Calculating amplitude from np.fft

Question

I appear to be calculating incorrect amplitudes for the original waves using np.fft.fft.

The plot of the fft shown is shown, as you can see the amplitudes shown are around 3 and 1.5, but if you look at the code I’m using amplitudes 7 and 3 to generate the signal. This plot should have two spikes which go up to y=3 at x=13 and y=7 at x=15

What do I need to do to see the proper amplitudes (3 and 7) in my graph?

I can experimentally see the constant I need to multiply my amplitudes by is around 2.3, but how do I calculate this number exactly?

import numpy as np
import matplotlib.pyplot as plt

t0 = 0
t1 = 20
n_samples = 1000

xs = np.linspace(t0, t1, n_samples)
# Generate signal with amplitudes 7 and 3
ys = 7*np.sin(15 * 2 * np.pi * xs) + 3*np.sin(13 * 2 * np.pi * xs)

np_fft = np.fft.fft(ys)
amplitudes = 1/n_samples * np.abs(np_fft) #This gives wrong results

frequencies = np.fft.fftfreq(n_samples) * n_samples * 1/(t1-t0)

plt.plot(frequencies[:len(frequencies)//2], amplitudes[:len(np_fft)//2])
plt.show()

Asked By: Keatinge

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Source

Answer 1

I think you are miscalculating the amplitude. You should change the

amplitudes = 1 / n_samples * np.abs(np_fft)

to

 amplitudes = 2 / n_samples * np.abs(np_fft)

result:

import numpy as np
import matplotlib.pyplot as plt

t0 = 0
t1 = 1
n_samples = 10000

xs = np.linspace(t0, t1, n_samples)
ys = 7 * np.sin(15 * 2 * np.pi * xs) + 3 * np.sin(13 * 2 * np.pi * xs)

plt.subplot(2, 1, 1)
plt.plot(xs, ys)

np_fft = np.fft.fft(ys)
amplitudes = 2 / n_samples * np.abs(np_fft) 
frequencies = np.fft.fftfreq(n_samples) * n_samples * 1 / (t1 - t0)

plt.subplot(2, 1, 2)
plt.semilogx(frequencies[:len(frequencies) // 2], amplitudes[:len(np_fft) // 2])

plt.show()

The peaks of amplitudes are not exactly 7 and 2 but if you increase n_samples they will become more accurate.

Answered By: Foad S. Farimani

Calculating amplitude from np.fft

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