Approximate Fourier expansion: its properties and applications

Qurban A. Memon

doi:10.1117/12.258226

14 November 1996 Approximate Fourier expansion: its properties and applications

Qurban A. Memon

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Proceedings Volume 2847, Applications of Digital Image Processing XIX; (1996) https://doi.org/10.1117/12.258226
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

For signal representation, it is always desired that a signal be represented using minimum number of parameters. An important criterion of signal representation is the orthogonality of the constituent basis functions of a transform. There are various orthogonal transforms such like Karhunen-Loeve, discrete cosine, Haar, discrete Fourier etc., but the choice of a particular transform in a given application depends on the amount of reconstruction error that can be tolerated and the computational resources available. The approximate Fourier expansion (AFE) for non- periodic signals with theoretically uncorrelated coefficients has previously been proposed. In this paper, we will give system interpretation to approximate AFE using generalized harmonic analysis. Furthermore, we will investigate some mathematical properties of discrete AFE. Finally, we will apply AFE expansion to images, and show that for purposes of decorrelation is better than discrete Fourier transform. For comparison purposes, the results will also be compared with discrete cosine transform. Computer simulation results will also be presented.

Citation Download Citation

Qurban A. Memon "Approximate Fourier expansion: its properties and applications", Proc. SPIE 2847, Applications of Digital Image Processing XIX, (14 November 1996); https://doi.org/10.1117/12.258226

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KEYWORDS

Fourier transforms

Bandpass filters

Computer simulations

Distortion

Data modeling

Information technology

Signal processing

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