2005Unpublished venueRequires access

Fourier Methods

H. J. Pain

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Abstract

This chapter contains sections titled: Fourier Series Application of Fourier Sine Series to a Triangular Function Application to the Energy in the Normal Modes of a Vibrating String Fourier Series Analysis of a Rectangular Velocity Pulse on a String The Spectrum of a Fourier Series Fourier Integral Fourier Transforms Examples of Fourier Transforms The Slit Function The Fourier Transform Applied to Optical Diffraction from a Single Slit The Gaussian Curve The Dirac Delta Function, its Sifting Property and its Fourier Transform Convolution The Convolution Theorem

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What this paper is about

This chapter contains sections titled: Fourier Series Application of Fourier Sine Series to a Triangular Function Application to the Energy in the Normal Modes of a Vibrating String Fourier Series Analysis of a Rectangular Velocity Pulse on a String The Spectrum of a Fourier Series Fourier Integral Fourier Transforms Examples of Fourier Transforms The Slit Function The Fourier Transform Applied to Optical Diffraction from a Single Slit The Gaussian Curve The Dirac Delta Function, its Sifting Property and its Fourier Transform Convolution The Convolution Theorem

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Available abstract

This chapter contains sections titled: Fourier Series Application of Fourier Sine Series to a Triangular Function Application to the Energy in the Normal Modes of a Vibrating String Fourier Series Analysis of a Rectangular Velocity Pulse on a String The Spectrum of a Fourier Series Fourier Integral Fourier Transforms Examples of Fourier Transforms The Slit Function The Fourier Transform Applied to Optical Diffraction from a Single Slit The Gaussian Curve The Dirac Delta Function, its Sifting Property and its Fourier Transform Convolution The Convolution Theorem

Key concepts: Fourier sine and cosine series, Fourier inversion theorem, Sine and cosine transforms, Discrete-time Fourier transform, Fourier transform, Fourier series, Fourier analysis, Fractional Fourier transform

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