## 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]