Fast Fourier Transform and Convolution Algorithms

1. Front Matter

   Pages I-XII

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2. Introduction

   • Henri J. Nussbaumer

   Pages 1-3

3. Elements of Number Theory and Polynomial Algebra

   • Henri J. Nussbaumer

   Pages 4-31

4. Fast Convolution Algorithms

   • Henri J. Nussbaumer

   Pages 32-79

5. The Fast Fourier Transform

   • Henri J. Nussbaumer

   Pages 80-111

6. Linear Filtering Computation of Discrete Fourier Transforms

   • Henri J. Nussbaumer

   Pages 112-150

7. Polynomial Transforms

   • Henri J. Nussbaumer

   Pages 151-180

8. Computation of Discrete Fourier Transforms by Polynomial Transforms

   • Henri J. Nussbaumer

   Pages 181-210

9. Number Theoretic Transforms

   • Henri J. Nussbaumer

   Pages 211-240

10. Back Matter

    Pages 241-276

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In the first edition of this book, we covered in Chapter 6 and 7 the applications to multidimensional convolutions and DFT's of the transforms which we have introduced, back in 1977, and called polynomial transforms. Since the publication of the first edition of this book, several important new developments concerning the polynomial transforms have taken place, and we have included, in this edition, a discussion of the relationship between DFT and convolution polynomial transform algorithms. This material is covered in Appendix A, along with a presentation of new convolution polynomial transform algorithms and with the application of polynomial transforms to the computation of multidimensional cosine transforms. We have found that the short convolution and polynomial product algorithms of Chap. 3 have been used extensively. This prompted us to include, in this edition, several new one-dimensional and two-dimensional polynomial product algorithms which are listed in Appendix B. Since our book is being used as part of several graduate-level courses taught at various universities, we have added, to this edition, a set of problems which cover Chaps. 2 to 8. Some of these problems serve also to illustrate some research work on DFT and convolution algorithms. I am indebted to Mrs A. Schlageter who prepared the manuscript of this second edition. Lausanne HENRI J. NUSSBAUMER April 1982 Preface to the First Edition This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms.

• Algorithms
• Digitales Filter
• Faltung (Math.)
• Fourier
• Fourier-Transformation
• convolution

• Department d’Electricité, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

  Henri J. Nussbaumer

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