In real and complex fields, unitary and paraunitary (PU) matrices have found many applications in signal processing. There has recently been interest in extending these ideas to the case of finite fields. In this paper, we will study the theory of PU filter banks (FB’s) in GF(y) with y prime. Various properties of unitary and PU matrices in finite fields will be studied. In particular, a number...

We investigate the design of subband coders without the traditional perfect-reconstruction constraint on the filters. The coder uses scalar quantizers, and its filters and bit allocation are designed so as to optimize a rate-distortion criterion. Our results hold for a broad class of ratedistortion criteria that satisfy certain convexity properties. We begin by showing that optimality can be ac...

This paper presents a lifting-domain design of filter banks with a given McMillan degree. It is based on the M -channel lifting factorizations of the degree-0 and 1 building blocks I − 2uv† and I − uv† + z−1uv†, with v†u = 1. Paraunitariness further requires u = v. The proposed lifting factorization has a unity diagonal scaling throughout, and guarantees perfect reconstruction (PR) even when th...

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parametrization of wavelet space, one can deene a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus g to the (g ? 1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorizatio...

This paper examines erasure resilience of oversampled filter bank (OFB) codes, focusing on two families of codes based on cosinemodulated filter banks (CMFB). We first revisit OFBs in light of filter bank and frame theory. The analogy with channel codes is then shown. In particular, for paraunitary filter banks, we show that the signal reconstructionmethods derived from the filter bank theory a...

This paper presents the optimal design and performance analysis of the linear phase paraunitary (LPPU) M band lter banks in the frame of the vector quantized image coding. First, by maximizing the uni ed coding gain, which is expressed in terms of intra-band correlation, as well as inter-band energy compaction, the LPPU M band lter banks for the general factorization form are designed. Then, th...

This paper is concerned with the optimal design and performance analysis of the linear phase paraunitary (LPPU) M band lter banks in the frame of the vector quantized image coding. First, we derive an uni ed coding gain for VQ in terms of the intra-band correlation, as well as the inter-band energy compaction. Hence, by maximizing the coding gain, the LPPU M band lter banks for the general fact...

AIT, Bangalore, India UVCE, Bangalore, India Corresponding Author: H. Umadevi ___________________________________________________________________________ Abstract OFDM is novel multicarrier modulation (MCM) technique. It has strong advantage of being a generic transmission scheme whose actual characteristics can be widely customized to fulfill several requirements and constraints of an advanced...

This chapter takes up the design of discrete wavelet transforms based on oversampled filter banks. In this case the wavelets form an overcomplete basis, or frame. In particular, we consider the design of systems that are analogous to Daubechies’ orthonormal wavelets — that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case....