【正文】 Ω= 2π f/fs f= Ω fs/2π 以數字頻率 Ω 表示的數字頻率特性，只有當采樣頻率選定后才能確定。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 720 Magnitude response for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。當 沿單位圓移動，最靠近極點 p時，幅度響應為最大值，即 和極點 p的相位相符時 ,可獲得最大幅度 .而且極點位置越靠近單位圓 ,這個最大值就越大 . 11()j jH ep ep? ?? ? ?? ?1jep?? 到 的 距 離? je?je??FIGURE 725 Graphical view of filter shape. Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 729 Filter shape for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 733 Frequency response for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 731 Filter shapes for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 727 Filter shape for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 722 Magnitude response for fs = 10 kHz for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。 圖 20log|H(Ω)|~ Ω 和 Θ(Ω) ~ Ω 的表示的 幅度響應和相位響應。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 模擬頻率 f 與數字頻率 Ω 數字濾波器的形狀 |H(Ω)|設計可不依賴采樣頻率(sampling frequency)，但所選的采樣頻率將影響濾波器輸入頻率的范圍。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 715 Pulse passed through b filter. Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 713 Frequency response for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 710 Frequency responses for mon filters. Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 79 Frequency response for Example . Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright 169。幅度響應是增益對數字頻率（弧度 )的關系圖 .相位響應是相位 (弧度 )對數字頻率 (弧度 )的關系圖 .數字頻率范圍是 1()1 0 . 4 jH e ???? ?~3???解 : 弧度間隔選擇是任意的 ,要獲得更高的準確度可選用更小的間隔 .對于 弧度 ,采用非極坐標計算 : 3 / 4???3 / 411( 3 / 4) )331 0. 41 0. 4(c os ( ) s i n( ) )44111 0. 4 ( 0. 70 71 0. 70 71 ) 1. 28 28 0. 28 281 1. 28 28 0. 28 281. 28 28 0. 28 28 1. 28 28 0. 28 280. 74 34 0. 16 39 0. 76 12 0. 21 70jHejjjjjjj????????????? ? ? ? ?????? ? ? ?幅度響應是周期性的 ,每 2 弧度重復一次 ,幅度響應是偶函數 ?( ) ( )HH? ? ? ?相位響應是周期性的 ,每 2 弧度重復一次 ,幅度響應是奇函數 ?( ) ( )??? ? ? ? ?所以 ,一般沒有必要記錄幅度響應和相位響應在 左邊部分 ,而且 ,考慮 的值沒有實際意義 ,所以實際數字濾波器的頻率響應一般畫出 部分 . 幅度響應 :線性增益 對數字頻率 的曲線畫出 。因為相位差為 86186。 對于任一給定頻率 Ω ，輸出的幅度是濾波器的增益和 輸入幅度的積，輸出的相位是濾波器的相位差和輸入 相位的和。 （無單位，或 dB 20log|H(Ω)| ) Θ(Ω) 是數字