Wavelets in Signal and Image Analysis

The intention of this paper is to pro vide an elementary introduction to the subject of discret e-time wavelets. It defines the discret e-t ime wavelet s and reviews t heir properties in a syste mat ic and consiste nt way. Different kinds of ort hogona lity between the wavelets are addressed and the corres pond ing sufficient and necessary condit ions ar e derived . It is shown when discret e-t ime wavelets can be samples of continuous-t ime wavelet s. The condit ions for shift-invari an ce of discrete-time wavelet representations are given in det ail. The appearance of two biorthogonal representation sets of discrete-ti me wavelet s from t he binary subband decomposition /reconstruction of signals is pointed out . When t he numher of different representation scales is finit e, it is shown that in order to obtain the orthogonality betwe en wavelet s, the known requircm cnt for wavelet generating filter can be relaxed .

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