The energy compaction performance of two-channel paraunitary finite impulse response (FIR) filter banks for finitelength signals is investigated. A detailed non-iterative design procedure for boundary filters which are optimal in a weighted mean square error (MSE) sense in the Fourier domain is presented. Simulation results are given for twochannel paraunitary FIR filter banks based on minimump...

The Symmetric Delay Factorization (SDF) is introduced in 1] for synthesizing linear phase paraunitary lter banks and is applied successfully in 2] for designing Time-Varying Filter Banks (TVFB). This paper describes a minimal and complete generalized symmetric delay factorization valid for a larger class of paraunitary lter banks, and for an arbitrary (even and odd) number of channels. The appr...

It has been proposed that all M -channel paraunitary (PU) multirate filter banks over GF(2) can be described using the product of basic lattice blocks. In this paper this conjecture is proven by considering a redefinition of degree-0 lattice blocks. A factorisation algorithm that factors all degree-J PU filter banks over GF(2) is presented. In the course of this work M -channel type-I matrices ...

Keywords: Toeplitz matrices Spectral factorization Paraunitary filters Filter design In this work we present the explicit expression of all rectangular Toeplitz matrices B, C which verify the equation BB H + CC H = al for some a > 0. This matrix equation arises in some signal processing problems. For instance, it appears when designing the even and odd components of paraunitary filters, which a...

The perfect reconstruction conditions for a timevarying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is ...

In this paper we present a method to design paraunitary polyphase matrices of critically sampled rational filter banks. The method is based on (P,Q) shift-invariant systems, and so any kind of rational splitting of the frequency spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system with smallest P and Q that map of a band of input spectrum to the output spectrum are obt...

PARAUNITARY COSINE MODULATED PERFECT RECONSTRUCTION FILTER BANKST Yuan-Pel Lm and P. P Vaidyanathan Dept of Electrical Engineering, 116-81 California Institute of Technology Pasadena. CA 91125 In this paper, we construct two-dimensional (2D) FIR paraunitary Cosine Modulated Filter Banks (CMFB). All the analysis and synthesis filters are cosinemodulated versions of a 2D non-separable prototype; ...

This paper introduces a new Blind Source Separation algorithm for convolutive mixtures. In addition to separate sources, this algorithm respects the paraunitary property of the model considered, obtained after whitening observations. In order to do this, the equalizer is factorized in a novel manner. After a presentation of theoretical results, a numerical algorithm is then derived. This algori...

Tight Weyl–Heisenberg frames in `(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time–frequency plane is not attainable unless some redundancy is introduced. That is the reason for consideri...

In this paper we obtain a new parameterization of all FIR paraunitary two-channel filter banks. Unlike other approaches which make use of a lattice structure or a cascade algorithm, we show that our technique provides a direct explicit expression of all FIR orthogonal filters, with no need of iteration procedures. Thus, in order to design a L-tap 2-channel paraunitary filterbank, it suffices to...