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One of the challenges in Cognitive Radio (CR) is efficiently monitoring a wideband radio frequency (RF) spectrum in order to identify unoccupied bands. Compressive Sensing (CS) has recently been proposed to address this problem. Typical CS techniques, however, involve random projections followed by a computationally intensive signal reconstruction process. Since spectral monitoring does require full signal reconstruction - only identification of occupied regions to avoid - we propose a novel spectrum monitoring approach based on the Nyquist Folding Receiver (NYFR) in conjunction with the Analytic Wavelet Transform. The NYFR performs analog compression via a non-uniform sampling process that induces a chirp-like modulation on each received signal. This induced modulation can be measured using time-frequency analysis techniques to determine the original RF band of origin without full signal reconstruction. This paper investigates the feasibility of using the Analytic Wavelet Transform to perform NYFR information recovery in support of CR wideband spectrum sensing.