between each filter coefficient of the low-pass unit filter L 1 0. Figure 11 shows the frequency-gain characteristics of the low-pass unit filter L 1 0 and the low-pass unit filter L 1 1 generated by inserting a "0" between each filter coefficient. (A) is based on The linear coordinate axis represents the gain, and (b) represents the gain using the logarithmic coordinate axis. In Figure 11 here, the gain and frequency $ paper dimensions are applicable to the Chinese National Standard (CNS) A4 specifications (210X297 mm) -14- 200303648 A7 B7 V. Description of the invention (11) (Please read the notes on the back before filling This page) are benchmarked at 1. From Fig. 11, it can be seen that if the number of "0" inserted between the filter coefficients is η, the frequency axis (period in the flat direction) of the frequency-gain characteristic becomes 1 / η. (2-2) Series connection of low-pass unit filter Lin By connecting unit filters in series, the coefficients of each unit filter are multiplied / added to each other to make new filter coefficients. Hereinafter, for example, when the series number of the low-pass element filter L 10 is m, this is described as (L10) m. Figure 12 shows the low-pass element filter L 1 0, (L 1 0) 2, (L 1 0) 4, (L 1 0) 8 frequency-gain characteristics, (a) represents the gain on a straight axis, and (b) represents the gain on a log axis. In Figure 12 here, the gain and frequency are both referenced at 1. When there is only one low-pass element filter L 1 0, the amplitude is 0. The clock at position 5 is 0. 25. When the number of series is increased, the passband of the filter becomes narrower. For example, for a field of m = 8, the amplitude becomes 0. The clock at position 5 is 0. 1 2 5. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. As can be seen from the above Figure 12, the low-pass unit filter L10 has a very steep cut-off frequency characteristic of the frequency characteristic. The above characteristics. With this low-pass element filter L 1 0, characteristics equivalent to those of the basic element filter F0 1 can be obtained. Although the frequency-gain characteristics of the basic unit filter F0 1 are not particularly shown, the shoulders (passing areas) of the characteristics are slightly increased, so the above-mentioned series connection is slightly difficult to use. At this point, the basic unit filter F 1 丨 is ideal. Low-pass element filter (L 1 0) m, can obtain extremely deep straight paper size even in low frequency area. Applicable to China National Standard (CNS) A4 specification (210X297 mm) -15- 200303648 A7 B7 V. Description of the invention ( 12) Connected lowering characteristics. (Please read the notes on the back before filling this page) (2-3) Low-pass unit secondary filter L2n Low-pass unit secondary filter L2n is required to have a severe cut-off characteristic 'suitable for use in series connection The final segment of the filter. For example, the low-pass unit secondary filter L20 is generated by connecting two basic unit filters F0 in series in series, as shown in FIG. FIG. 14 shows a circuit configuration of the low-pass unit secondary filter L20. As shown in Fig. 14, the low-pass unit secondary filter L20 is formed by connecting two basic unit filters (F0) 31 "and 32 ·! In the vertical direction. Figure 15 shows the frequency-gain characteristics of the low-pass unit secondary filter L20. (A) represents the gain on a straight axis and (b) represents the gain on a logarithmic axis. In Fig. 15, the gain and frequency are also referenced by 1. From Figure 15, it can be seen that the cut-off characteristic is very sharp and the shoulder (passing area) is raised. This low-pass unit secondary filter L20 is most suitable for the final stage of the filter block. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs and the case of the low-pass unit filter L 1 η, the filter coefficients of the low-pass unit secondary filter L2n (η 2 1) are filtered twice in the low-pass unit. The filter coefficients of the filter L20 are generated by inserting n "0" s between the filter coefficients. In addition, by connecting m low-pass unit secondary filters L2n in series, new filter coefficients can be made. The frequency-gain characteristic of the low-pass unit second-order filter (L2n) π becomes narrower when the number of cascades m is larger. Even at low frequencies, extremely deep direct drop characteristics can be obtained. This paper size applies to China National Standard (CNS) A4 specification (210X 297 mm) -16- 200303648 Α7 Β7 V. Description of the invention (13) (2-4) High-pass unit filter Hln (Please read the precautions on the back before (Fill in this page) The filter coefficients of the high-pass element filter Η 10 are generated by performing a moving average calculation on the filter coefficients of the basic element filters F2 and F 3 as shown in Figure 16. Figure 17 shows the circuit configuration of the high-pass unit filter Η 10. As shown in Figure 17, in the high-pass unit filter Η 10, the input signal passes through two basic unit filters (F2) 41, (F3) 42, and the output signal of one basic unit filter 42 is connected by The D-type flip-flop 43 in the latter stage is delayed by only 1 clock CK. Next, the output signal of the basic unit filter 41 is added by the adder 44 and the output signal of the basic unit filter 42 delayed by 1 clock by the D-type flip-flop 43, and the addition output is reduced by 1 / The amplitude is reduced twice and output. In the case of the bone-eliminating cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs, the same as in the case of the low-pass unit filter L 1 η, the filter coefficient of the high-pass unit filter Η 1 η (η-1) is determined by the high-pass unit filter Η 1 It is generated by inserting n "0" between each filter coefficient of Ο. In addition, by connecting m high-pass unit filters Η 1 η in series, a new filter coefficient can be made. The frequency-gain characteristic of the high-pass unit filter (Hln) m. The larger the number of series m, the narrower the passband width. Even at high frequencies, extremely deep direct drop characteristics can be obtained. Figure 18 shows the frequency-gain characteristics of the high-pass element filter Η 1 1 and the high-pass element filter Η 1 1 generated by inserting one ^ 0 ″ between each filter coefficient. From Figure 18, it can be seen that even in the case of a high-pass unit filter, inserting n ^ 0 "between filter coefficients can make the frequency axis (period of the flat direction) of the frequency-gain characteristic 1 / η. This paper size applies Chinese National Standard (CNS) A4 specification (210X297 mm) -17- 200303648 A7 _ B7 V. Description of the invention (14) (Please read the precautions on the back before filling this page) In addition, Section 1 9 The figure shows the frequency-gain characteristics of the high-pass element filter Η 1 0, (Η 1 0) 2, (Η 1 0) 4, and (Η 1 0) 8. (a) represents the gain on a linear coordinate axis, and (b) represents Gain is expressed on a logarithmic axis. In FIG. 19, the gain and frequency are also referenced by 1. When there is only one high-pass unit filter H10, the amplitude is 0. The clock at position 5 is 0. 25. When the number of series is increased, the passband width of the filter becomes narrower. For example, the amplitude becomes 0. The clock at position 5 is 0. 375. As can be seen from the above Fig. 19, the high-pass unit filter H10 has a characteristic that the cut-off frequency portion of the frequency characteristic has a very steep slope, and a characteristic of 106 dB / octave or more can be obtained. Regarding the high-pass element filter (Η 1 0) m, extremely deep direct drop characteristics can also be obtained in the high-frequency region. Comparing the eighteenth and nineteenth figures, and the eleventh and twelfth figures shown previously, it can be seen that the high-pass element filter (Η 10) m and the low-pass element filter (L10) are symmetrical filters. (2-5) High-pass unit secondary filter H2n The high-pass unit secondary filter H2n printed by the 8th Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs is required to have a severe cut-off characteristic, which is suitable for use in series-connected filters. The final stage. For example, the high-pass unit secondary filter H20, as shown in Figure 20, is generated by connecting two basic unit filters F 1 in series in series. Figure 21 shows the circuit configuration of the high-pass unit secondary filter H20. As shown in FIG. 21, the high-pass unit secondary filter H20 is configured by vertically connecting two basic unit filters (F1) 51 ″ and 51 ″. Figure 22 shows the frequency-gain characteristics of the high-pass unit secondary filter H20. (A) represents the gain with a linear coordinate axis, and (b) represents the paper scale with logarithmic coordinates. The Chinese National Standard (CNS) A4 specification (210X297 cm) -18) 200303648 A7 B7 V. Description of Invention (15) (Please read the precautions on the back before filling this page) The axis indicates gain. In Figure 22, the gain and frequency are also normalized with ^ 1 ″. From Figure 22, it can be seen that the cut-off characteristic is very sharp and the shoulder (passing area) is raised. This high-pass unit secondary filter H20 is most suitable for the final stage of the filter block. As in the case of the low-pass element filter L 1 η, the high-pass element secondary filter Η2η (η-1) has the waveritter coefficients inserted between the filter coefficients of the high-pass element secondary filter Η20. η "0". In addition, by connecting m high-pass unit secondary filters Η2η in series, a new filter coefficient can be made. The frequency-gain characteristic of the secondary filter (H2n) m of the high-pass unit becomes narrower when the number of cascades m is greater, and it can obtain extremely deep direct drop characteristics even at high frequencies. (3) Penetration in the frequency band Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs, 8 Industrial Consumer Cooperative, Penetration in the frequency band, using more than 4 unit filters in series. FIG. 23 shows the frequency-gain characteristics of the low-pass unit filters (L 1 0) 4, (L 1 1) 4, (L13) 4, and (L17) 4. In addition, Fig. 24 shows a graph in which these four frequency-gain characteristics are integrated into one graph. The gains and frequencies of Figures 23 and 24 are also benchmarked with "1". Fig. 25 shows an appropriate combination of a low-pass unit filter (L 1 0) 4, (L 1 1) 4, (L 1 3) 4, (L 1) having the frequency characteristics shown in Figs. 23 and 24 above. 7) 4 is an example of frequency band penetration. As shown in FIG. 24, when the low-pass unit filters (L 1 0) 4, (L 1 1) 4, (L Π) 4, and (L 1 7) 4 are appropriately combined, each characteristic 値 cancels each other out and Performs penetration in the frequency band. In addition, using these waveforms as a basic combination, this paper size applies the Chinese National Standard (CNS) A4 specification (210X 297 mm) -19- 200303648 A7 B7_ V. Description of the invention (16) Reverse the frequency axis as needed By moving in the direction, a filter can be made to pass only a desired frequency band. (Please read the precautions on the back before filling this page) Figure 25 (a) is a combination of 4 low-pass element filters (L 10) 4, (L 1 1) 4, (L Π) 4, (L 1 7) 4 and the frequency characteristics obtained when these are connected in series. According to this, it can be obtained that the extremely low frequency region becomes a low-pass filter in the pass range, but a slight leakage occurs (however, this leakage occurs in the part that exceeds -106dB and can be ignored). Figure 25 (b) shows that in addition to the four low-pass unit filters (L10) 4, (L 1 1) 4, (L 1 3) 4, and (L 1 7) 4, a combined low-pass unit is added twice. Filter (L27) 8 and the frequency characteristics obtained when these are connected in series. According to this result, an extremely narrow region at a low frequency becomes a pass region, and a low-pass filter having an amount of fall of 200 dB or more can be obtained. And there is no leakage at all. Fig. 25 illustrates the use of a low-pass unit filter (L 1 n) printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs (m ^ 4) or a low-pass unit secondary filter (L2n) m (m- 4) An example of frequency band penetration, but a high-pass unit filter (Hln) m (mg 4) or a high-pass unit secondary filter (H2n) m (m -4) Domain penetration is also possible. In addition, through the combination of these various unit filters (Lin) m, (L2n) m, (Hln) m, (lihi) m to perform frequency band penetration is also possible. Fig. 26 shows other examples of penetration in the frequency band. (4) Tilt adjustment (slope conversion) By fixing the clock position to -6dB, and adding the frequency characteristics, this paper scale applies the Chinese National Standard (CNS) 8-4 specification (210X297 mm) -20- 200303648 A7 B7. V. The gradient of the waveform of the invention description (17) becomes a sharp method, which makes the necessary frequency characteristics easier to achieve. That is, in order to contain the characteristic within the desired frequency range, it would be convenient if the slope of the waveform of the frequency characteristic can be adjusted. Fig. 27 is a method for explaining the slope conversion method of the fixed -6 d B position. The frequency-gain characteristic graphs used ('a') represent gains on a straight axis, and (b) represent gains on a logarithmic axis. In FIG. 27, the gain and frequency are also referenced by 1. Here, the original data uses the frequency-gain characteristic (①) of the low-pass element filter L10 to explain the situation where the tilt is severe when the position is fixed at -6dB. As described above, when two low-pass unit filters l 10 are connected in series, the tilt can be sharpened, but the clock position at -6 d B is shifted to the left (low-frequency side) (②). Here, the operations described below are performed. First take the center of the gain 値 (= 0 _ 5) as the axis, and invert the frequency-gain characteristic of the low-pass element filter (L 1 0) 2 shown in ② (③). This is by subtracting the filter coefficient of the low-pass unit filter (L 1 0) 2 from the unit pulse of the reference gain 値 "1" (equivalent to the filter coefficients of center 値 1 and all other 0) by matching the delay. And find it. The frequency-gain characteristic of ③ shows the characteristics of the local-pass filter (herein referred to as an inverting high-pass filter). Next, 'two inversion high-pass filters shown in (3) are connected in series. The slope of the frequency-gain characteristic obtained by this becomes more acute, and the clock position of -6dB moves to the right (high-frequency side) (④). At this time, by making the number of serially connected inverse high-pass filters the same as in the case of ② (2), the amount of movement to the high-frequency side and the amount of movement to the low-frequency side can be made. National Standard (CNS) A4 specification (21 × 297 mm) I --------_ equipment-(Please read the precautions on the back before filling out this page) Ordered by the Intellectual Property Bureau of the Ministry of Economic Affairs, Consumer Consumption Cooperatives System-21-200303648 A7 B7 V. Description of the invention (18) (Please read the notes on the back before filling this page) to the same extent. Finally, invert the frequency-gain characteristic shown in (4), using the center of the gain (= 0.5) as the axis. This is obtained by subtracting the filter coefficient of ④ from the unit pulse of the reference gain 値 "1" by matching the delay. Observe that the frequency characteristics of the input data ① and the frequency characteristics of the output data ⑤ intersect at a clock position of -6dB. The slope of the frequency characteristics of the output data ⑤ is even more severe than that of the input data ①. (5) Circuit example Next, an actual circuit example is shown. The target specifications are shown in Figure 2-8. That is, the design of the low-pass filter with an attenuation of 106 dB / octave or more is the goal here. Figure 29 shows a circuit example of a low-pass filter that achieves this target specification. The attenuation 値 depends on the number of filters connected in series, and the attenuation in the case of 4 connected in series is about 40dB / octave. This time, it is necessary to have an attenuation of more than 106dB. In principle, there are 8 filters connected in series. The consumer cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs printed the circuit shown in Figure 29, showing that there are 8 low-pass unit filters L 1 0, 8 low-pass unit filters L 1 1, and low-pass unit filters L1. There are 8 low-pass element filters L 1 7 and 4 low-pass element secondary filters L27. They are formed in series in this order. From Fig. 29, it can be seen that according to the filter design method of this embodiment mode, a low-pass filter having a desired characteristic can be obtained by a very simple configuration in which the same unit filter is repeatedly constructed. In addition, the internal structure of each unit filter is as described above. All paper sizes must be in accordance with Chinese National Standards (CNS) 8-4 specifications (210X29 * 7 mm). -22- 200303648 A7 B7 V. Description of invention (19) The number of lines, as described below, requires only a relatively small amount. L108. . . . . . . . 6x 8 = 48 (Please read the notes on the back before filling this page) L118. . . . . . . . 6x 8 = 48 L138. . . . . . . . 6x 8 = 48 L174. . . . . . . . 6x 4 2 24 L278. . . . . . . . 1 2x 8 = 96 total. . . . . . . . 264 There are only four types of filter coefficients necessary for each branch line output, 1/16, 1/16, -8/16, and 8/16. In particular, _8 / 16 = -1/2 and 8/16 = 1/2 can greatly simplify the calculation circuit. The Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs prints Figure 30, showing the frequency-gain characteristics of the low-pass filter shown in Figures 29 and 9, where (a) represents the gain on a straight axis and (b) represents the logarithm The coordinate axis represents the gain. In addition, Fig. 31 is an enlarged view of the passage area of the frequency-gain characteristic shown in Fig. 30. (a) represents the gain on a linear axis and (b) represents the gain on a logarithmic axis. As can be seen from Figs. 30 and 31, the low-pass filter of Fig. 29 meets the target specifications shown in Fig. 28. In addition, if the portion of the pass area is slightly (within 3 d B) exceeding (0 v er s h ο 〇 t), the above-mentioned slope conversion may be performed when it is desired to flatten this. Next, an example in which a band-pass filter for FM / AM broadcasting is constituted by penetration in the frequency band will be described. When the filter design method of this embodiment is used, when the center frequency Fc of the band-pass filter or the sampling frequency Fs of the signal can be freely determined, the filter can be simplified by optimizing the frequency penetration conditions Composition. This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) -23- 200303648 A7 _____ B7_ V. Description of the invention (20) (Please read the precautions on the back before filling this page) Now assume bandpass filtering The relationship between the center frequency Fc and the sampling frequency Fs of the signal is Fs = 4 * Fc. At Fc = 450KHz, Fs = 1. 8MHz. In such a setting, it is not necessary to combine the low-pass filter and the high-pass filter to make the necessary frequency band penetrate through the characteristics 値 cancellation of each other, and it is possible to directly directly connect the high-pass filter in series. Design a band-pass filter. For example, only a series connection of the high-pass unit filter Η 1 1 can constitute a band-pass filter for FM, and the frequency bandwidth (by the band width) can be adjusted by the number of connections m. Furthermore, by connecting the high-pass unit filter (H2n) m to the subsequent stage of the high-pass unit filter (Hll) m, the tilt of the frequency characteristics can be adjusted. Fig. 32 shows a design example of an FM band-pass filter having a center frequency Fc of 450 kHz. In the example in FIG. 32, a band-pass filter is formed by connecting a plurality of high-pass unit filters (H11) 12, (H21) 5 in series. Figure 33 shows the frequency characteristics of the FM bandpass filter shown in Figure 32, Figure 33 (a) shows the overall frequency-gain characteristics, and Figure 33 (b) shows the frequency-phase in combination. characteristic. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs As shown in Figure 33 (a), the center frequency Fc is 450kHz, and the band width of the -80dB part is about 400kHz. A very good bandpass filter is obtained. Some leaks occur slightly, but this leak occurs in the part above -80dB, which can be almost ignored. In addition, as shown in Fig. 33 (b), the linearity of the phase is achieved in the pass band. According to the band-pass filter configured in this way, the number of division lines necessary for the whole is only a relatively small amount as described below. This paper size applies to Chinese National Standard (CNS) A4 specification (210X297 mm) -24- 200303648 A 7 B7 V. Description of invention (21) HI 1. . . . . . 12x 12 = 144 H215. . . . . . . . 12x 5 = 60 (Please read the notes on the back before filling out this page) Total. . . . . . . . 204 Further, there are only four kinds of filter coefficients necessary for the output of each branch line, such as -1Π 6, 1/16, -8/16, and 8/16. Can greatly simplify the calculation circuit. Fig. 34 shows a design example of an AM bandpass filter having a center frequency Fc of 450 kHz. In the example in FIG. 34, the complex low-pass unit filters (L13) 4, (L17) 5, (L115) 4, (L131) ) 12 constitutes a band-pass filter. Fig. 35 shows the frequency characteristics of the band pass filter for AM shown in Fig. 34, Fig. 35 (a) shows the overall frequency-gain characteristics, and Fig. 33 (b) shows the frequency-phase characteristics together. . As shown in FIG. 35 (a), the center frequency Fc is 450 kHz, and the frequency bandwidth of the part of -80 dB is about 20 kHz, and a very good band pass filter can be obtained. Leaks also occur in this case, but this leak occurs in the part falling above -80dB, which can be almost ignored. In addition, as shown in Fig. 35 (b), the linearity of the phase is achieved in the pass band. Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs, 8th Industrial Cooperative, Figure 36 shows another design example of an FM bandpass filter with a center frequency Fc of 450kHz and a frequency band of -80dB. In the example in FIG. 36, a band-pass filter is formed by connecting a high-pass unit filter (H21) 4 and a low-pass unit filter (L23) in series. According to the example in FIG. 36, the necessary number of division lines for the entirety is as described below. Compared with the example shown in FIG. 32, a band pass filter having the same frequency characteristics can be obtained in a simpler configuration. This paper size applies to Chinese National Standard (CNS) A4 specification (210X 297 mm) -25- 200303648 A7 B7 V. Description of invention (22) H214. . . . . . 12x 4 = 48 L231. . . . . . 12x 1 = 12 C, please read the notes on the back and fill in the tribute) Total. . . . . . . . Fig. 37 shows the frequency characteristics of the band-pass filter for FM (frequency modulation) shown in Fig. 36, Fig. 37 (a) shows the overall frequency-gain characteristics, and Fig. 37 (b) also shows Combined display frequency-phase characteristics. As shown in Fig. 37 (a), a very good band-pass filter having the above characteristics can be obtained. The leakage that occurs in this case is caused by the drop above -80dB, which can be almost ignored. In addition, as shown in Fig. 37 (b), the linearity of the phase is achieved in the pass band. The device for implementing the design method of the digital filter of the embodiment described above can be realized by means of hardware configuration, DSP, software, and the like. For example, when implemented by software, the filter design device of this embodiment actually consists of a computer's CPU or MPU, RAM, ROM, etc., and operates by programs stored in RAM, ROM, or hard disk. And it came true. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs, that is, recording a computer program that causes a computer to operate in a manner that enables the computer to perform the functions of the embodiment described above on a recording medium such as CD-ROM, and This is realized by reading into the computer. As a recording medium for recording the above-mentioned computer program, in addition to a CD-ROM, a floppy disk, a hard disk, a magnetic tape, an optical disk, a Mo, a DVD, a nonvolatile memory card, or the like can be used. In addition, it is also possible to download the above computer program to a computer through a network such as the Internet. That is, the paper dimensions of various unit filters Lln, L2n, Hln, H2n are applied to the Chinese National Standard (CNS) A4 specification (210X 297 mm) -26- 200303648 A 7 B7 V. Description of the invention (23) Filtering The device coefficients are held in advance in memory such as RAM or ROM. When the user instructs any combination of the unit filters Lln, L2n, Hln, H2n, the CPU uses the information of the filter coefficients held in the above memory. By calculating the filter coefficients corresponding to the indicated combination, α can be obtained. For example, various unit filters Lln, L2n, Hln, H2n are converted into icons in advance (corresponding to the icons, the filter coefficients are used as information). Save). The user can arrange the icons on the display screen in any combination to make the CPU automatically calculate the filter coefficients corresponding to the arrangement. In addition, if the obtained filter coefficients are automatically subjected to a fast Fourier transform (FFT), and the results are displayed as a frequency-gain characteristic graph, the characteristics of the designed filter can be confirmed, and the filter design can be performed more easily. . In addition, the function of the above-mentioned implementation type is not only realized by a computer executing a supplied computer program, but the program and the operating system (OS) of the computer or other application software together realize the function of the above-mentioned implementation type. When all or part of the processing of the supplied computer program is performed by a computer expansion interface card or a function expansion unit to realize the functions of the above-mentioned implementation type, the relevant computer programs are also included in the implementation of the present invention. Type. As explained in detail above, in this embodiment mode, a basic unit filter using a specified basic number sequence as a filter coefficient is used as a basis, and one or more unit filters are used. The combination is designed to have The FIR filter with the required frequency characteristics, so it can be filtered only by the unit. The paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm). I ------- install-(Please read the back Please fill in this page for the matters needing attention) Order printed by the Bone Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs -27- 200303648 A7 B7 V. Description of the invention (24) (Please read the precautions on the back before filling this page) The combination of devices is automatically generated Complex filter coefficients. That is, the "filter design method" becomes very simple and easy, and even a non-skilled technician can design the filter extremely easily. In addition, the number of branch lines necessary to use the filter circuit designed in this embodiment mode is very small, and the filter coefficients necessary for the output of each branch line are only -1/16, 1/16, -8 / 16, 8/16, etc. 4 kinds. Can greatly simplify the calculation circuit. In other words, the number of circuit components (especially the multiplier) can be greatly reduced, and the filter circuit scale can be reduced. At the same time, the power consumption can be reduced and the calculation load can be reduced. In addition, the filter circuit designed according to this embodiment mode has a very simple structure in which the same mode is repeated, and the number of steps can be shortened during integration, which has the advantage of being easily 1C. In addition, it is possible to obtain an excellent filter characteristic in which the blocking characteristic is greatly improved and the phase characteristic is extremely straight. Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs and the Industrial Cooperative Cooperative. In addition, the above description only shows a design example of a low-pass filter or a band-pass filter. However, by changing the combination of unit filters, it can be simply designed in the same way. A high-pass filter, a band elimination filter, a com filter, a wave filter, and an analog arbitrary wave filter. In the above embodiment, LOn to L3n are shown as an example of the basic unit filter, but it is not limited to this. That is, using the numbers "1" and "8" in absolute terms, and using a number series different from that in Fig. 2 as the filter and wave filter coefficients of the basic unit filter. In addition, in the above-mentioned embodiment, four types of Lln, L2n, Hln, and H2n are shown as examples of the simple filter, but it is not limited thereto. This paper size applies Chinese National Standard (CNS) A4 specification (210X297 mm) -28- 200303648 A7 ___B7_ V. Description of the invention (25) (Please read the precautions on the back before filling this page) In other aspects, the above implementation type The aspect is only an example of the embodiment of the present invention, and the technical scope of the present invention should not be limitedly interpreted based on this. That is, the present invention can be variously modified without departing from its spirit and its main features. According to the present invention described above, a digital filter can be designed by arbitrarily combining one or more unit filters made of a basic unit filter using a specified elementary number array as a filter coefficient, and only by combining units Filters have complex filter coefficients, and even non-skilled technicians can carry out filter design very simply. . In addition, according to the present invention, the number of branch lines necessary for the designed digital filter circuit only needs to be very small, and the type of filter coefficients necessary for the output of each branch line is also very small. The composition becomes extremely simple. In other words, the number of circuit components (especially the multiplier) can be greatly reduced, and the filter circuit scale can be reduced. At the same time, the power consumption can be reduced and the calculation load can be reduced. In addition, the designed filter circuit has a very simple structure by repeating the same pattern, which can shorten the number of operations when integrated, and can be easily realized in 1C. Printed by the Consumer Property Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs Industrial Applicability The present invention is very useful in that an FIR digital filter having a desired frequency characteristic can be easily designed. In addition, the present invention is also very useful in that an FIR digital filter that can achieve a desired frequency characteristic with a small circuit scale and high accuracy can be simply designed. This paper size applies to China National Standard (CNS) A4 (210X297 mm) -29-