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Proceedings Paper

Relationships between the Fourier transform and the wavelet transform
Author(s): Howard L. Resnikoff; C. Sidney Burrus
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Paper Abstract

This paper derives the relationship between the coefficients of the Fourier expansion of a periodic signal and the coefficients of the wavelet expansion of the same signal. The formula derived shows how the Fourier concept of frequency and the wavelet concept of scale are related and how the wavelet coefficients display the information contained in the signal in a new way. The relationship also shows how the wavelet expansion can be used to approximately calculate the Fourier coefficients.

Paper Details

Date Published: 1 November 1990
PDF: 10 pages
Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); doi: 10.1117/12.23487
Show Author Affiliations
Howard L. Resnikoff, Aware, Inc. (United States)
C. Sidney Burrus, Aware, Inc. and Rice Univ. (United States)


Published in SPIE Proceedings Vol. 1348:
Advanced Signal Processing Algorithms, Architectures, and Implementations
Franklin T. Luk, Editor(s)

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