A Closed-Form Solution to the Design Problem of 2-D FIR Digital Filters with Arbitrary Frequency Responses

Zhu Weiping

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A Closed-Form Solution to the Design Problem of 2-D FIR Digital Filters with Arbitrary Frequency Responses

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- A Closed-Form Solution to the Design Problem of 2-D FIR Digital Filters with Arbitrary Frequency Responses
- Acta Electronica Sinica Issue 10, (1996)
- 作者机构：
  
  南京邮电学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN713.702
- Published：1996
- 稿件说明：
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[1]朱卫平.具有任意频响的二维FIR数字滤波器设计的闭式最小二乘解[J].电子学报,1996(10):36-41+56.

Zhu Weiping. A Closed-Form Solution to the Design Problem of 2-D FIR Digital Filters with Arbitrary Frequency Responses[J]. Acta Electronica Sinica, 1996, (10).
[1]朱卫平.具有任意频响的二维FIR数字滤波器设计的闭式最小二乘解[J].电子学报,1996(10):36-41+56. DOI：

Zhu Weiping. A Closed-Form Solution to the Design Problem of 2-D FIR Digital Filters with Arbitrary Frequency Responses[J]. Acta Electronica Sinica, 1996, (10). DOI：

摘要

本文研究具有任意频响特性的二维ＦＩＲ数字滤波器的最小二乘设计问题。通过最小化频域平方误差函数并揭示与设计问题有关的一些矩阵的性质，得到了滤波器系数的闭式解。使用导出的闭式表达式，可根据给定的频响指标方便地计算滤波器的脉冲响应，从而设计程序十分简单、运算量很小。

Abstract

In this paper

the least-square design problem of 2-D FIR digital filters with arbitrary frequency responses is studied. A closed-form solution for filter coefficients is obtained by minimizing the frequency-domain squared-error function and revealing some properties of the matrices related to the design problem. By using the derived closed-form expression

the impulse response of the designed filter can conveniently be evaluated from the specified frequency response

resulting in a significantly simplified design procedure and an extremely reduced computational burden.

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