A fast implementation of wavelet transform form - band lter banks
نویسندگان
چکیده
An orthogonal m-band discrete wavelet transform has an O(m 2) complexity. In this paper we present a fast implementation of such a discrete wavelet transform. In an orthonormal m-band wavelet system, the vanishing moments (which corresponds to the approximation order and smoothness) and orthogonality conditions are imposed on the scaling lter (or lowpass lter) only. Given a scaling lter, one can design the other m?1 wavelet lters (or highpass lters). It's well-known that there are innnitely many solutions in such designing procedure. Here we choose one speciic type of solutions and implement the corresponding wavelet transform in a scheme which has complexity O(m). Thus for any scaling lter, one can always construct a full orthogonal m-band wavelet matrix with an O(m) discrete wavelet transform.
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