Digital Signal Processing Structures: Block and Multidemensional Formulation and Distributed Arithmetic

Tech ReportIn this report we will consider a special class of digital filter structure; and by structure we mean the particular arrangement and sequence of arithmetic and storage operations to realize a desired signal processing function. The more conventional structures consist of an interconnection of arithmetic operations such as addition and multiplication with storage elements such as memory registers. The filter is implemented in hardware by wireing together electronic modules that perform these functions or in software by a program that directs a general purpose computer to carry out the operations. These structures area analogous to analog or continuous time active and passive filters; indeed, many digital structures have exact analog counterparts as active filters

M-Band Multiwavelet Systems

Conference PaperIn this paper we investigate multiwavelet systems whose scaling functions have disjoint support. We demonstrate that, with the exception of a trivial case, this property may not be attained by two band multiwavelet systems. We show that to enjoy this property, it is indeed necessary to invoke <i>M</i>-band multiwavelet systems. This indicates the existence of tilings of the time-frequency plane that may be obtained with <i>M</i>--band multiwavelet systems but not with two band multiwavelet systems. Hence <i>M</i>--band multiwavelet systems are inherently more powerful than two band multiwavelet systems and deserve a thorough investigation. Finally, we derive K<sup>th</sup order balancing conditions for <i>M</i>--band multiwavelet systems. These conditions will enable <i>M</i>--band multiwavelet systems to be used for practical digital signal processing applications

Adaptive Iterative Reqeighted Least Squares Design of LP FIR Filters

Conference paperThis paper presents an efficient adaptive algorithm for designing FIR digital filters that are efficient according to an Lp error criteria. The algorithm is an extension of Burrus' iterative reweighted least-squares (IRLS) method for approximating Lp filters. Such algorithm will converge for most significant cases in a few iterations. In some cases however, the transition bandwidth is such that the number of iterations increases significantly. The proposed algorithm controls such problem and drastically reduces the number of iterations required

On the Design of LP IIR Filters with Arbitrary Frequency Response

Conference PaperThis paper introduces an iterative algorithm for designing IIR digital filters that minimize a complex approximation error in an Lp sense. The algorithm combines ideas that have proven successful in the similar problem of Lp FIR filter design. We use iterative prefiltering techniques common in applications such as parameter estimation together with an Iterative Reweighted Least Squares (IRLS) method. The result is a double iterative approach that generates IIR filters of arbitrary magnitude and phase response and arbitrary numerator and denominator orders. Such filters can be used in a variety of applications in which the typical L2 or Minimax error criteria might not be suitable

Introduction to Wavelets and Wavelet Transforms : A Primer

New Jerseyxiv, 265 p, Fig, 25 cm

New class of wavelets for signal approximation

Conference PaperThis paper develops a new class of wavelets for which the classical Daubechies zero moment property has been relaxed. The advantages of relaxing higher order wavelet moment constraints is that within the framework of compact support and perfect reconstruction (orthogonal and biorthogonal) one can obtain wavelet basis with new and interesting approximation properties. This paper investigates a new class of wavelets that is obtained by setting a few lower order moments to zero and using the remaining degrees of freedom to minimize a larger number of higher order moments. The resulting wavelets are shown to be robust for representing a large classes of inputs. Robustness is achieved at the cost of exact representation of low order polynomials but with the advantage that higher order polynomials can be represented with less error compared to the maximally regular solution of the same support