e.g. let's say we have a signal with B = 100 Hz that is sampled at 400 Hz. The anti-aliasing filter will remove replicas, and there is nothing to alias, and we downsample. If we downsample by 2, we will get signal of 200 Hz. But what's stopping us? Can we downsample by 4, or 8?

(why can't we downsample by 4, get B = 400Hz, then have a new sampling rate at 800 Hz?)

Similarly, is there a limit to how much we want to upsample?

  • $\begingroup$ The bandwidth of signal does not change by sampling rate, but we create replica with sampling operation. Replica is the original spectrum shifted by multiple of sample frequency. Thus sampling at 400Hz two replicas are distant at 400Hz, downsampling by 4, sampling freq is 100Hz two replicas are distant at 100Hz ... The distance must be greater than signal bandwidth to avoid aliasing, as your name lol. $\endgroup$ – AlexTP May 4 '17 at 6:50
  • $\begingroup$ downsampling is the process of throwing out samples AFTER it has already been sampled $\endgroup$ – aliasing May 4 '17 at 7:08
  • $\begingroup$ sampling at 400Hz, replicas R0 R1 R2 R3 are distant at 400Hz each other. Downsample by 2 to 200Hz, you have R0 R00 R1 R11 R2 R22 R3 R33 who are distant at 200Hz to each other. $\endgroup$ – AlexTP May 4 '17 at 7:54

Nyquist. If your signal is real and has a BW of B = 100 Hz (meaning DC to 100 Hz), then the most you can downsample by is 2, in order to obey Nyquist and have a sampling rate that is at least 2B = 200 Hz. Note you will typically want to sample more beyond this limit to allow room for reasonable filtering.

  • $\begingroup$ But why can't we downsample by 4, get B = 400Hz, then have a new sampling rate at 800 Hz? $\endgroup$ – aliasing May 4 '17 at 6:38
  • $\begingroup$ Downsample by 4 means to divide the sampling rate by 4. So if you are sampling at 400 Hz the new sampling rate is 100 Hz. Meanwhile your signal bandwidth is not affected- the signal bandwidth is still 100 Hz (downsampling does not change your signal, when done correctly). $\endgroup$ – Dan Boschen May 4 '17 at 10:38

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