Amplitude sampling

Pablo Martínez-Nuevo, Hsin-Yu Lai, Alan V. Oppenheim

Abstract: The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information. The approach is based on applying a one-level level-crossing detector to the result of adding a sawtooth waveform to the source signal. The source signal is then represented by the level-crossing times. For analysis purposes, the output of the level-crossing detector is interpreted as the result of applying a multi-level level crossing detector to the monotonic function consisting of the sum of the source signal and an appropriate linear ramp. This monotonic function is then uniformly sampled in amplitude with the source signal again represented by the level crossing times of the monotonic function. We refer to this technique as amplitude sampling. The approach can equivalently be viewed as nonuniform time sampling of the original source signal or uniform amplitude sampling of the monotonic function to which it is transformed. In this paper we explore this approach and, in particular, present duality and frequency-domain properties for the functions involved in the transformation and develop and compare two iterative algorithms for recovery of the source signal.