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.