Simultaneous minimization of various worst case measures of error in FIR filter bank

Yuichi Kida; Takuro Kida

doi:10.1117/12.795609

5 September 2008 Simultaneous minimization of various worst case measures of error in FIR filter bank

Yuichi Kida, Takuro Kida

Proceedings Volume 7075, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications XI; 70750F (2008) https://doi.org/10.1117/12.795609
Event: Optical Engineering + Applications, 2008, San Diego, California, United States

Abstract

We present the optimum running-type approximation of FIR filter bank that minimizes various worst-case measures of error, simultaneously, with respect to each of two different sets of signals. The first set is a set of piecewise analytic time-limited but approximately band-limited signals. When a supreme signal that realizes the prescribed worst-case measure of error exists, we prove, firstly, that there exists one-to-one correspondence between error in a wide time interval and error in a small interval. Based on this one-to-one correspondence, we prove that the approximation presented in this paper is the optimum in some sense. Secondly, we consider a set of band-limited signals with a main-lobe and a pair of small side-lobes and obtain similar conclusion.

Citation Download Citation

Yuichi Kida and Takuro Kida "Simultaneous minimization of various worst case measures of error in FIR filter bank", Proc. SPIE 7075, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications XI, 70750F (5 September 2008); https://doi.org/10.1117/12.795609

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