Re: Harmonic distortion of a input signal

[Terry Jan Reedy]

On 5/19/2013 6:49 PM, Oscar Benjamin wrote:

import numpy as np

Create a square wave signal:

x = np.zeros(50)
x[:25] = -1
x[25:] = +1
x
array([-1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,
        -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,  1.,
         1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,
         1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])

Compute the magnitude spectrum:

spect = abs(np.fft.fft(x)[:25])
spect
array([  0.        ,  31.85194222,   0.        ,  10.67342282,
          0.        ,   6.47213595,   0.        ,   4.69726931,
          0.        ,   3.73254943,   0.        ,   3.13762901,
          0.        ,   2.7436023 ,   0.        ,   2.47213595,
          0.        ,   2.28230601,   0.        ,   2.15105461,
          0.        ,   2.06487174,   0.        ,   2.01589594,   0.        ])

Find the index of the maximum element:

np.argmax(spect)
1

So the peak is the lowest non-zero frequency component of the DFT. In
Hz this corresponds to a frequency of 1/T where T is the duration of
the signal.

While you were answering a specific question, I think the above is a 
nice tutorial example, because it is more meaningful than arbitrary 
operations applied to random data.



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