Delta-Ramp Encoder for Amplitude Sampling and Its Interpretation as Time Encoding

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 the delta-ramp encoder which consists of applying a one-level level-crossing detector to the result of adding an appropriate sawtooth-like waveform to the input signal. The output samples are the time instants of these level crossings, thus representing a time-encoded version of the input signal. For theoretical purposes, this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one which is then uniformly sampled in amplitude. The monotonic function is then represented by the times at which the signal crosses a predefined and equally-spaced set of amplitude values. We refer to this technique as amplitude sampling. The time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal. We derive duality and frequency-domain properties for the functions involved in the transformation. Iterative algorithms are proposed and implemented for recovery of the original source signal. As indicated in the simulations, the proposed iterative amplitude-sampling algorithm achieves a faster convergence rate than frame-based reconstruction for nonuniform sampling. The performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density.

FRI-TEM: Time Encoding Sampling of Finite-Rate-of-Innovation Signals

“…In this section, we present our main results where we show that for the sampling kernel choice (14), we can uniquely identify the FSCs from the IF-TEM time instants. Specifically, we show that for a particular choice of the IF-TEM parameters, the matrix A defined in ( 19) is left invertible.…”

“…Time encoding machines (TEM) provide an alternative digital representation of analog signals [7]- [14], which is asynchronous, that is, no global clock is required unlike conventional analog to digital converters. This leads to lower power consumption and reduced electromagnetic interference [6].…”

On High-Resolution Adaptive Sampling of Deterministic Signals

“…Then, the high-resolution sampling MSE, M SE S , formulated in (23) is related to the high-rate quantization MSE in (25) via…”

“…The sampling design in [23], [24] is based on either the local properties of the stochastic process whose realizations are sampled, or the local behavior of deterministic signals exhibited in their Taylor expansion. Another attractive nonuniform sampling approach was introduced lately in [25], defining the samples based on the crossings of uniformly-spaced signal-amplitude levels thereby enabling a signal representation using only the sampling time points. This remarkable general idea of describing nonuniformly sampled data by the time-points also appears in our practical sampling method, however, our high-resolution case leads to significant conceptual differences with respect to [25], as will be explained later in this paper.…”

Bandlimited signal reconstruction from leaky integrate-and-fire encoding using POCS

“…1). Time encoding is attracting more and more interest in data acquisition [1], [2], [3], [4], [5], [6], [7], [8], [7], [9], [10] as the downscaling of semiconductor integration is increasing time precision while resulting in less amplitude accuracy [11], [12], [13]. This is also part of the trend on event-based sampling [14] with more general objectives such as having acquisition activity dependent on input activity for power efficiency.…”