A two dimensional image is analyzed for its frequency content, and an estimate of the scaling correlation between pixels at multiple resolutions and spatial translations is returned. The following graphics manipulation program solves this problem, and converts between standard image file formats. The FFT uses cosines, sines and exponentials to represent a signal, and is most useful for representing linear functions.
Wavelets offer a new method to analyze complex signals.
The aim of the wavelet transform is to 'express' an input signal into a series of coefficients of specified energy . The discrete numbers associated with each coefficient contain all the information needed to completely describe the signal provided one knows which analyzing wavelet was used for the decomposition. The wavelet transform partitions a signal with respect to spatial frequency. The father wavelet provides an approximate or blurred version of the signal at successive resolutions, while the mother wavelet captures the detail at each resolution. The wavelet transform of a 2-D signal returns a coefficient matrix which maps all the spatial relationships at multiple scales in the horizontal, vertical and diagonal directions.