python - Understanding matplotlib magnitude

i'm having problems understanding output generated matplotlib's magnitude_spectrum function call.

i have generated sine 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 plot resulting magnitude spectrum, after dividing number of fft bins

s1_magspec = plt.magnitude_spectrum(s1,fs=f_s) plt.plot(s1_magspec[0]/len(s1_magspec[0]))

the result single spike @ 50khz, magnitude of 50, opposed expected 100.

can explain why is?

here link ipython notebook describing showing afforementioned code , resulting plot:

it looks has default setting fft window used. documentation says default hanning window. if use boxcar window instead:

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

you'll peak @ 100, straight numpy fft.

by way, if edited question put in line of code creating s1_magspec rather relying on notebook viewer, link undoubtedly break someday.

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