Identification and Restoration of a Class of Aliased Signals

by Walia, Aasma

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