數位濾波器架構設計及量化分析

Design of Digital Filter Structures and Quantization Analysis

陳美代(Mei-Dai Chen)

指導教授 ： 貝蘇章

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.01643

摘要

本篇論文是以高階數位等化器為基礎，將其原本為串聯的頻率轉換函數以許多不同的架構實現，以便觀察每種結構的差別。雖然套入架構裡面的數學總式是相同的，但是隨著架構設計的不同，會造成不同影響！尤其有是後期所發展出來的架構，因為其參數皆有經過標準化的處理，故其對數字的性質所表現出來的結果會比其他未經標準化的架構穩定很多。
接著將原為串聯的頻率轉換函數導成並聯的形式，並且亦將其用已經討論過的架構實現，去觀察串聯和並聯的差異性。一般來說，並聯的架構對於雜訊的影響會比串聯來的小。
最後則將輸入訊號以及所有的架構的參數以不同的有限長字元長度去做限制與量化，觀察並分析此一舉動所帶來的影響。

關鍵字

高階數位等化器 ； 串聯 ； 頻率轉換函數 ； 並聯 ； 有限長字元長度 ； 量化

並列摘要

A family of digital parametric equalizers based on high-order Butterworth, Chebyshev type I, Chebyshev type II, and elliptic analog prototype filter was proposed in [16]. Compared to the conventional biquadratic equalizers, such equalizers can have flatter passband and sharper band edges at the expense of higher computational cost.
Here, we will review this kind of equalizer, and realize it by several of structures, such as transposed, ladder and lattice, normalized lattice, state space, and decoupled. The transfer function of this high-order parametric equalizer is first derived in cascade form, and we will derive it in parallel form to observe the effects between the cascade and the parallel form. Then we also set the coefficients of the realization structures to be quantized with the finite word length so that we can observe how the performances are affected by quantization errors.

並列關鍵字

digital parametric equalizers ； cascade form ； parallel form ； finite word length ； quantization

參考文獻

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[6] D. J. Shpak, “Analytical Design of Biquadratic Filter Sections for Parametric Filters,” J. Audio Eng. Soc., 40, 876 (1992).

[8] F. Harris and E. Brooking, “A Versatile Parametric Filter Using Imbedded All-Pass Sub-Filter to Independently Adjust Bandwidth, Center Frequency, and Boost or Cut,” Presented at the95th Convention of the AES, New York, October 1993, AES Preprint 3757.

[14] S. J. Orfanidis, “Digital Parametric Equalizer Design with Prescribed Nyquist - Frequency Gain,” J. Aud. Eng. Soc., 45, 444 (1997).