Bandpass sampling criteria for nonlinear systems

Sampling criteria for nonlinear systems with a band-pass input are developed in this paper. It is well known that nonlinear systems may produce an output signal with a larger bandwidth than that of their input signal. According to the Nyquist sampling theorem, the sampling rate needs to be at least twice the maximum frequency of the output signal; otherwise, the sampled output would be aliased. However, if the input is a bandpass signal, the spectrum of the output signal often occupies multiple frequency bands. In this case, it is possible, by using the bandpass sampling concept, to sample the output signal at a rate much lower than the Nyquist sampling frequency. In this paper, all conditions in which bandpass sampling can be achieved are derived for nonlinear systems up to the third order. Furthermore, for nonlinear systems higher than the third order, some conditions in which bandpass sampling can be guaranteed are derived. The result can be used to choose an appropriate sampling frequency for nonlinear systems of an arbitrary order.