A Universal Formula for the Complete Bandpass Sampling Requirements of Nonlinear Systems

Abstract

A nonlinear system driven by a bandpass input signal may produce an output signal that occupies multiple frequency bands. This makes bandpass sampling the output signal of the nonlinear system without causing aliasing a challenging task. Although the bandpass sampling theory for linear systems is well developed, its counterpart for nonlinear systems is relatively immature in the sense that complete bandpass sampling requirements have only been developed up to third-order nonlinear systems. In this paper, a novel method is used to derived the complete bandpass sampling requirements for nonlinear systems of an arbitrary order. The strategy used by this method is to build the constraints on the sampling frequency for th-order nonlinear systems upon those for ( 1)th-order nonlinear systems. This process makes the derivation easily extendable to nonlinear systems of any order. The derivation method also gives an insight into the mechanism for formularizing the constraints on the bandpass sampling frequency. As a result, a universal formula for the complete bandpass sampling requirements for nonlinear systems of any order is derived. This formula consolidates the bandpass sampling theory for nonlinear systems and facilitates the selection of the bandpass sampling frequency for nonlinear systems driven by bandpass input signals.

Analog‐to‐Digital Conversion for Cognitive Radio: Subsampling, Interleaving, and Compressive Sensing

“…This issue was addressed in Ref. [10] where a universal formula for subsampling in nonlinear systems was developed for single-band applications. In dual-band receiver applications, the main problem of subsampling is the possible overlapping between the replicas of the two desired signals in the IF frequency band.…”

“…It can be easily shown (see Ref. [10]) that the range of the sampling frequencies that guarantees that those intermodulation products do not overlap in the sampled output spectrum is given by…”