Orthogonal wavelet transforms and filter banks

Summary form only given. A new class of orthogonal basis functions that can be relevant to signal processing has recently been introduced. These bases are constructed from a single smooth bandpass function ψ(t), the wavelet, by considering its translates and dilates on a dyadic grid 2ⁿ, 2ⁿm of points, ψ_n,m(t)=2^-n/2ψ(2^-n t-m). It is required that ψ(t) be well localized in both the time and frequency domain, without violating the uncertainty principle. Any one-dimensional signal can be represented by the bidimensional set of its expansion coefficients. Multidimensional signals can also be expanded in terms of wavelet bases. An algorithm for computing the expansion coefficients of a signal in terms of wavelet bases has been found, the structure of which is that of a pruned-tree quadrature mirror multirate filter bank. The construction of wavelet bases and their relation to filter banks, together with several design techniques for wavelet generating quadrature mirror filters and examples, are reviewed