Discussion of SNR after sub-sampling of multiple bandpass signals

Using a sub-sampling theorem of multiple bandpass signals and digital frequency conversion techniques, multi-band-pass signals can be directly sampled and processed. If the sampling rate is lower than twice the maximum frequency of the signal, the signal-to-noise ratio (SNR) will be worse. The relationships of SNR of the sampled signal, analog filter before analog-to-digital conversion and sampling rate are discussed. The results have some applications for digital receivers.