# Theory and Algorithms for Pulse Signal Processing

## TL;DR

This paper develops theoretical frameworks and algorithms for directly performing signal processing operations like addition, multiplication, and convolution on pulse train representations of analog signals, enabling efficient real-time analysis.

## Contribution

It introduces a novel theoretical approach and algorithms for online signal processing directly on pulse trains without reconstructing the original signals.

## Key findings

- Algorithms successfully process simulated data.
- Application to ECG signals demonstrates noise subtraction.
- Mean pulse rate less than 20 pulses per second.

## Abstract

The integrate and fire converter transforms an analog signal into train of biphasic pulses. The pulse train has information encoded in the timing and polarity of pulses. While it has been shown that any finite bandwidth analog signal can be reconstructed from these pulse trains with an error as small as desired, there is a need for fundamental signal processing techniques to operate directly on pulse trains without signal reconstruction. In this paper, the feasibility of performing online the signal processing operations of addition, multiplication, and convolution of analog signals using their pulses train representations is explored. Theoretical framework to perform signal processing with pulse trains imposing minimal restrictions is derived, and algorithms for online implementation of the operators are developed. Performance of the algorithms in processing simulated data is studied. An application of noise subtraction and representation of relevant features of interest in electrocardiogram signal is demonstrated with mean pulse rate less than 20 pulses per second.

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Source: https://tomesphere.com/paper/1901.01140