# Python code

import numpy as np
import matplotlib.pyplot as plt

dur = 20
fs = 1024
freq = np.arange(1, 500, 1)
t1 = np.arange(0, dur, 1/fs)
x1 = np.sum([np.sin(2*np.pi*f*t1) for f in freq], axis=0)

nfft = 1024
X1 = np.fft.fft(x1, nfft)[:nfft//2]
f1 = np.arange(0, nfft//2) * fs / nfft

plt.figure()
plt.title('Baseline FFT Output')
plt.plot(f1, np.abs(X1))
plt.grid()
plt.xlim([0, nfft/2])
plt.show()

step = 10
x2 = x1[::step]   # some kind of downsampling??
fs2 = fs/10

nfft = 1024
X2 = np.fft.fft(x2, nfft)[:nfft//2]
f2 = np.arange(0, nfft//2) * fs2 / nfft

plt.figure(figsize=(10,5))
plt.title('New FFT Output')
plt.plot(f2, np.abs(X2) / nfft)
plt.xlabel('Hz')
plt.grid()
plt.xlim([0, 18])
plt.show()