【摘要】：全通IIR數(shù)字濾波器在數(shù)字信號處理領(lǐng)域有著廣泛的應(yīng)用，它可用做相位均衡器，也可用于濾波器組、半帶濾波器和陷波濾波器的設(shè)計。因此它的設(shè)計問題吸引了許多學者的關(guān)注。 本文針對全通IIR數(shù)字濾波器的minimax設(shè)計問題展開研究。首先建立全通IIR數(shù)字濾波器的頻率響應(yīng)誤差設(shè)計模型；然后結(jié)合一般IIR數(shù)字濾波器的設(shè)計算法，得到四種全通IIR數(shù)字濾波器minimax頻率響應(yīng)誤差設(shè)計算法；最后提出迭代重加權(quán)方法設(shè)計具有近似均勻群延遲誤差的全通濾波器，并將其應(yīng)用于半帶濾波器的設(shè)計。本文主要做了以下工作： （1）首先分析全通IIR數(shù)字濾波器相位響應(yīng)誤差和頻率響應(yīng)誤差的關(guān)系，建立全通IIR數(shù)字濾波器頻率響應(yīng)誤差設(shè)計模型。全通IIR數(shù)字濾波器在全頻域[0, π]范圍內(nèi)幅頻響應(yīng)恒為一，它的設(shè)計問題是一個純相位逼近問題。本文分析了全通濾波器的頻率響應(yīng)誤差與相位響應(yīng)誤差之間的對應(yīng)關(guān)系，并基于此分析建立頻率響應(yīng)誤差設(shè)計模型，以實現(xiàn)全通IIR數(shù)字濾波器的優(yōu)化設(shè)計。 （2）其次結(jié)合一般IIR數(shù)字濾波器設(shè)計算法，提出全通IIR數(shù)字濾波器minimax頻率響應(yīng)誤差設(shè)計的四種算法。由于全通IIR數(shù)字濾波器的minimax頻率響應(yīng)誤差設(shè)計問題在形式上和一般IIR數(shù)字濾波器的minimax頻率響應(yīng)誤差設(shè)計問題是一樣的，所以直接采用一般IIR數(shù)字濾波器最大頻率響應(yīng)誤差最小化方法進行全通IIR數(shù)字濾波器minimax設(shè)計。把一般IIR數(shù)字濾波器minimax設(shè)計的direct_SM，SCLS_SM，direct_GN，，SCLS_GN算法結(jié)合全通IIR數(shù)字濾波器頻率響應(yīng)的特定形式，得到四種新的全通IIR數(shù)字濾波器minimax設(shè)計算法。仿真實例說明了所提方法的有效性。 （3）最后建立全通IIR數(shù)字濾波器設(shè)計的迭代重加權(quán)minimax方法，并應(yīng)用于半帶濾波器設(shè)計。通過以上四種方法得到具有等波紋相位誤差的全通IIR數(shù)字濾波器，但其帶邊附近群延遲誤差較大。為了減小最大群延遲誤差，迭代應(yīng)用濾波器群延遲誤差的包絡(luò)線對頻率響應(yīng)誤差進行加權(quán)，可得到具有等波紋群延遲誤差的全通濾波器；然后采用得到的全通IIR數(shù)字濾波器進一步設(shè)計具有等波紋群延遲誤差的半帶濾波器。仿真實例證明了所提方法的可行性。
文內(nèi)圖片：
圖片說明：低通濾波器的幅頻響應(yīng)圖
[Abstract]:All-pass IIR digital filter has a wide range of applications in the field of digital signal processing. It can also be used as a phase equalizer, as well as in the design of filter banks, half-band filters and notch filters. Therefore, its design problem has attracted the attention of many scholars. In this paper, the minimax design of all-pass IIR digital filter is studied. Firstly, the frequency response error design model of all-pass IIR digital filter is established, and then four minimax frequency response error design algorithms of all-pass IIR digital filter are obtained combined with the design algorithm of general IIR digital filter. Finally, an iterative reweighting method is proposed to design an all-pass filter with approximate uniform group delay error, and it is applied to the design of half-band filter. The main work of this paper is as follows: (1) firstly, the relationship between phase response error and frequency response error of all-pass IIR digital filter is analyzed, and the design model of frequency response error of all-pass IIR digital filter is established. The amplitude-frequency response of all-pass IIR digital filter is constant in the range of full frequency domain [0, 蟺]. Its design problem is a pure phase approximation problem. In this paper, the corresponding relationship between the frequency response error and the phase response error of the all-pass filter is analyzed, and the design model of the frequency response error is established to realize the optimal design of the all-pass IIR digital filter. (2) secondly, combined with the general IIR digital filter design algorithm, four algorithms for minimax frequency response error design of all-pass IIR digital filter are proposed. Because the minimax frequency response error design problem of all-pass IIR digital filter is the same as the minimax frequency response error design problem of general IIR digital filter, the minimax design of all-pass IIR digital filter is carried out directly by using the maximum frequency response error minimizing method of general IIR digital filter. Combining the direct_SM,SCLS_SM,direct_GN,SCLS_GN algorithm of general IIR digital filter minimax with the specific form of frequency response of all-pass IIR digital filter, four new all-pass IIR digital filter minimax design algorithms are obtained. A simulation example shows the effectiveness of the proposed method. (3) finally, an iterative reweighted minimax method for all-pass IIR digital filter design is established and applied to the design of half-band filter. The all-pass IIR digital filter with equal wavy phase error is obtained by the above four methods, but the group delay error near the band edge is large. In order to reduce the maximum group delay error, the frequency response error can be weighted iteratively by using the envelope of filter group delay error, and the all-pass filter with equal wavy group delay error can be obtained, and then the half-band filter with equal wavy group delay error can be further designed by using the obtained all-pass IIR digital filter. The feasibility of the proposed method is proved by a simulation example.
【學位授予單位】：杭州電子科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN713.7

【參考文獻】

相關(guān)期刊論文 前2條

1 趙瑞杰;賴曉平;;復(fù)FIR數(shù)字濾波器幅值約束Chebyshev設(shè)計[J];電子學報;2006年09期

2 韓治國;王紅梅;許輝;;基于窗函數(shù)和特征濾波器的半帶濾波器設(shè)計[J];計算機仿真;2013年08期

本文編號：2510575