Direct signal recovery trade-offs in threshold crossing sampling

Abstract

We present an investigation of a method for directly obtaining the 2M equally-sampled amplitude values of the analog input signal s(t) from the 2M locations {t_i} where it intersects with a reference r(t)= Acos(2πf_rt).
Previous schemes for accurately recovering a bandlimited signal s(t) from its sinusoid-crossing (SC) locations {t_i} have been done only indirectly using spectral methods. The Fourier components {c(m)} are first calculated directly from {t_i} where i = −M, −M+1, ..., M−1 and m = −M, −(M+1), ..., M. Equally-sampled amplitude values {s(iΔ)} of s(t), where Δ is the sampling interval are then recovered by inverse Fourier transforming {c(m)}.
Threshold sampling is attractive because it can be implemented simply using a single comparator circuit which in essence is just a one-bit analog-to-digital (AD) converter. The main challenge in threshold crossing sampling is being able to recover the complete information about s(t) from its detected threshold locations.
This paper evaluates the trade-off between high-accuracy sampling and high frequency sampling in a new method for calculating accurately {s(iΔ)} directly from {t_i}. This capability is important in signal processing because many integral and differential equations are solved numerically using equally-sampled sets of data values.