[Paper Review] Filters for High Rate Pulse Processing

Bradley K. Alpert, Rob Horansky+6 more|arXiv (Cornell University)|Dec 7, 2012

Radiation Detection and Scintillator Technologies3 citations

TL;DR

This paper proposes a time-domain filter construction method for high-rate pulse processing that improves energy resolution by enforcing orthogonality to baseline offsets and exponential pulse tails, reducing sensitivity to pulse pile-up. The method outperforms standard optimal filtering by maintaining resolution at high count rates, especially with short pulse records and closely spaced events.

ABSTRACT

We introduce a filter-construction method for pulse processing that differs in two respects from that in standard optimal filtering, in which the average pulse shape and noise-power spectral density are combined to create a convolution filter for estimating pulse heights. First, the proposed filters are computed in the time domain, to avoid periodicity artifacts of the discrete Fourier transform, and second, orthogonality constraints are imposed on the filters, to reduce the filtering procedure's sensitivity to unknown baseline height and pulse tails. We analyze the proposed filters, predicting energy resolution under several scenarios, and apply the filters to high-rate pulse data from gamma-rays measured by a transition-edge-sensor microcalorimeter.

Motivation & Objective

• To address the limitations of standard optimal filtering in high-rate pulse processing, particularly sensitivity to baseline drift and pulse pile-up.
• To develop a filter construction method that operates entirely in the time domain to avoid discrete Fourier transform artifacts.
• To improve robustness against unknown baseline heights and residual pulse tails through explicit orthogonality constraints.
• To enable better energy resolution and higher output pulse rates in high-count-rate applications such as transition-edge-sensor microcalorimeters.
• To evaluate the performance of filters constrained to be orthogonal to constants and exponentials in realistic high-rate gamma-ray data.

Proposed method

• The filter is constructed directly in the time domain using noise autocovariance instead of the noise power spectral density, avoiding periodicity artifacts from the discrete Fourier transform.
• The filter optimization is subject to explicit constraints: fixed length, orthogonality to constants (baseline insensitivity), and orthogonality to one or more exponential decay functions (pulse tail insensitivity).
• The method uses the average pulse shape and estimated noise autocovariance from pulse-free segments to compute filters that minimize variance under these constraints.
• The filters are applied via discrete convolution with measured data to estimate pulse amplitudes, with peak amplitude taken as the maximum of the convolution output.
• The approach is validated using real gamma-ray data from a transition-edge-sensor microcalorimeter at varying count rates.
• Performance is evaluated by comparing energy resolution and output pulse rate across standard DFT-based optimal filters and the proposed constrained filters.

Experimental results

Research questions

• RQ1 How does time-domain filter construction with orthogonality constraints improve energy resolution compared to standard optimal filtering in high-rate pulse processing?
• RQ2 To what extent do filters orthogonal to exponentials reduce sensitivity to pulse pile-up and residual tails in high-count-rate data?
• RQ3 How does the choice of decay time constant τ affect the performance of filters orthogonal to exponentials?
• RQ4 What is the trade-off between sensitivity to isolated pulses and robustness to piled-up pulses in the proposed filter framework?
• RQ5 Can the proposed method maintain high energy resolution and output pulse rate under extreme count rates, such as 1000 Hz?

Key findings

• At a 1000 Hz input rate with short 10.24 ms records, the filter orthogonal to both constants and exponentials (τ = 6 ms) achieved a 45% higher output pulse rate than the standard DFT-computed filter.
• The same filter achieved a 40% higher output pulse rate than the baseline-insensitive filter alone, with better energy resolution than either.
• For the 97.431 keV line, energy resolution varied as 128.3 ± 3.2 eV across τ = 3–10 ms, showing mild sensitivity to τ choice.
• The filter orthogonal to exponentials significantly reduced peak leakage and improved peak height at high rates, especially for closely piled-up pulses.
• The standard DFT-based filter and the baseline-insensitive filter showed similar performance in isolation, but both suffered from bias in piled-up conditions.
• The method demonstrated notable improvement over standard filtering despite imperfectly satisfied assumptions of linear superposition and exponential decay.