加權最小平方似等漣漪可變分數延遲有限脈衝響應濾波器設計

在設計一個有限脈衝響應的濾波器時，加權最小平方法是一個大家所熟知的方法，而且也已經被延伸用來設計一個可變分數延遲的濾波器。以這個方式來設計，其效率比傳統使用Lagrange內插方式來的好。在加權最小平方法中，加權函數是很重要的，已經有一些作者提出，經由設計適當的加權函數，這個加權最小平方法可以產生類似等漣漪的結果。在這篇論文中，這個想法進一步延伸來設計一個可變分數延遲的濾波器，頻率響應達到了類似等漣漪的效果，誤差的峰值比純粹用加權最小平方法來設計，下降了約6.7dB。

關鍵字

等漣漪；加權最小平方法；有限脈衝響應濾波器；分數延遲

並列摘要

To design an FIR filter, the Weighted Least Squares Method is a well-known method. And it has already been extended to design a variable fractional delay filter. It is presented that the efficiency is better than the method based on Lagrange interpolation. The weighting function is very important in the Weighted Least Squares method. Some authors have presented that if a suitable weighting function is used to design the filter, the Weighted Least Squares method can produce the quasi-equiripple result. In this paper, this ideal is extended to design a quasi-equiripple variable fractional delay FIR filter. The presented method is superior to the plain Weighted Least Squares design in the peak absolute error by about 6.7 dB.

並列關鍵字

Equiripple ； FIR filters ； fractional delay ； WLS

參考文獻

[3] V. R Algazi and M. Suk, “On the frequency weighted least squares design of finite duration filters, ” IEEE Trans. Circuits Syst., vol. CAS-30, pp. 723-739, Oct. 1983.

[4] Y. C. Lim, J.-H. Lee, C. K. Chan, and R.-H. Yang, “A weighted least-squares algorithm for quasi-equiripple FIR and IIR digital filter design,” IEEE Trans. on Signal Processing, vol. 40, no. 3, pp. 551-558, Mar. 1992.

[5] H. Johansson and P. Lowenborg, “On the design of adjustable fractional delay FIR filters,” IEEE Trans. Circuits Syst. II, vol. 50, pp. 164-169, Apr. 2003.

[7] W.-S. Lu and T.-B. Deng, “An improved weighted least-squares design of FIR digital filters with variable fractional delay,” Proc. 1999 IEEE Int. Symp. Circuits and Systems, Orlando, FL, May 1999.

[8] M. C. Pease E, Methods of Matrix Algebra. Academic Press, New York, 1965.

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加權最小平方似等漣漪可變分數延遲有限脈衝響應濾波器設計

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