As the title shows, I want to define my own continuous wavelet by Python. However, I don't know how to achieve this exactly.
The formula of my wavelet mother function is below
It looks something like the Mexican hat wavelet, but they are different.
So how can I define such a custom wavelet by Python, then CWT can be performed using this wavelet?
Per this you need a function that takes a number of points and a scale to provide as a wavelet argument
So we define it as such:
import math
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
mother_wavelet = lambda z : np.exp(-z*z/4)*(2-z*z)/(4*math.sqrt(math.pi))
def mexican_hat_like(n,scale):
x = np.linspace(-n/2,n/2,n)
return mother_wavelet(x/scale)
Let's test it. We note that in fact something that looks very similar to yours is available. The difference is in scaling a and also the constant is front looks slightly different. Note math.sqrt(2) scaling for the Ricker wavelet
points = 100
a = 4.0
vec_ours = mexican_hat_like(points, a)
vec_theirs = signal.ricker(points, a*math.sqrt(2))
plt.plot(vec_ours, label = 'ours')
plt.plot(vec_theirs, label = 'ricker')
plt.legend(loc = 'best')
plt.show()
Here is the graph:
mother_wavelet inside the function mexican_hat_like?
x = np.linspace(-n/2,n/2,n) return mother_wavelet(x/scale) so not sure what you mean? I am not sure what are the 'true' values of wavelets but you can change your x-s there