全通IIR数字滤波器的设计和应用
发布时间：2019-07-05 14:01
【摘要】：全通IIR数字滤波器在数字信号处理领域有着广泛的应用，它可用做相位均衡器，也可用于滤波器组、半带滤波器和陷波滤波器的设计。因此它的设计问题吸引了许多学者的关注。 本文针对全通IIR数字滤波器的minimax设计问题展开研究。首先建立全通IIR数字滤波器的频率响应误差设计模型；然后结合一般IIR数字滤波器的设计算法，得到四种全通IIR数字滤波器minimax频率响应误差设计算法；最后提出迭代重加权方法设计具有近似均匀群延迟误差的全通滤波器，并将其应用于半带滤波器的设计。本文主要做了以下工作： （1）首先分析全通IIR数字滤波器相位响应误差和频率响应误差的关系，建立全通IIR数字滤波器频率响应误差设计模型。全通IIR数字滤波器在全频域[0, π]范围内幅频响应恒为一，它的设计问题是一个纯相位逼近问题。本文分析了全通滤波器的频率响应误差与相位响应误差之间的对应关系，并基于此分析建立频率响应误差设计模型，以实现全通IIR数字滤波器的优化设计。 （2）其次结合一般IIR数字滤波器设计算法，提出全通IIR数字滤波器minimax频率响应误差设计的四种算法。由于全通IIR数字滤波器的minimax频率响应误差设计问题在形式上和一般IIR数字滤波器的minimax频率响应误差设计问题是一样的，所以直接采用一般IIR数字滤波器最大频率响应误差最小化方法进行全通IIR数字滤波器minimax设计。把一般IIR数字滤波器minimax设计的direct_SM，SCLS_SM，direct_GN，，SCLS_GN算法结合全通IIR数字滤波器频率响应的特定形式，得到四种新的全通IIR数字滤波器minimax设计算法。仿真实例说明了所提方法的有效性。 （3）最后建立全通IIR数字滤波器设计的迭代重加权minimax方法，并应用于半带滤波器设计。通过以上四种方法得到具有等波纹相位误差的全通IIR数字滤波器，但其带边附近群延迟误差较大。为了减小最大群延迟误差，迭代应用滤波器群延迟误差的包络线对频率响应误差进行加权，可得到具有等波纹群延迟误差的全通滤波器；然后采用得到的全通IIR数字滤波器进一步设计具有等波纹群延迟误差的半带滤波器。仿真实例证明了所提方法的可行性。
文内图片：
图片说明：低通滤波器的幅频响应图
[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.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713.7
本文编号：2510575
文内图片：
图片说明：低通滤波器的幅频响应图
[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.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713.7
【参考文献】
相关期刊论文 前2条
1 赵瑞杰;赖晓平;;复FIR数字滤波器幅值约束Chebyshev设计[J];电子学报;2006年09期
2 韩治国;王红梅;许辉;;基于窗函数和特征滤波器的半带滤波器设计[J];计算机仿真;2013年08期
本文编号：2510575
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