1st Edition

Brief Notes in Advanced DSP Fourier Analysis with MATLAB

    354 Pages 17 Color & 205 B/W Illustrations
    by CRC Press

    354 Pages 17 Color & 205 B/W Illustrations
    by CRC Press

    354 Pages 17 Color & 205 B/W Illustrations
    by CRC Press

    Based on the authors’ research in Fourier analysis, Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® addresses many concepts and applications of digital signal processing (DSP). The included MATLAB® codes illustrate how to apply the ideas in practice.

    The book begins with the basic concept of the discrete Fourier transformation and its properties. It then describes lifting schemes, integer transformations, the discrete cosine transform, and the paired transform method for calculating the discrete Hadamard transform. The text also examines the decomposition of the 1D signal by so-called section basis signals as well as new forms of 2D signal/image representation and decomposition by direction signals/images. Focusing on Fourier transform wavelets and Givens–Haar transforms, the last chapter discusses the problem of signal multiresolution.

    This book presents numerous interesting problems and concepts of unitary transformations, such as the Fourier, Hadamard, Hartley, Haar, paired, cosine, and new signal-induced transformations. It aids readers in using new forms and methods of signals and images in the frequency and frequency-and-time domains.

    Discrete Fourier Transform

    Properties of the discrete Fourier transform

    Fourier transform splitting

    Fast Fourier transform

    Codes for the paired FFT

    Paired and Haar transforms

    Integer Fourier Transform

    Reversible integer Fourier transform

    Lifting schemes for DFT

    One-point integer transform

    DFT in vector form

    Roots of the unit

    Codes for the block DFT

    General elliptic Fourier transforms

    Cosine Transform

    Partitioning the DCT

    Paired algorithm for the N-point DCT

    Codes for the paired transform

    Reversible integer DCT

    Method of nonlinear equations

    Canonical representation of the integer DCT

    Hadamard Transform

    The Walsh and Hadamard transform

    Mixed Hadamard transformation

    Generalized bit and transformations

    T-decomposition of Hadamard matrices

    Mixed Fourier transformations

    Mixed transformations: continuous case

    Paired Transform-Based Decomposition

    Decomposition of 1D signals

    2D paired representation

    Fourier Transform and Multiresolution

    Fourier transform

    Representation by frequency-time wavelets

    Time-frequency correlation analysis

    Givens–Haar transformations




    Artyom M. Grigoryan, Merughan Grigoryan