It is a challenging task to design orthogonal filter banks, especially multidimensional (MD) ones. In the onedimensional (1D) two-channel finite impulse response (FIR) filter bank case, several design methods exist. Among them, designs based on spectral factorizations (by Smith and Barnwell) and designs based on lattice factorizations (by Vaidyanathan and Hoang) are the most effective and widel...

In this study, base on traditional lapped transform’s properties, inherit from some of the special characteristic properties of discrete cosine transform, trigonometric identities and the structure of linear phase filter banks. We present some theoretic properties in the generalized structure of linear phase paraunitary filter bank and build some examples corresponding to these properties. Thes...

A novel approach to the design and implementation of four-channel paraunitary filter banks is presented. It utilizes hypercomplex number theory, which has not yet been employed in these areas. Namely, quaternion multipliers are presented as alternative paraunitary building blocks, which can be regarded as generalizations of Givens (planar) rotations. The corresponding quaternionic lattice struc...

In this paper, we present a novel way to design biorthogonal and paraunitary linear phase(LPPUFB) lter banks. The square error of the perfect reconstruction condition is expressed in quadratic form of lter coe cients and the cost function is minimized by solving linear equation iteratively without nonlinear optimization. With some modi cations, the method can be extended to the design of paraun...

In this paper a blind MIMO space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a parameterization of such filters is proposed. Theoretical developments then lead to a numerical algorithm that sweeps all pairs of delayed outputs. This algorithm involves the solution of a polynomial...

Paraunitary lter banks are important for several signal processing tasks. In this paper, we consider the task of adapting the coeecients of a multichan-nel FIR paraunitary lter bank via gradient ascent or descent on a chosen cost function. The proposed generalized algorithms inherently adapt the system's parameters in the space of paraunitary l-ters. Modiications and simpliications of the techn...

This paper presents a new method for designing orthonormal wavelet filter banks using the Remez exchange algorithm. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary filter banks. From the orthonormality and regularity of wavelets, we derive some conditions that m...

This paper addresses the problem of obtaining an explicit expression of all real FIR paraunitary filters. In this work, we present a general parameterization of 2-channel FIR orthogonal filters. Unlike other approaches which make use of a lattice structure, we show that our technique designs any orthogonal filter directly, with no need of iteration procedures. Moreover, in order to design an L-...

Most orthogonal signal decompositions, including block transforms, wavelet transforms, wavelet packets, and perfect reconstruction filterbanks in general, can be represented by a paraunitary system matrix. Here, we consider the general problem of finding the optimal P x P paraunitary transform that minimizes the approximation error when a signal is reconstructed from a reduced number of compone...