Continuous Time Digital Signal Processing and Signal Reconstruction

Continuous Time (CT) Systems offer several advantages over traditional digital signal processing (DSP); however, CT is not linear time invariant like DSP. Since discrete time and DSP are linear time invariant, signal reconstruction is applied after all signal processing steps have been completed. A DSP approach cannot be applied to continuous time systems. For CT systems, level crossing sampling signals are nonlinear. For linearity to hold in CT systems, signal reconstruction must be applied before any signal processing steps. In 2003, Tsividis showed an asynchronous zero order hold is the simplest signal reconstruction algorithm for CT. In 2008, Schell and Tsividis demonstrated an offline exact reconstruction algorithm with greater than 100 dB signal-to-noise and distortion ratio (SINAD). This paper focuses on CT level crossing signal reconstruction. For practical CT signal reconstruction, a low complexity approximation to offline signal reconstruction is preferred with higher signal-to-noise ratio than simple asynchronous zero order hold reconstruction. A Gaussian-sinc( ) reconstruction kernel is investigated as an approximation to offline reconstruction.

I. Continuous Time System Introduction

Continuous time digital signal processing (CT- DSP) is an emerging subfield of signal processing [1]–[12]. Continuous time (CT) systems were first developed in the 1950's for control system applications. In 1962, Inose, et al. [7] developed and characterized a CT asynchronous delta-sigma (Δ∑) analog-to-digital converter. When the integral or sum, ∑, of the error signal, Δ, is equal to a threshold level, the asynchronous feedback changes state. An accurate Δ∑ demodulator technique was developed by Lazar and Tóth [8] in 2004. In 2003, Tsividis published his research work on the benefits of CT, which led to significant CT systems research. Kurchuk, et al. [9] developed a GHz speed LC ADC in 2012. Kim, et al. [10] developed a CT Δ∑ low power ADC for wearable electrocardiogram (ECG) applications in 2022.