Relationships between the Fourier transform and the wavelet transform
Howard L. Resnikoff, C.S. Burrus · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
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.