www.gusucode.com > wavelet工具箱matlab源码程序 > wavelet/wavelet/infowsys.m
function infowsys %INFOWSYS Information on wavelet packets. % % Wavelet Packets % %1. Wavelet Packets definition. % % Start: % an orthogonal wavelet psi, h and g the two filters % associated with the wavelet. % Both h and g are of length 2N. % % Wavelet packets generation: % % define by induction the set of functions % Wn for n = 0, 1, 2, ... % % W2n(x) = 2^{0.5}*sum ( h(k) Wn(2x-k) : for k = 0 to 2N-1) % W2n+1(x) = 2^{0.5}*sum ( g(k) Wn(2x-k) : for k = 0 to 2N-1) % % where W0 = phi and W1 = psi. % % The functions Wn are obtained roughly speaking by % superposition of 1/2-scaled and translated versions % of functions of lower index. % % Wavelet packets interpretation: % % Since all the Wn are supported by the same interval % [0,2N-1], Wn oscillates approximately n times and % then n can be interpreted as a frequency parameter. % % %2. Wavelet Packet Atoms. % % Starting from the Wn, let us consider the three-index % family of wavelet packet atoms, obtained by dyadic % dilations and translations of Wn: % % Wj,n,k (x) = 2^{-j/2} Wn(2^{-j} x - k) % % For a given value of j: % Wj,n,k allow to analyze the fluctuations of a given % signal roughly: % - around the position 2^{j}*k, % - at the scale 2^{j} % - at various frequencies n/2N, for n = 0 to 2^j-1. % M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 12-Mar-96. % Last Revision: 01-Jul-1999. % Copyright 1995-2002 The MathWorks, Inc.