# Difference between revisions of "Short Notes on Wavelets"

## Integer Haar Wavelets, Python implementation

### 1D Case

This is a trivial implementation of Haar integer-to-integer wavelets.

The d array (list or numpy.array) has to be power of 2.

Note that resulting values typically use 1 more bit than original ones - if source values are in [0..N) interval, then resulting values are in (-N, N) interval.

#### Using Lists

```def haar_int_fwd_1d(d):
if len(d) == 1:
return d
even = d[::2]
odd = d[1::2]
hp = [j - i for i, j in zip(even, odd)]
lp = [i + (w >> 1) + (w % 2) for i, w in zip(even, hp)]
return haar_int_fwd_1d(lp) + hp

def haar_int_inv_1d(d):
if len(d) == 1:
return d
even = haar_int_inv_1d(d[:len(d) >> 1])
odd = d[len(d) >> 1:]
lp = [i - (j >> 1) - (j % 2) for i, j in zip(even, odd)]
hp = [i + j for i, j in zip(lp, odd)]
return [x for t in zip(lp, hp) for x in t]```

#### Using numpy Array's

```import numpy as np

def haar_int_fwd_1d_np(d):
if len(d) == 1:
return d
hp = d[1::2] - d[::2]
lp = d[::2] + (hp >> 1) + (hp % 2)
return np.concatenate((haar_int_fwd_1d_np(lp), hp))

def haar_int_inv_1d_np(d):
if len(d) == 1:
return d
lp = haar_int_inv_1d_np(d[:len(d) >> 1])
hp = d[len(d) >> 1:]
even = lp - (hp >> 1) - (hp % 2)
return np.ravel(np.column_stack((even, even + hp)))```

### 2D Extension

The list-based version is not provided.

TBP