Relationships between the Fourier transform and the wavelet transform

Howard L. Resnikoff; C. Sidney Burrus

doi:10.1117/12.23487

1 November 1990 Relationships between the Fourier transform and the wavelet transform

Howard L. Resnikoff, C. Sidney Burrus

Proceedings Volume 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations; (1990) https://doi.org/10.1117/12.23487
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

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.

Citation Download Citation

Howard L. Resnikoff and C. Sidney Burrus "Relationships between the Fourier transform and the wavelet transform", Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); https://doi.org/10.1117/12.23487

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