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import matplotlib.pyplot as plt
import numpy as np
from scipy.fft import rfft, rfftfreq
n, T = 100, 0.01 # number of samples and sampling interval
tau = n*T
t = np.arange(n) * T
fcc = (20, 20.5) # frequencies of sines
xx = (np.sin(2 * np.pi * fc_ * t) for fc_ in fcc) # sine signals
f = rfftfreq(n, T) # frequency bins range from 0 Hz to Nyquist freq.
XX = (rfft(x_) / n for x_ in xx) # one-sided FFT normalized to magnitude
i0, i1 = 15, 25
f_cont = np.linspace(f[i0], f[i1], 501)
fg1, axx = plt.subplots(1, 2, sharey='all', tight_layout=True,
figsize=(6., 3.))
for c_, (ax_, X_, fx_) in enumerate(zip(axx, XX, fcc)):
Xc_ = (np.sinc(tau * (f_cont - fx_)) +
np.sinc(tau * (f_cont + fx_))) / 2
ax_.plot(f_cont, abs(Xc_), f'-C{c_}', alpha=.5, label=rf"$f_x={fx_}\,$Hz")
m_line, _, _, = ax_.stem(f[i0:i1+1], abs(X_[i0:i1+1]), markerfmt=f'dC{c_}',
linefmt=f'-C{c_}', basefmt=' ')
plt.setp(m_line, markersize=5)
ax_.legend(loc='upper left', frameon=False)
ax_.set(xlabel="Frequency $f$ in Hertz", xlim=(f[i0], f[i1]),
ylim=(0, 0.59))
axx[0].set(ylabel=r'Magnitude $|X(f)/\tau|$')
fg1.suptitle("Continuous and Sampled Magnitude Spectrum ", x=0.55, y=0.93)
fg1.tight_layout()
plt.show()
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