From the Publisher:
With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter.


0201000296B04062001

The Design and Analysis of Computer Algorithms

FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

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The Design and Implementation of FFTW3

From the Publisher:
This is undoubtedly the most accessible book on digital signal processing (DSP) available to the beginner. Using intuitive explanations and well-chosen examples, this book gives you the tools to develop a fundamental understanding of DSP theory. The author covers the essential mathematics by explaining the meaning and significance of the key DSP equations. Comprehensive in scope, and gentle in approach, the book will help you achieve a thorough grasp of the basics and move gradually to more sophisticated DSP concepts and applications.

/pdf/understanding-digital-signal-processing-1tunqv7j3t.pdf

Understanding digital signal processing

A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log_{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.

/pdf/the-chirp-z-transform-algorithm-2bu061tl7o.pdf

The chirp z-transform algorithm

A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the 'fast Fourier transform' algorithm. The transform may be applied to the problem of calculating convolutions of long integer sequences by means of integer arithmetic.

/pdf/the-fast-fourier-transform-in-a-finite-field-2on8h7e95k.pdf

The fast Fourier transform in a finite field

This chapter contains sections titled: Introduction, An Algorithm Suggested by Chirp Filtering

A Linear Filtering Approach to the Computation of the Discrete Fourier Transform

The Hilbert transform has traditionally played an important part in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform plays a similar role in digital signal processing. In this paper, the Hilbert transform relations, as they apply to sequences and their z-transforms, and also as they apply to sequences and their Discrete Fourier Transforms, will be discussed. These relations are identical only in the limit as the number of data samples taken in the Discrete Fourier Transforms becomes infinite. The implementation of the Hilbert transform operation as applied to sequences usually takes the form of digital linear networks with constant coefficients, either recursive or non-recursive, which approximate an all-pass network with 90° phase shift, or two-output digital networks which have a 90° phase difference over a wide range of frequencies. Means of implementing such phase shifting and phase splitting networks are presented.

Theory and Implementation of the Discrete Hilbert Transform

This collection of papers is the result of a desire to make available reprints of articles on digital signal processing for use in a graduate course offered at MIT. The primary objective was to present reprints in an easily accessible form. At the same time, it appeared that this collection might be useful for a wider audience, and consequently it was decided to reproduce the articles (originally published between 1965 and 1969) in book form.The literature in this area is extensive, as evidenced by the bibliography included at the end of this collection. The articles were selected and the introduction prepared by the editor in collaboration with Bernard Gold and Charles M. Rader.The collection of articles divides roughly into four major categories: z-transform theory and digital filter design, the effects of finite word length, the fast Fourier transform and spectral analysis, and hardware considerations in the implementation of digital filters.

A Fast Fourier Transform Algorithm Using Base 8 Iterations

The literature on sampled-data filters, although extensive on design methods, has not treated adequately the important problems connected with the actual realization of the obtained filters with finite arithmetic elements. Beginning with a review of the traditional design procedures a comparison is made between the different canonical realization forms and their related computational procedures. Special attention is directed to the problems of coefficient accuracy and of rounding and trucation effects . A simple expression is derived which yields an estimate of the required coefficient accuracy and which shows clearly the relationship of this accuracy to both sampling rate and filter complexity.

Some Practical Consideration in the Realization of Linear Digital Filters

This discussion served as an introduction to the Hardware Implementations session of the IEEE Workshop on Fast Fourier Transform Processing. It introduces the problems associated with implementing the FFT algorithm in hardware and provides a frame of reference for characterizing specific implementations. Many of the design options applicable to an FFT processor are described, and a brief comparison of several machine organizations is given.

Mit Press

Papers

A Linear Filtering Approach to the Computation of the Discrete Fourier Transform

Theory and Implementation of the Discrete Hilbert Transform

A Fast Fourier Transform Algorithm Using Base 8 Iterations

Some Practical Consideration in the Realization of Linear Digital Filters

Fast Fourier Transform Hardware Implementations—An Overview