Optical Haar wavelet transform with Computer-generated holograms

摘要

1 Introduction For signal analysis and processing,a Fourier transform (FT) represents a signal in terms of its frequency contents. After the limitations of simple Fourier transformation were observed,especially for transient signals,windowed or short-time Fourier transforms and later wavelet transform (WT' s) were introduced. A WT represents the signal in terms of a family of functions that is derived from a single basic function called a wavelet,by dilation (scaling) and translation (shift)operations. Fourier transformation gives global frequency information about the signal,whereas wavelet transformation gives local frequency information in the signal. With a WT,a scene (signal) can be decomposed into space-frequency (time-frequency) components. This space-frequency (time-frequency)representation nature of a WT leads to its many promising applications in multiresolution image analysis,data compression,pattern recognition,fractal analysis,transient signal,and image processing,etc.