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SCaVis manual

# Fast Wavelet Transform (FWT)

Snippet from Wikipedia: Fast wavelet transform

The Fast Wavelet Transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets.

Here is FWT for 1D array using Haar method. We use ` Transform` class for this task:

```from math.jwave import Transform
from math.jwave.transforms import *
from math.jwave.transforms.wavelets import *

t=Transform(  FastWaveletTransform( Haar02( ) ))
arrTime = [1, 10, 12, 8, 1, 1, 1, 1. ]
arrFreq = t.forward( arrTime ) # 1-D FWT Haar forward
print arrFreq.tolist()
arrReco = t.reverse( arrFreq ) # 1-D FWT Haar reverse
print arrReco.tolist()```

The output of this code is:

```[12.374368670764577, 9.545941546018389, -4.499, 0.0, -6.363, 2.8284, 0.0, 0.0]
[1, 10, 12, 8, 1, 1, 1, 1. ]```

## FWT in 2D

Now let us consider a FWT transformation of 2D array. This is an extension of the above script:

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