Study of Sub-Nyquist Sampling Techniques for Multi-band Signals

Shannon-Nyquist sampling theorem is the most fundamental and well known for transforming a continuous-time band-limited signal into its discrete-time form. Over the years, many other methods have been developed for the same. The sampling frequency i.e. the number of samples taken per second, is one of the important characteristics of the sampling process. Since high sampling frequency is very tedious to achieve in the practical world, one desire to have a sampling frequency as low as possible. This paper investigates the classical Sub-Nyquist sampling methods named as Demodulation, Undersampling and Periodically Non-uniform Sampling which reduces the sampling frequency below the Nyquist rate, assuming a multiband or bandpass signal with known frequency support. It will present a comparative study of these methods in terms of the sampling frequency with respect to both the Nyquist rate and the minimal sampling frequency possible, additional hardware circuitry needed and their suitability to multi-band inputs.