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1999•Birkhäuser Boston eBooksRequires access

Discrete and Fast Fourier Transforms

Yves Nievergelt

Open publisher page 2 citations

Abstract

This chapter introduces a few features of the Discrete Fourier Transform (DFT) and its computation through the Fast Fourier Transform (FFT), which interpolates finite sequences of numbers by Fourier Series. The Fast Fourier Transform provides a comparison and contrast with the Fast Haar and Daubechies Wavelet Transforms in a context that involves complex exponentials and some linear algebra but that does not yet require calculus. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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What this paper is about

This chapter introduces a few features of the Discrete Fourier Transform (DFT) and its computation through the Fast Fourier Transform (FFT), which interpolates finite sequences of numbers by Fourier Series. The Fast Fourier Transform provides a comparison and contrast with the Fast Haar and Daubechies Wavelet Transforms in a context that involves complex exponentials and some linear algebra but that does not yet require calculus. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Available abstract

This chapter introduces a few features of the Discrete Fourier Transform (DFT) and its computation through the Fast Fourier Transform (FFT), which interpolates finite sequences of numbers by Fourier Series. The Fast Fourier Transform provides a comparison and contrast with the Fast Haar and Daubechies Wavelet Transforms in a context that involves complex exponentials and some linear algebra but that does not yet require calculus. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Key concepts: Discrete Fourier transform (general), Harmonic wavelet transform, Discrete-time Fourier transform, Non-uniform discrete Fourier transform, Fractional Fourier transform, Fourier transform, Fourier inversion theorem, Mathematics

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