Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

This paper considers the problem of reconstructing a bandlimited signal from its nonuniform samples. Based on a discrete-time equivalent model for nonuniform sampling, we propose the differentiator-multiplier cascade, a multistage reconstruction system that recovers the uniform samples from the nonuniform samples. Rather than using optimally designed reconstruction filters, the system improves the reconstruction performance by cascading stages of linear-phase finite impulse response (FIR) filters and time-varying multipliers. Because the FIR filters are designed as differentiators, the system works for the general nonuniform sampling case and is not limited to periodic nonuniform sampling. To evaluate the reconstruction performance for a sinusoidal input signal, we derive the signal-to-noise-ratio at the output of each stage for the two-periodic and the general nonuniform sampling case. The main advantage of the system is that once the differentiators have been designed, they are implemented with fixed multipliers, and only some general multipliers have to be adapted when the sampling pattern changes; this reduces implementation costs substantially, especially in an application like time-interleaved analog-to-digital converters (TI-ADCs) where the timing mismatches among the ADCs may change during operation.