The optimal finite impulse response (FIR) filter design has been very popular in science and engineering over many decades due to its guaranteed stability and wide variety of applications, especially for transmission systems. Designing eigen-filters is a common signal processing paradigm. Given a fixed filter length, the objective function is formulated in terms of passband and stop-band energies, and then the appropriate optimization technique is employed to determine the impulse response. In this paper, we would like to present a novel computationally-efficient optimal eigen-filter design scheme. Since the signal processing storage devices become less and less costly and more and more powerful, designing long FIR filters dynamically to address different channel conditions and modulations becomes crucial in modern telecommunication and signal processing applications. Computationally-efficient filter design schemes, which can be facilitated in real-time, are in high demand. Our proposed technology is based on fast eigen-decomposition. The computational complexity of our proposed new method is O(M2) compared to O(M3) of the conventional technique.
[1]
P. Vaidyanathan.
Multirate Systems And Filter Banks
,
1992
.
[2]
Mohammed A. Hasan,et al.
Minor and major subspace computation of large matrices
,
2002,
2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).
[3]
Truong Q. Nguyen,et al.
Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters
,
1987
.
[4]
Mohammed A. Hasan.
Algorithms for computating principal and minor invariant subspaces of large matrices
,
2003,
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..
[5]
Qiang Ye,et al.
Algorithm 845: EIGIFP: a MATLAB program for solving large symmetric generalized eigenvalue problems
,
2005,
TOMS.