ESTIMATING A MIXTURE OF SINUSOIDS WITH MULTI-CHANNEL UNLIMITED SAMPLING

This paper considers the estimation of a mixture of sinusoids in an unlimited sensing framework. A modulo analog-to-digital converter (ADC) is employed to fold back the input signal into a bounded interval before samples are token. We show that, for a band-limited signal, when the sampling rate satisfies a certain condition that is closely related to the dynamic range of the modulo ADC, the first-order difference of the original samples can be uniquely decomposed as a sum of the first-order difference of the modulo samples and a constant with only three possible values. This enables us to formulate the problem of estimating a mixture of sinusoids as a joint sparse signal recovery and unknown integer parameters estimation problem, which can be efficiently solved via a mixed-integer linear program. In addition, a multi-channel sampling architecture is employed to form a “virtual” modulo ADC with an enlarged dynamic range. This improvement helps reduce the sampling rate for estimating sinusoidal mixtures. Numerical simulations are conducted to illustrate the performance of the proposed method.