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Signal Approximation with Fourier Transform based on Scaling Orthonormal Basis Function

Tohid Aribi

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wavelet bases has opened a new bridge between approximation theory and signal processing. It is possible to keep the simplicity while improving the performance with non-linearities in a sparse representation. The analysis results imply that proposed method has lots of efficiency over other methods.