python - How to define my own continuous wavelet by using Python?

Question

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?

Answer 1

根据这个，您需要一个函数，该函数需要多个点和一个比例作为wavelet参数提供

所以我们这样定义：

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)

让我们测试一下。我们注意到，实际上可以使用与您的非常相似的东西。不同之处在于缩放比例a，并且常数是正面看起来略有不同。注意math.sqrt(2)Ricker 小波的缩放

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()

这是图表：