Short Notes on Wavelets

Integer Haar Wavelets, Python implementation

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

In the following, d can be either list, or numpy.array.

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]