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Fourier series and the discrete Fourier transform

A. S. Sehmi

Open publisher page 1 citations

Abstract

This chapter introduces the real and complex Fourier series. The Fourier integral is developed as a method for extracting spectral information from signals in the continuous time domain. The Fourier transform is developed and leads to the discrete Fourier transform. Important properties of the discrete Fourier transform and issues in its practical usage are explained. The discrete Fourier transform is related to the z-transform and other uses for it are highlighted.

About this research paper

What this paper is about

This chapter introduces the real and complex Fourier series. The Fourier integral is developed as a method for extracting spectral information from signals in the continuous time domain. The Fourier transform is developed and leads to the discrete Fourier transform. Important properties of the discrete Fourier transform and issues in its practical usage are explained. The discrete Fourier transform is related to the z-transform and other uses for it are highlighted.

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Available abstract

This chapter introduces the real and complex Fourier series. The Fourier integral is developed as a method for extracting spectral information from signals in the continuous time domain. The Fourier transform is developed and leads to the discrete Fourier transform. Important properties of the discrete Fourier transform and issues in its practical usage are explained. The discrete Fourier transform is related to the z-transform and other uses for it are highlighted.

Key concepts: Discrete-time Fourier transform, Discrete Fourier transform (general), Non-uniform discrete Fourier transform, Fractional Fourier transform, Fourier transform, Discrete Fourier series, Short-time Fourier transform, Harmonic wavelet transform

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