    ## 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.

Wavelet

### Related Functions

Define wavelet, Load wavelet, Save wavelet, Decompose, Approximation, Detail

### References

Daubechies , Rioul/Vetterli