Understanding matplotlib magnitude_spectrum output

Question

I'm having problems understanding the output generated by matplotlib's magnitude_spectrum function call. I have generated a sine with 50khz frequency, ``` f_s = 488000.0 # Hz t = np.arange(0.0, 1.0, 1/f_s) s1 = 100*np.sin(2*np.pi*50000*t) ``` I then plot the resulting magnitude spectrum, after dividing by the number of FFT bins ``` s1_magspec = plt.magnitude_spectrum(s1,Fs=f_s) plt.plot(s1_magspec[0]/len(s1_magspec[0])) ``` The result is a single spike at 50khz, but with a magnitude of 50, as opposed to the expected 100. Can anybody explain why this is? Here is a link to an ipython notebook describing showing the afforementioned code and the resulting plot: http://nbviewer.ipython.org/gist/bkinman/22cc15d3ad3b9b2db09e

Accepted Answer

It looks like it has to do with the default setting for the FFT window used. The documentation says that the default is a Hanning window. If you use a boxcar window instead:

```
s1_magspec = plt.magnitude_spectrum(s1, Fs=f_s, window=np.ones(s1.shape))
```

you'll get your peak at 100, just like with a straight numpy FFT.

By the way, it would be good if you edited your question to put in the line of code creating `s1_magspec` rather than relying on the notebook viewer, the link to which will undoubtedly break someday.

Understanding matplotlib magnitude_spectrum output

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