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IRWT

Inverse Real Wavelet Transform

Calling Sequence

sig = iRWT(rwt,scale);

Parameters

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.

Description

Reconstruct original signal from Continuous Wavelet Transform

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

Bibliography

Mallat, "A Wavelet Tour of Signal Processing"; 4.3.1 Real Wavelets.

Authors

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