Conventional design techniques for analysis and synthesis filters in subband processing applications guarantee perfect reconstruction of the original signal from its subband components. The resulting filters lose, however, their optimality when additive noise, due for example, to signal quantization, disturbs the subband sequences. In this paper, we propose filter design techniques that minimize the reconstruction mean squared error taking into account the second order statistics of signals and noise in the case of either stochastic or deterministic signals. A novel recursive, pseudo-adaptive algorithm is proposed for efficient design of these filters. Analysis and derivations are extended to two dimensional signals and filters using powerful Kronecker product notation. A prototype application of the proposed ideas in subband coding is presented. Simulations illustrate the superior performance of the proposed filter banks versus conventional perfect reconstruction filters.<<ETX>>
[1]
Lennart Ljung,et al.
System Identification: Theory for the User
,
1987
.
[2]
Stéphane Mallat,et al.
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
,
1989,
IEEE Trans. Pattern Anal. Mach. Intell..
[3]
P. P. Vaidyanathan,et al.
Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial
,
1990,
Proc. IEEE.
[4]
M. Vetterli.
Multi-dimensional sub-band coding: Some theory and algorithms
,
1984
.
[5]
S. Biyiksiz,et al.
Multirate digital signal processing
,
1985,
Proceedings of the IEEE.
[6]
Stefanos D. Kollias,et al.
Optimal filter banks for signal reconstruction from noisy subband components
,
1996,
IEEE Trans. Signal Process..
[7]
John W. Woods,et al.
Subband coding of images
,
1986,
IEEE Trans. Acoust. Speech Signal Process..