Design of Multistage Decimation Filters Using Cyclotomic Polynomials: Optimization and Design Issues

This paper focuses on the design of multiplier-less decimation filters suitable for oversampled digital signals. The aim is twofold. On one hand, it proposes an optimization framework for the design of constituent decimation filters in a general multistage decimation architecture. The basic building blocks embedded in the proposed filters belong, for a simple reason, to the class of cyclotomic polynomials (CPs): the first 104 CPs have a z-transfer function whose coefficients are simply {-1,0,+1}. On the other hand, the paper provides a bunch of useful techniques, most of which stemming from some key properties of CPs, for designing the proposed filters in a variety of architectures. Both recursive and non-recursive architectures are discussed by focusing on a specific decimation filter obtained as a result of the optimization algorithm. Design guidelines are provided with the aim to simplify the design of the constituent decimation filters in the multistage chain.Comment: Submitted to CAS-I, July 07; 11 pages, 5 figures, 3 table

Design and implementation of computationally efficient digital filters

Ph.DDOCTOR OF PHILOSOPH

Linear-Phase FIR Digital Filter ‎Design with Reduced Hardware Complexity using Discrete Differential Evolution

Optimal design of xed coe cient nite word length linear phase FIR digital lters for custom ICs has been the focus of research in the past decade. With the ever increasing demands for high throughput and low power circuits, the need to design lters with reduced hardware complexity has become more crucial. Multiplierless lters provide substantial saving in hardware by using a shift add network to generate the lter coe cients. In this thesis, the multiplierless lter design problem is modeled as combinatorial optimization problem and is solved using a discrete Di erential Evolution algorithm. The Di erential Evolution algorithm\u27s population representation adapted for the nite word length lter design problem is developed and the mutation operator is rede ned for discrete valued parameters. Experiments show that the method is able to design lters up to a length of 300 taps with reduced hardware and shorter design times

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

Design of Computationally Efficient Digital FIR Filters and Filter Banks

Ph.DDOCTOR OF PHILOSOPH

Design of discrete-time filters for efficient implementation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 325-333).The cost of implementation of discrete-time filters is often strongly dependent on the number of non-zero filter coefficients or the precision with which the coefficients are represented. This thesis addresses the design of sparse and bit-efficient filters under different constraints on filter performance in the context of frequency response approximation, signal estimation, and signal detection. The results have applications in several areas, including the equalization of communication channels, frequency-selective and frequency-shaping filtering, and minimum-variance distortionless-response beamforming. The design problems considered admit efficient and exact solutions in special cases. For the more difficult general case, two approaches are pursued. The first develops low-complexity algorithms that are shown to yield optimal or near-optimal designs in many instances, but without guarantees. The second focuses on optimal algorithms based on the branch-and-bound procedure. The complexity of branch-and-bound is reduced through the use of bounds that are good approximations to the true optimal cost. Several bounding methods are developed, many involving relaxations of the original problem. The approximation quality of the bounds is characterized and efficient computational methods are discussed. Numerical experiments show that the bounds can result in substantial reductions in computational complexity.by Dennis Wei.Ph.D

Applications of MATLAB in Science and Engineering

The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest