请用python写出FeedbackVMD algorithm (FVMD)的代码
时间: 2024-05-13 15:18:42 浏览: 9
Feedback-VMD算法是一种信号分解方法,它将信号分解为多个本征模式,可以用于信号降噪、分析和重构。下面是使用Python实现Feedback-VMD算法的代码:
``` python
import numpy as np
from scipy.signal import hilbert
def feedback_vmd(signal, alpha, tau, K, maxiter):
"""
Feedback-VMD algorithm.
Parameters:
signal (array): The input signal to be decomposed.
alpha (float): The regularization parameter for the feedback term.
tau (float): The time step for the feedback term.
K (int): The number of intrinsic mode functions.
maxiter (int): The maximum number of iterations.
Returns:
imfs (array): The intrinsic mode functions.
res (array): The residual signal.
"""
# Define the kernel function
def kernel(x, y):
return np.exp(-(x-y)**2 / (2*tau**2))
# Initialize the variables
N = len(signal)
h = np.zeros((K, N))
g = np.zeros((K, N))
omega = np.zeros((K, N))
lambda_ = np.zeros(K)
imfs = np.zeros((K, N))
res = signal.copy()
# Perform the decomposition
for k in range(K):
for i in range(maxiter):
# Compute the Hilbert transform
hil = hilbert(res)
hil = np.imag(hil)
# Compute the center frequency
omega[k,:] = np.fft.fftfreq(N, d=1/N) + lambda_[k]
# Compute the projection
h[k,:] = np.real(np.fft.ifft(np.fft.fft(res) * kernel(omega[k,:], omega[k,0])))
# Compute the feedback term
if k > 0:
g[k,:] = alpha * np.sum(h[:k,:], axis=0)
# Update the IMF
imfs[k,:] = h[k,:] - g[k,:]
res = res - imfs[k,:]
# Update the center frequency
lambda_[k] = lambda_[k] + np.mean(omega[k,:] - np.fft.fftfreq(N, d=1/N))
# Check for convergence
if np.sum(np.abs(imfs[k,:])) < 1e-10:
break
return imfs, res
```
其中,输入参数`signal`是要分解的信号,`alpha`是反馈项的正则化参数,`tau`是反馈项的时间步长,`K`是分解出的本征模式数目,`maxiter`是最大迭代次数。输出结果`imfs`是分解后的本征模式,`res`是剩余信号。