pfwt_ym.m

来自「beamlet变化的工具箱」· M 代码 · 共 82 行

function w = PFWT_YM(u,L,deg)
% PFWT_YM -- Partial Forward Wavelet Transform (periodized Meyer Wavelet)
%  Usage
%    w = PFWT_YM(x,L,deg)
%  Inputs
%    u    unbiased fourier transform of 1-d signal x; length(x) = 2^J
%    L    Coarsest Level of V_0;  L << J
%    deg  degree of polynomial window 2 <= deg <=4
%  Outputs
%    w    1-d wavelet transform of x
%
%  Description
%    The Meyer wavelet is defined in the frequency domain.
%    The algorithm is very different from usual quadrature
%    mirror filter algorithms.  See the Ph. D. Thesis of
%    Eric Kolaczyk. To reconstruct use IWT_YM.
%	 This is a variant of the FWT_YM algorithm based on the assumption
%	 that one is starting from the frequency domain; in particular
%	 from the unbiased Fourier transform of the original signal;
%	 see fft_ua, ifft_ua.
%
%  See Also
%    IWT_YM, CoarseMeyerCoeff, DetailMeyerCoeff, FineMeyerCoeff
%

	if L < 3,
		'L must be >= 3.  Enter new value of L or hit Ctrl-C to break.'
		L = input('L = ?');
	end
%
	nn = length(u);
	J = log2(nn);
	fhat = UFT2FFT(u);
%
%  Compute Coefficients at Coarse Level.
%

	w(1:(2^L)) = CoarseMeyerCoeff(fhat,L,nn,deg);

%
%  Loop to Get Detail Coefficients for levels  j=L,...,J-2.
%
	for j = L:(J-2),
	  w((2^j+1):(2^(j+1))) = DetailMeyerCoeff(fhat,j,nn,deg);
	end
%
%  Calculate Fine Level Detail Coefficients (for j=J-1).
%
	w((2^(J-1)+1):(2^J)) = FineMeyerCoeff(fhat,nn,deg);
%
%	Normalize as isometry
%
	w = w .* nn;	
%
%  PFWT_YM is adapted from the code for FWT_YM in Wavelab .701
%  FWT_YM is Copyright (c) Eric Kolaczyk, 1994.
%  PFWT_YM is Copyright (c) David L. Donoho, 1998.
%     
    
%   
% Part of WaveLab Version .701
% Built Tuesday, January 30, 1996 8:25:59 PM
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%   
    

%
% Part of BeamLab Version:200
% Built:Friday,23-Aug-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%
%
% Part of BeamLab Version:200
% Built:Saturday,14-Sep-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%