Identification and Restoration of a Class of Aliased Signals

A fundamental theorem of Digital Signal Processing is Shannon's sampling theorem, whichdictates the minimum rate (called the Nyquist rate") at which a continuous-time signalmust be sampled in order to faithfully reproduce the signal from its samples. If a signalcan be reproduced from its samples, then clearly no information about the original signalhas been lost in the sampling process. However, when a signal is sampled at a rate lowerthan the Nyquist Rate, the true spectral content of the original signal is distorted due toaliasing," wherein frequencies in the original signal greater than the sampling frequencyappear as lower frequencies in the sampled signal. This distortion is generally held to beirrecoverable, i.e., whenever aliasing occurs, information is considered to be inevitably lost.This research challenges this notion and presents a technique for identifying aliasingand recovering an unaliased version of a signal from its aliased samples. The method isapplicable to frequency-modulated (FM) signals with a continuous instantaneous frequency(IF), and utilizes analysis of the IF of the aliased signal to 1) determine whether the signalhas potentially been aliased and, if so, 2) compensate for the aliasing by reconstructingan estimate of the true IF of the signal. Time-frequency methods are used to analyzethe potentially aliased signal and estimate the IF, together with modulation, re-samplingand interpolation stages to reconstruct an estimate of the unaliased signal. The proposedtechnique can yield excellent reconstruction of FM signals given ideal estimates of the IF