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  • Video 
    Fourier Analysis: Overview

    Fourier Analysis: Overview

    This video presents an overview of the Fourier Transform, which is one of the most important transformations in all of mathematical physics and engineering. This series will introduce the analytic theory of the Fourier Transform, along with the Fast Fourier Transform (FFT) algorithm for efficient computations. We will explore lots of applications in image compression, audio analysis, and solving partial differential equations.

    Course related:
    EIE3331 Communication Fundamentals, EE3312 Linear Systems, and EIE4413 Digital Signal Processing
    Subjects:
    Mathematics and Statistics
    Keywords:
    Fourier transformations
    Resource Type:
    Video
     
  • e-book 
    Fast Fourier Transforms

    Fast Fourier Transforms

    This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting. This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.

    Subjects:
    Computing, Data Science and Artificial Intelligence and Mathematics and Statistics
    Keywords:
    Fourier transformations Textbooks
    Resource Type:
    e-book