傅立葉變換與濾波器形狀(文件)
【正文】 Ω= 2π f/fs f= Ω fs/2π 以數(shù)字頻率 Ω 表示的數(shù)字頻率特性，只有當(dāng)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(dāng) 沿單位圓移動(dòng)，最靠近極點(diǎn) p時(shí)，幅度響應(yīng)為最大值，即 和極點(diǎn) p的相位相符時(shí) ,可獲得最大幅度 .而且極點(diǎn)位置越靠近單位圓 ,這個(gè)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(yīng)和相位響應(yīng)。2022 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 模擬頻率 f 與數(shù)字頻率 Ω 數(shù)字濾波器的形狀 |H(Ω)|設(shè)計(jì)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(yīng)是增益對(duì)數(shù)字頻率（弧度 )的關(guān)系圖 .相位響應(yīng)是相位 (弧度 )對(duì)數(shù)字頻率 (弧度 )的關(guān)系圖 .數(shù)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(zhǔn)確度可選用更小的間隔 .對(duì)于 弧度 ,采用非極坐標(biāo)計(jì)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(yīng)是周期性的 ,每 2 弧度重復(fù)一次 ,幅度響應(yīng)是偶函數(shù) ?( ) ( )HH? ? ? ?相位響應(yīng)是周期性的 ,每 2 弧度重復(fù)一次 ,幅度響應(yīng)是奇函數(shù) ?( ) ( )??? ? ? ? ?所以 ,一般沒(méi)有必要記錄幅度響應(yīng)和相位響應(yīng)在 左邊部分 ,而且 ,考慮 的值沒(méi)有實(shí)際意義 ,所以實(shí)際數(shù)字濾波器的頻率響應(yīng)一般畫出 部分 . 幅度響應(yīng) :線性增益 對(duì)數(shù)字頻率 的曲線畫出 。因?yàn)橄辔徊顬?86186。 對(duì)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(wú)單位，或 dB 20log|H(Ω)| ) Θ(Ω) 是數(shù)字
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