CH02_SEC05_HAAR.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [12, 8]
plt.rcParams.update({'font.size': 18})


x = np.arange(0,1,0.001)
n = len(x)
n2 = int(np.floor(n/2))
n4 = int(np.floor(n/4))

f10 = np.zeros_like(x)
f10[:n2] = 1
f10[n2:] = -1

f21 = np.zeros_like(x)
f21[:n4] = 1
f21[n4:n2] = -1
f21 = f21 * np.sqrt(2)

f22 = np.zeros_like(x)
f22[n2:(n2+n4)] = 1
f22[(n2+n4):] = -1
f22 = f22 * np.sqrt(2)

# x = np.concatenate((-1, 0, x, 1, 2))
x = np.append([-1,0],x)
x = np.append(x,[1,2])

f10 = np.pad(f10, (2, 2), 'constant')
f21 = np.pad(f21, (2, 2), 'constant')
f22 = np.pad(f22, (2, 2), 'constant')

fig,axs = plt.subplots(3,1)
axs[0].plot(x,f10,color='k',linewidth=2)
axs[0].set_xlim(-0.2,1.2)
axs[0].set_ylim(-1.75,1.75)
axs[1].plot(x,f21,color='k',linewidth=2)
axs[1].set_xlim(-0.2,1.2)
axs[1].set_ylim(-1.75,1.75)
axs[2].plot(x,f22,color='k',linewidth=2)
axs[2].set_xlim(-0.2,1.2)
axs[2].set_ylim(-1.75,1.75)
plt.show()

x = np.arange(-5,5,0.001)
fMexHat = (1-np.power(x,2)) * np.exp(-np.power(x,2)/2)
plt.plot(x,fMexHat,color='k',linewidth=2)
plt.show()