Reconstruct
Purpose
Description
Example
Macro Synopsis
Modules
Related Functions
References
Purpose
Inverse discrete wavelet transform
Description
"Reconstruct" reconstructs a signal from its wavelet decomposition
(discrete wavelet transform).
The only parameter is the
- number n of octaves of the discrete wavelet transform.
If we have the approximation 
and detail 
signal at octave i (see the manual section of Decompose) we define new signals
by
Thus the new signals are upsampled versions of the original signals.
The approximation at octave i-1 is
where mathtextmt2conv denotes a convolution operation.
Starting at the last octave n, this iteration is repeated until we finally
get the reconstructed signal 
.
Example
First, decompose a signal by applying Decompose , confirm the number of
octaves suggested; then pass the result to "Reconstruct" , leaving the number of
octaves unchanged.
The result from reconstruction should be equal to the original signal.
(Don't mind the padding that will occur if the signal length was not a
power of 2.)
Macro Synopsis
y = WaveletReconst(x,n);
signal x,y;
int n;
Note that x must be a discrete wavelet transform (DWT) signal.
Modules
Wavelet
Related Functions
Define wavelet, Load wavelet,
Save wavelet, Decompose,
Approximation, Detail
References
Daubechies [6], Rioul/Vetterli [7]