1 November 1990 Relationships between the Fourier transform and the wavelet transform
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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.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Howard L. Resnikoff, 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); doi: 10.1117/12.23487; https://doi.org/10.1117/12.23487
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