We have a signal sampled att 22 kHz that we want to interpolate to 40 kHz.
So we can do this by upsampling by a factor 20, then downsampling by a factor 11. My question regards the choice of cut-off frequencies after the upsampling and the downsampling.
The old Nyquist frequency was at $11$ kHz so it would make sense to me to low-pass frequencies above $11$ kHz after upsampling - we're basically replicating our signal 20 times across the new spectra, right? The correct cut-off is apparently 20 kHz, but I can't quite wrap my head around that fact.
We then downsample by a factor 11 to 40 kHz. Now the correct LP cut-off is 11 kHz. I am seriously confused. Can anyone shed some wisdom here?