具有離散係數之一維及二維濾波器設計

Design of 1-D and 2-D digital filters with and discrete coefficients

陳重嘉(Chung-Chia Chen)

指導教授 ： 李枝宏

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.01318

摘要

由於近年來數位信號處理這個領域迅速發展，而數位濾波器設計更是發展的基礎。在本論文中，我們藉由WLS以及Karmarkar 演算法，提出了幾種Minimax的方法，來對低延遲有限脈衝響應Nyquist濾波器及二維低通濾波器進行最佳化設計。
另外，一般有限脈衝響應濾波器的架構都會使用到乘法器，這使得執行速度會變慢。因此，我們使用CORDIC演算法配合最佳化設計使係數離散化，如此就不需要乘法器。
由本論文中所用的一維濾波器及二維濾波器設計實例結果，可以證明所提出的方法是可行的。

關鍵字

一維及二維濾波器 ； 離散係數

並列摘要

Recently, the field of digital signal processing is developed quickly, and design of digital filters plays a key role for the development. We propose several minimax design methods based on WLS and Karmarkar’s algorithms for optimally designing FIR Nyquist filters with low group delay and 2-D lowpass filters.
In addition, the circuit of FIR filters must have the multipliers and this makes the computation speed slow. Therefore, we use CORDIC algorithm to discretize filter coefficients, and won’t need any multipliers in circuit implementation.
From the examples presented in each chapter of this thesis, we show the effectiveness of the proposed design techniques.

並列關鍵字

1-D and 2-D digital filters ； discrete coefficients

參考文獻

[1] Xi Zhang and Toshinori Yoshikawa, “Design of FIR Nyquist Filters with Low Group Delay”, IEEE Trans. Signal Processing, vol.47, pp.1454-1458, May 1999

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[3] Cheng-Shing Wu, An-Yeu Wu and Chih-Hsiu Lin, “A High-Performance / Low-Latency Vector Rotational CORDIC Architecture Based on Extended Elementary Angle Set and Trellis-Based Searching Schemes”, IEEE Trans. Circuits and Systems, vol.50, pp.589-601, Sep. 2003

[4] Yong-Ching Lim, Ju-Hong Lee, C. K. Chen and Rong-Huan Yang, “A Weighted Least Squres Algorithm for Quansi-Equiripple FIR and IIR Digital Filter Design”, IEEE Trans. Signal Processing, vol.40, pp.551-558, Mar. 1992

[5] Tian-Bo Deng, Wu-Sheng Lu, “Weighted Least-Squares Method for Designing Variable Fractional Delay 2-D FIR Digital Filters”, IEEE Trans. Circuits and Systems, vol.47, pp.114-124, Feb. 2000