Haar wavelet

haar_wavelet.py

import math

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats


# Generate some data
a = 1.99

# Create a figure
fig = plt.figure()
ax = fig.add_subplot(111)

def plot(dist, label):
    x = np.linspace(stats.gamma.ppf(0.01, a), stats.gamma.ppf(0.99, a), len(dist)).tolist()
    ax.plot(x, dist, lw=2, label=label)

# Plot the true PDF
x = np.linspace(stats.gamma.ppf(0.01, a), stats.gamma.ppf(0.99, a), 300).tolist()
y = stats.gamma(a).pdf(x)
plot(y, 'PDF')

# Apply the Haar wavelet
def decompose(x: list) -> (list, list):
    averages = [0] * math.ceil(len(x) / 2)
    coefficients = [0] * math.ceil(len(x) / 2)
    for i, j in enumerate(range(0, len(x), 2)):
        averages[i] = (x[j] + x[min(j+1, len(x)-1)]) / 2
        coefficients[i] = averages[i] - x[j]
    return averages, coefficients

w, c = decompose(y)
plot(w, 'Haar 1')
for i in range(3):
    w, c = decompose(w)
    plot(w, f'Haar {i+2}')

plt.legend()
plt.show()