Real-time digital signal recovery for a low-pass transfer function system with multiple complex poles

TL;DR

This paper introduces a real-time digital signal recovery method for systems with multiple complex poles, enabling accurate waveform reconstruction despite distortions and delays, applicable to sensors and amplifiers near their frequency limits.

Contribution

A novel DSP-based moving average algorithm for real-time, DC-accurate waveform recovery from complex-pole low-pass systems, unaffected by initial conditions or transient signals.

Findings

Accurately recovers source waveform in real time

Unaffected by initial conditions and transients

Applicable to sensors and amplifiers near resonance

Abstract

In order to solve the problems of waveform distortion and signal delay by many physical and electrical systems with linear low-pass transfer characteristics with multiple complex poles, a general digital-signal-processing (DSP)-based method of real-time recovery of the original source waveform from the distorted output waveform is proposed. From the convolution kernel representation of a multiple-pole low-pass transfer function with an arbitrary denominator polynomial with real valued coefficients, it is shown that the source waveform can be accurately recovered in real time using a particular moving average algorithm with real-valued DSP computations only, even though some or all of the poles are complex. The proposed digital signal recovery method is DC-accurate and unaffected by initial conditions, transient signals, and resonant amplitude enhancement. The noise characteristics of the data recovery shows inverse of the low-pass filter characteristics. This method can be applied to most sensors and amplifiers operating close to their frequency response limits or around their resonance frequencies to accurately deconvolute the multiple-pole characteristics and to improve the overall performances of data acquisition systems and digital feedback control systems.