Harmonic Sampling and Reconstruction of Wideband Undersampled Waveforms: Breaking the Code

In this paper, a method for measuring wideband waveforms correctly when undersampling is used as a digitizing technique is presented. Two major challenges arise when undersampling wideband waveforms: overlapping of aliased spectral bins of the digitized waveform and ambiguity in spectral bins standing on multiples of the Nyquist frequency. Those challenges are more pronounced when using wideband modulated signals to excite nonlinear devices. The theory behind a correct undersampled measurement is based on the use of an irrational relation between the undersampling frequency and the spectral resolution of the waveform to measure. This is the key to a successful harmonic sampling used today in large-signal network analyzers when wideband modulated waveforms are to be measured. Inverting the problem, such theory is also the solution for reconstructing wideband undersampled waveforms based on a single measurement and with a relatively short record of measured data. It is a solution for RF sampling and cognative radios where the digital processing is moving toward the antenna of the receiver.