Design of Computationally Efficient Digital FIR Filters and Filter Banks

Ph.DDOCTOR OF PHILOSOPH

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

Computationally efficient FIR digital filters

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

Design of Multiplierless Decimation Filters Using an Extended Search of Cyclotomic Polynomials

This brief addresses the design of multiplierless decimation filters using an extended set of cyclotomic polynomials (CPs) as constituent filters. It extends the results presented in a companion paper by one of the coauthors to CPs with indexes in the set 1, ⋯, 200, and it presents the z-transfer functions of all CPs with indexes from 61 to 200. One of the key observations stemming from the results of this brief is that CPs with indexes in the set 105, ⋯, 200 still have very effective coefficients, i.e., integers belonging to -1, 0, +1 , but z-transfer functions have to be recursive. Regardless of the application to multirate filters considered in this brief, these polynomials can also be used for designing classical finite-impulse response filters. Moreover, this brief provides guidelines to simplify the design of constituent decimation filters in multistage architectures and to reduce computational complexity of the proposed filters. Finally, comparisons are given with respect to other techniques in the literature