Maintaining The Sampling Theorem Criterion
Since downsampling reduces the sampling rate, we must be careful to make sure the Shannon-Nyquist sampling theorem criterion is maintained. If the sampling theorem is not satisfied then the resulting digital signal will have aliasing. To ensure that the sampling theorem is satisfied, a low-pass filter is used as an anti-aliasing filter to reduce the bandwidth of the signal before the signal is downsampled; the overall process (low-pass filter, then downsample) is called Decimation. Note that if the original signal had been bandwidth limited, and then first sampled at a rate higher than the Nyquist minimum, then the downsampled signal may already be Nyquist compliant, so the downsampling can be done directly without any additional filtering. Downsampling only changes the sample rate not the bandwidth of the signal. The only reason to filter the bandwidth is to avoid the case where the new sample rate would become lower than the Nyquist requirement and then cause the aliasing by being below the Nyquist minimum.
Thus, in the current context of downsampling, the anti-aliasing filter must be a low-pass filter. However, in the case of sampling a continuous signal, the anti-aliasing filter can be either a low-pass filter or a band-pass filter.
A bandpass signal, i.e. a band-limited signal whose minimum frequency is different from zero, can be downsampled avoiding superposition of the spectra if certain conditions are satisfied, see e.g. .
Read more about this topic: Decimation (signal Processing)
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