具有2的次方項係數之FIR和IIR數位濾波器組最佳化設計

Abstract

正交鏡像濾波器組被廣範的使用在複速率系統，它能將輸入訊號分解成數個相等頻寬的次頻帶訊號。但因人類的知覺，例如聽覺和視覺，敏感度並不是均勻的分布於頻帶上，因此非均勻濾波器組在杲些方面的應用要重要於正交鏡像濾波器組。在本篇論文中，我們會專注於這兩種架構濾波器組的研究。 CORDIC演算法是一套執行角度量化的方法，它能夠在角度空間中量化係數，比起係數空間來得更緊密。此外，CORDIC演算法所量化的係數，可以被表示成2的次方項係數的形式。另外，該演算法已達成高速率和低複雜度的VLSI電路實現，不須要用到乘法器，僅須移位器、多工器和加法器。基於上述的理由，我們提出CORDIC演算法用來達成理想化的設計。我們也提出了WLS演算法結合CORDIC演算法以及基於CORDIC架構下的基因演算來做設計。 上述這些演算法的設計結果，均近似於連續係數演算法所設計出的結果。一些設計參數甚至較連續係數演算法的結果要好。我們証明了此演算法值得在更進一步的設計中採用。

Quadrature Mirror Filter banks is widely used in multirate system. It can divid input signal into several subband signals. Owing to human sense, like sense of hearing , sense of sight, is not uniformly distributed in frequency, Non-uniform Division Filter banks is even more important than QMF in some aspects. In this thesis, we focus on both structure of filter banks. CORDIC algorithm is an approach to perform angle quantization. It can quantize coefficients in angle space which is denser than coefficient space. Besides, coefficients quantized by CORDIC algorithm can be represented in signed power of two form. In addition, the algorithm can be realized high speed and low complexity VLSI circuits, without using multiplier, need only shifter, multiplexer and adder. For these reasons, we propose CORDIC algorithm for optimal design. We also combine WLS algorithm and CORDIC algorithm or use genetic algorithm based on CORDIC algorithm. The results designed by these kinds of algorithm approximate to the results designed by continuous coefficient algorithm. Some design parameters are even better than later. We prove these algorithm which is worthy for further application.