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The Regularized Fast Hartley Transform

Low-Complexity Parallel Computation of the FHT in One and Multiple Dimensions

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  • © 2022

Overview

Authors:
  1. Keith John Jones

    1. Wyke Technologies Ltd., Weymouth, UK

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  • Describes solutions to 1-D and m-D versions of the FHT and the real-data FFT targeted at applications
  • Achieves the computational density of the most advanced commercially-available solutions for greatly reduced silicon resources
  • Presents simple design variations that enable one to optimize the use of the available silicon resources

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xix
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  2. The Discrete Fourier and Hartley Transforms

    1. Front Matter

      Pages 1-1
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    2. Background to Research

      • Keith John Jones
      Pages 3-21

    3. The Real-Data Discrete Fourier Transform

      • Keith John Jones
      Pages 23-34

    4. The Discrete Hartley Transform

      • Keith John Jones
      Pages 35-50

  4. Applications of Regularized Fast Hartley Transform

    1. Front Matter

      Pages 135-135
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    2. Derivation of Radix-2 Real-Data Fast Fourier Transform Algorithms Using Regularized Fast Hartley Transform

      • Keith John Jones
      Pages 137-160

    3. Computation of Common DSP-Based Functions Using Regularized Fast Hartley Transform

      • Keith John Jones
      Pages 161-187

  6. Results of Research

    1. Front Matter

      Pages 245-245
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    2. Summary and Conclusions

      • Keith John Jones
      Pages 247-252

  7. Back Matter

    Pages 253-320
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Keywords

About this book

This book describes how a key signal/image processing algorithm – that of the fast Hartley transform (FHT) or, via a simple conversion routine between their outputs, of the real‑data version of the ubiquitous fast Fourier transform (FFT) – might best be formulated to facilitate computationally-efficient solutions. The author discusses this for both 1-D (such as required, for example, for the spectrum analysis of audio signals) and m‑D (such as required, for example, for the compression of noisy 2-D images or the watermarking of 3-D video signals) cases, but requiring few computing resources (i.e. low arithmetic/memory/power requirements, etc.). This is particularly relevant for those application areas, such as mobile communications, where the available silicon resources (as well as the battery-life) are expected to be limited. The aim of this monograph, where silicon‑based computing technology and a resource‑constrained environment is assumed and the data is real-valued in nature, hasthus been to seek solutions that best match the actual problem needing to be solved.

Authors and Affiliations

  • Wyke Technologies Ltd., Weymouth, UK

    Keith John Jones

About the author

Dr. Keith John Jones received his Ph.D in Computer Science from Birkbeck College, London University and his M.Sc in Applicable Mathematics from Cranfield Institute of Technology. He has an entry in “Who’s Who in Science and Engineering” (2008-present) and in “The Dictionary of International Biography” (otherwise known as “The Cambridge Blue Book”) (2008-present). He is currently a consultant at Wyke Technologies Ltd., Weymouth, Dorset (2015-present), having previously been employed as a mathematician/algorithmist/programmer & system designer for TRL Technology Ltd., Tewkesbury, Gloucestershire and, prior to that, for QinetiQ, Winfrith, Dorset. In 2010 he published “The Regularized Fast Hartley Transform: Optimal Formulation of Real-Data Fast Fourier Transform for Silicon‑Based Implementation in Resource-Constrained Environments”. He has 10 patents and has published extensively in the field.

Bibliographic Information

  • Book Title: The Regularized Fast Hartley Transform

  • Book Subtitle: Low-Complexity Parallel Computation of the FHT in One and Multiple Dimensions

  • Authors: Keith John Jones

  • DOI: https://doi.org/10.1007/978-3-030-68245-3

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-68244-6Published: 03 September 2021

  • Softcover ISBN: 978-3-030-68247-7Published: 04 September 2022

  • eBook ISBN: 978-3-030-68245-3Published: 03 September 2021

  • Edition Number: 2

  • Number of Pages: XIX, 320

  • Number of Illustrations: 57 b/w illustrations

  • Topics: Signal, Image and Speech Processing, Theory of Computation, Communications Engineering, Networks

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