While trying with the mne downsampling module, I encountered some behavior
that I am unable to explain myself.
My understanding of downsampling is that it is an operation to decrease the
sample rate of x by keeping the first sample and then every nth sample after
the first.
My understanding of downsampling is that it is an operation to decrease
the sample rate of x by keeping the first sample and then every nth sample
after the first.
Resampling typically consists of two steps: low-pass filtering to avoid
aliasing, then sample rate reduction (subselecting samples from the
resulting signal). The low-passing actually changes the values, so the
subselection-of-filtered-data step will not necessarily yield points that
were "on" the original signal.
May I know whether this issue is due to the ringing artifacts or due to
other problems?
In this case it's likely due to the (implicit) low-pass filtering in the
frequency-domain resampling of the signal. It looks pretty reasonable to
me. If you want to play around with it a bit, you can
1. Call scipy.signal.resample directly on your data and see how closely it
matches.
2. Pad your signal, call scipy.signal.resample, and remove the (now
reduced-length) padding -- this is what MNE does internally.
3. Use scipy.signal.resample_poly directly on your data.
4. Manually low-pass filter and then directly subselect samples from the
low-passed signal, which is what resample_poly does internally.
Hopefully these all give similar results for your signal(s).
Also note that the resample example (https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.resample.html) shows upsampling, i.e. the data has a lower sampling rate than the resampled result. However, in the case of downsampling it is usually necessary to avoid aliasing of frequencies above the resampled Nyquist frequency. Therefore, the signal is typically low-pass filtered before the resampling step. As Eric mentioned, this anti-aliasing filter is what actually changes the signal values, but it is necessary to avoid aliasing artifacts.
AFAIK, scipy.signal.resample doesn't include an anti-aliasing filter, but both scipy.signal.resample_poly as well as scipy.signal.decimate apply such a low-pass filter before resampling. That's also what MNE does.
I think the up- vs. downsampling distinction is also really important
for expectations here, as is the distinction between decimating and
resampling (I recall there was a thread about that a few years back with
similar confusion, if somebody wants to do the effort of searching for it)
> AFAIK, scipy.signal.resample doesn't include an anti-aliasing filter,
but both scipy.signal.resample_poly as well as scipy.signal.decimate apply
such a low-pass filter before resampling. That's also what MNE does.
scipy.signal.resample does frequency-domain resampling, so implicitly uses
a brick-wall filter at Nyquist when downsampling (unless you specify
something for the `window` argument, which gets applied in the frequency
domain in addition to the effective brick-wall filter).
