New answers tagged downsampling
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If you're using scipy.signal and processing signals offline, then you can just use decimate which handles the filtering for you. It also does zero-phase filtering by default, which you probably want for an EEG signal to avoid shifting the shape of the waveforms? (I know that's desirable for EKG, not sure about EEG.)
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Anti-aliasing filtering is applied just as any other LTI filtering: If your input data is $x[n]$, and the impulse response is $h[n]$, then your output will be
$$y[n] = x[n] \star h[n] $$
where $\star$ is the convolution operation, a.k.a. the anti-aliasing filtering in this context.
Your impulse response $h[n]$, ideally, corresponds to a lowpass brickwall ...
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