Solution P6.8.1
The code below truncates the function at 0.5 s and 0.2 s, showing the effect on its Fourier transform.
import numpy as np
import pylab
freq, tau = 250, 0.2
fsamp = 1000
duration = 10
t = np.arange(0, duration, 1/fsamp)
n = len(t)
f = np.cos(2 * np.pi * freq * t) * np.exp(-t/tau)
for thresh in (0.5, 0.2):
f[t > thresh] = 0.
F = np.fft.rfft(f)
freq = np.fft.rfftfreq(n, 1/fsamp)
pylab.plot(freq, abs(F))
pylab.show()
Apodization resulting from truncation of the time series at 0.5 s:
Apodization resulting from truncation of the time series at 0.2 s:
