A Recursive Method for Real-Time Waveform Fitting with Background Noise Rejection

TL;DR

This paper introduces a real-time, FPGA-compatible waveform fitting algorithm that effectively separates signal pulses from background noise, enhancing data analysis in high-throughput systems.

Contribution

A novel recursive, convolution-based method for real-time waveform fitting and background noise subtraction suitable for high sample-rate data acquisition.

Findings

Performs well in noisy environments

Comparable to specialized filters for energy and timing

Robust and universal filtering approach

Abstract

We present here a technique for developing a high-throughput algorithm to fit a combination of template pulse shapes while simultaneously subtracting parameterized background noise. By convolving the psuedoinverse of the least-squares fit design matrix along a regularly sampled waveform trace, the time evolution of the fit parameters for each basis function can be determined in real-time. We approximate these sliding linear fit response functions using piecewise polynomials, and develop an FPGA-friendly algorithm to be implemented in high sample-rate data acquisition systems. This is a robust universal filter that compares well to common filters optimized for energy calibration/resolution, as well as filters optimized for timing performance, even when significant noise components are present.