交錯取樣濾波器之設計

Design of FIR Filters by Using Interlaced Sampling Method

王柏翰(Po-Han Wang)

指導教授 ： 王鵬華

國立臺北大學/電機資訊學院/通訊工程研究所/碩士(2014年)

摘要

一般而言，實係數有限脈衝響應(finite impulse response, FIR)濾波器在高頻帶的頻率響應和預期的頻率響應之間總是會有誤差，這是因為預期的頻率響應值在最高頻率處通常為複數，但實係數FIR濾波器響應在最高頻率處的響應值必為實數所致。為了解決這個問題，本論文提議使用交互取樣(interlaced sampling) FIR濾波器架構，為了求解濾波器係數，我們探討了兩種設計法，一為最小方差(minimized squared error, MSE)法，另一為最平坦(maximally flat, MF)誤差法。利用這兩種方法都可以有效地解出交互取樣FIR濾波器的係數，所設計出的濾波器只要使用少量的係數，就可以在低、中、高頻帶都得到非常好的設計結果，在整個頻帶上的誤差都非常小。我們在本論文中推導出求解MSE和MF係數所需的方程式，使用的設計實例為分數延遲濾波器(fractional delay filter)與具分數延遲的微分器(differentiator)，我們探討了不同濾波器階數下的設計結果，實驗結果顯示交互取樣FIR濾波器的確可以達到非常理想的設計結果。

關鍵字

交錯取樣

並列摘要

There is an irreducible error in the high frequency band of a real-coefficient finite impulse response (FIR) filter. The issue occurs because at the highest frequency, the value of desired frequency response may be complex while the system response is real. This thesis proposes to use the interlaced sampling (IS) FIR filters to achieve precise approximation within the high frequency band. We use two methods to solve the filter coefficients.One is the minimized squared error (MSE) method, and another is the maximally flat (MF) error criterion. We apply the proposed IS FIR structure to designing the fractional delay filters and the digital differentiators with fractional delay. Both methods are effective in solving the inaccurate situations. Both have very small peak errors in the high frequency band. We will discuss the performance of the IS structure for various parameters. Both the MSE and MF methods have good performance with very small peak errors in the whole band.

並列關鍵字

Interlaced Sampling

參考文獻

[1] Peng-Hua Wang. Closed-form design of maximally

interlaced sampling method. In 2013 IEEE Workshop on Signal Processing Systems

[2] Peng-Hua Wang. Closed-form design of maximally

[3] Peng-Hua Wang. Peano kernels of fractional delay systems. In 2007 IEEE International

[4] Chien-Cheng Tseng and Su-Ling Lee. Weighted least squares design of wideband digital