Fourier transforms in Python

rfft for real signals, fftfreq for the axis that makes it readable.

import numpy as np
from scipy import fft

rate = 500
t = np.arange(0, 2, 1 / rate)
signal_wave = 2 * np.sin(2 * np.pi * 7 * t) + np.sin(2 * np.pi * 40 * t)

spectrum = fft.rfft(signal_wave)
freqs = fft.rfftfreq(t.size, d=1 / rate)
power = np.abs(spectrum)

top = np.argsort(power)[::-1][:2]
print(sorted(freqs[top].round(1)))
print(round(float(power.max()), 1), spectrum.dtype)
print(np.allclose(fft.irfft(spectrum, n=t.size), signal_wave))

How it works

1. rfft returns half the spectrum, which is all a real signal has.
2. rfftfreq needs the sample spacing to label the bins.
3. The peak bin is the dominant frequency.

Keywords and builtins used here

• as
• float
• print
• round
• sorted

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Step 3 of 3 in Linear algebra & signals, step 18 of 23 in Scientific computing with SciPy.

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