Paul - 2 months ago 6x
Python Question

# numpy's fast Fourier transform yields unexpected results

I am struggling with

`numpy`
's implementation of the fast Fourier transform. My signal is not of periodic nature and therefore certainly not an ideal candidate, the result of the FFT however is far from what I was expecting. It is the same signal, simply stretched by some factor. I plotted a sinus curve, approximating my signal next to it which should illustrate, that I use the FFT function correctly:

``````import numpy as np
from matplotlib import pyplot as plt

signal = array([[ 0.], [ 0.1667557 ], [ 0.31103874], [ 0.44339886], [ 0.50747922],
[ 0.47848347], [ 0.64544846], [ 0.67861755], [ 0.69268326], [ 0.71581176],
[ 0.726552  ], [ 0.75032795], [ 0.77133769], [ 0.77379966], [ 0.80519187],
[ 0.78756476], [ 0.84179849], [ 0.85406538], [ 0.82852684], [ 0.87172407],
[ 0.9055542 ], [ 0.90563205], [ 0.92073452], [ 0.91178145], [ 0.8795554 ],
[ 0.89155587], [ 0.87965686], [ 0.91819571], [ 0.95774404], [ 0.95432073],
[ 0.96326252], [ 0.99480947], [ 0.94754962], [ 0.9818627 ], [ 0.9804966 ],
[ 1.], [ 0.99919711], [ 0.97202208], [ 0.99065786], [ 0.90567128],
[ 0.94300558], [ 0.89839004], [ 0.87312245], [ 0.86288378], [ 0.87301008],
[ 0.78184963], [ 0.73774451], [ 0.7450479 ], [ 0.67291666], [ 0.63518575],
[ 0.57036157], [ 0.5709147 ], [ 0.63079811], [ 0.61821523], [ 0.49526048],
[ 0.4434457 ], [ 0.29746173], [ 0.13024641], [ 0.17631683], [ 0.08590552]])

sinus = np.sin(np.linspace(0, np.pi, 60))

plt.plot(signal)
plt.plot(sinus)
``````

The blue line is my signal, the green line is the sinus.

``````transformed_signal = abs(np.fft.fft(signal)[:30] / len(signal))
transformed_sinus = abs(np.fft.fft(sinus)[:30] / len(sinus))

plt.plot(transformed_signal)
plt.plot(transformed_sinus)
``````

The blue line is
`transformed_signal`
, the green line is the
`transformed_sinus`
.

Plotting only
`transformed_signal`
illustrates the behavior described above:

Can someone explain to me what's going on here?

UPDATE

I was indeed a problem of calling the FFT. This is the correct call and the correct result:

``````transformed_signal = abs(np.fft.fft(signal,axis=0)[:30] / len(signal))
``````

Numpy's `fft` is by default applied over rows. Since your `signal` variable is a column vector, `fft` is applied over the rows consisting of one element and returns the one-point FFT of each element.
Use the axis option of `fft` to specify that you want FFT applied over the columns of `signal`, i.e.,
``````transformed_signal = abs(np.fft.fft(signal,axis=0)[:30] / len(signal))