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So I have this signal sampled at 300 Hz to begin with and this is the frequency domain: Original Signal Time Domain

Original Signal Freq Domain

I apply a second order butterworth filter using scipy with a cutoff frequency of 12.6 Hz and this is the resultant signal in time and frequency domains:

sos = signal.butter(2, 12.6, 'low', fs=300, output='sos')
x_filt = signal.sosfiltfilt(sos, x)

Filtered Signal Time Domain Filtered Signal Freq Domain

My question is shouldn't those frequencies around 300 Hz be filtered out and appear as zero and why aren't they? Should I be using a higher order filter in order to filter out those higher frequencies?

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You sampled your signal at 300Hz.

That means your range of valid frequencies (for a real-valued signal) is -150Hz to +150Hz.

When you take the FFT, as you have done, the top half of the spectrum is really from -150Hz to 0$^-$Hz (the bin just before 0 frequency).

Use numpy.fft.fftshift to center the 0 frequency bin in the middle of your plots.

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  • $\begingroup$ Could you help me explain why there is still high frequency components in the filtered signal? $\endgroup$
    – Michael Pozzi
    Jun 1, 2022 at 15:09
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    $\begingroup$ @MichaelPozzi There aren't. Rather, once the signal is sampled, the spectrum is repeated to infinity in both directions. Once it's sampled at 300Hz, you can only see -150Hz to +150Hz (and any aliases if the original unsampled signal had frequency components higher than 150Hz). $\endgroup$
    – Peter K. ♦
    Jun 1, 2022 at 15:45

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