fft: why my main peak is lower than the side peak?

问题:

The original data is on the google drive. It is a two columns data, t and x. I did the following discrete fft transform. I don't quite understand that the main peak(sharp one) has a lower height than the side one. The second the subplot shows that it is indeed that the sharp peak(most close to 2.0) is the main frequency. The code and the figure is as follows:

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

freqUnit=0.012/(2*np.pi)
data = np.loadtxt(fname='data.txt')
t = data[:,0]
x = data[:,1]
n=len(t)
d=t[1]-t[0]

fig=plt.figure()
ax1=fig.add_subplot(3,1,1)
ax2=fig.add_subplot(3,1,2)
ax3=fig.add_subplot(3,1,3)

y = abs(fft(x))
freqs = fftfreq(n, d)/freqUnit

ax1.plot(t, x)
ax2.plot(t, x)
ax2.set_xlim(40000,60000)
ax2.set_ylim(0.995,1.005)
ax3.plot(freqs,y,'-.')
ax3.set_xlim(0,4)
ax3.set_ylim(0,1000)
plt.show()

回答1:

You need to apply a window function prior to your FFT, otherwise you will see artefacts such as the above, particularly where a peak in the spectrum does not correspond directly with an FFT bin centre.

See "Why do I need to apply a window function to samples when building a power spectrum of an audio signal?" question for further details.