irwt.sci

小波分解源代码

function sig = IRWT(rwt,scale)
// iRWT -- Inverse Real Wavelet Transform
//  Usage
//    sig = iRWT(rwt,scale);
//  Inputs
//    rwt	matrix n by nscale, output from RWT.m
//    scale	real signal, complementary part, output from RWTscale.m
//  Output
//    sig	1-d real signal. 
//  Side Effects
//  Description
//    We did not really calculate the scaling function. In fact, scale is 
//    a record of residual in Frequency Domain.
//    Why not use scaling function,
//	1. complicated to implement;
//	2. differ with various window, what's the difference in tracing
//	   a residual in Frequency domain than in space expanded by scaling
//	   function.
//  Algorithm
//    The result is PSEUDO Inverse Real Wavelet Transform. 
//  Examples
//     CantorMeasure = MakeFractal(1024,3,'Deterministic',[.5 0 .5]);
//     Devil  = cumsum(CantorMeasure); 
//     Devil_rwt = RWT(Devil,12,'Sombrero');
//     scale = RWTscale(Devil,Devil_rwt);
//     sig = iRWT(Devil_rwt,scale); 
//     subplot(211);  	plot(Devil);    
//     subplot(212);	plot(sig);
//  See Also
//    RWT   RWTscale
//  Description
//    Reconstruct original signal from Continuous Wavelet Transform
//  References
//    Mallat, "A Wavelet Tour of Signal Processing"; 4.3.1 Real Wavelets.
//
//  Copyright Aldo I Maalouf

 sz = size(rwt);
 
 dftsig = mtlb_fft(scale(:));
 for i = 1:sz(2),
        dftsig = dftsig + mtlb_fft(rwt(:,i));
 end;
 sig = real(mtlb_ifft(dftsig));
 endfunction