Detection accuracy in zero-crossing-based spectrum analysis and image reconstruction

We examine how the accuracy in describing the exact location of a signal crossing affects the quality of the spectrum or the reconstructed two-dimensional image that is computed by a representation of sampled zero crossings. The position of a zero crossing within a Nyquist interval is described by the ratio between the number of clock pulses that have elapsed before the crossing occurred and the total number of clock pulses that could fit within the interval. The pulses scale the Nyquist interval, and the greater their total number, the more accurate the description of the crossing location. In a real zero-crossing detector the ability to increase the total number of square pulses contained within the Nyquist interval is limited by the finite response time of its circuit components [Opt. Lett. 18, 1468 (1993)].