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- Fast Fourier Transform And Convolution Algorithms
- Computation of Convolutions and Discrete Fourier Transforms by Polynomial Transforms
- Nussbaumer, Henri J. - Fast Fourier Transform And Convolution Algorithms

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## Fast Fourier Transform And Convolution Algorithms

Download Nussbaumer, Henri J. Discrete and Fast Fourier Transforms, algorithmic processes widely used in quantum mechanics, signal Overview of the Continuous Fourier Transform and Convolutions. This paper assesses one class of algorithms, namely the fast Fourier transform FFT algorithms for exact analysis of discrete data. Henri J Nussbaumer Henri J. Fast Fourier Transform and Convolution Algorithms MR 4 I. Schur, ber die Gauschen Summen , Gttinger Nachr.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Fast polynomial transform algorithms for digital convolution Abstract: We have recently introduced new transforms, called polynomial transforms, which are defined in rings of polynomials and give efficient algorithms for the computation of multidimensional DFT's and convolutions. In this paper we present a method for computing one-dimensional convolutions by polynomial transforms. We show that this method is computationally efficient, even for large convolutions, and can be implemented with FFT-type algorithms, while avoiding the use of trigonometric functions and complex arithmetic. We then extend this technique to complex convolutions and to multidimensional convolutions.

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. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity.

## Computation of Convolutions and Discrete Fourier Transforms by Polynomial Transforms

MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. I was happy to, at least, have an idea how is it possible that the algorithm works :. Also in some other papers I found reference to weighting. And this is what bothers me now. There was no weighting function in complex FFT.

Fast Fourier Transform and Convolution Algorithms. Authors Henri J. Nussbaumer. Pages PDF · Elements of Number Theory and Polynomial Algebra.

## Nussbaumer, Henri J. - Fast Fourier Transform And Convolution Algorithms

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It seems that you're in Germany. We have a dedicated site for Germany. 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. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra.

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