如何从信号中去除频率 [英] How to remove frequency from signal

问题描述

我想从信号中去除一个频率(一个峰值)，并绘制没有该频率的函数.fft之后，我发现了频率和幅度，因此我不确定现在需要做什么.例如，我要删除我的最高峰(​​在图中标有红点).

I want to remove one frequency (one peak) from signal and plot my function without it. After fft I found frequency and amplitude and I am not sure what I need to do now. For example I want to remove my highest peak (marked with red dot on plot).

import numpy as np
import matplotlib.pyplot as plt

# create data
N = 4097
T = 100.0
t = np.linspace(-T/2,T/2,N)
f = np.sin(50.0 * 2.0*np.pi*t) + 0.5*np.sin(80.0 * 2.0*np.pi*t)

#plot function
plt.plot(t,f,'r')
plt.show()

# perform FT and multiply by dt
dt = t[1]-t[0]
ft = np.fft.fft(f) * dt      
freq = np.fft.fftfreq(N, dt)
freq = freq[:N/2+1]
amplitude = np.abs(ft[:N/2+1])
# plot results
plt.plot(freq, amplitude,'o-')
plt.legend(('numpy fft * dt'), loc='upper right')
plt.xlabel('f')
plt.ylabel('amplitude')
#plt.xlim([0, 1.4])


plt.plot(freq[np.argmax(amplitude)], max(amplitude), 'ro')
print "Amplitude: " + str(max(amplitude)) + "  Frequency: " + str(freq[np.argmax(amplitude)])

plt.show()

推荐答案

一种选择是将信号转换到频域，然后删除选定的频率.

One option is to transform the signal to the frequency domain then remove the selected frequency.

import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import rfft, irfft, fftfreq, fft

# Number of samplepoints
N = 500
# sample spacing
T = 0.1

x = np.linspace(0.0, (N-1)*T, N)
# x = np.arange(0.0, N*T, T)  # alternate way to define x
y = 5*np.sin(x) + np.cos(2*np.pi*x) 

yf = fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N//2)
#fft end

f_signal = rfft(y)
W = fftfreq(y.size, d=x[1]-x[0])

cut_f_signal = f_signal.copy()
cut_f_signal[(W>0.6)] = 0  # filter all frequencies above 0.6

cut_signal = irfft(cut_f_signal)

# plot results
f, axarr = plt.subplots(1, 3, figsize=(9, 3))
axarr[0].plot(x, y)
axarr[0].plot(x,5*np.sin(x),'g')

axarr[1].plot(xf, 2.0/N * np.abs(yf[:N//2]))
axarr[1].legend(('numpy fft * dt'), loc='upper right')
axarr[1].set_xlabel("f")
axarr[1].set_ylabel("amplitude")


axarr[2].plot(x,cut_signal)
axarr[2].plot(x,5*np.sin(x),'g')

plt.show()

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