Pulse Analysis Pipeline Overview

• Pulse analysis pipelines are specialized computational workflows that detect, extract, and quantify transient signals from complex, multivariate data streams.
• They integrate modular stages such as pulse recognition, baseline subtraction, noise modeling, and optimal filtering to enhance signal fidelity.
• These pipelines are versatile across domains, powering advancements in astrophysics, nuclear physics, and biomedical imaging with real-time scalability.

Pulse analysis pipelines are specialized computational frameworks designed for the detection, extraction, and quantitative characterization of transient or pulsatile signals embedded in time-series or multidimensional measurement data. Applications span experimental nuclear and particle physics, astrophysics (notably radio and X-ray astronomy), cryogenic rare-event searches, and biomedical or photonic systems. Pipelines integrate signal recognition, baseline estimation, noise modeling, matched or optimal filtering, parameter extraction, and rigorous statistical quality estimation, often in modular, computationally efficient designs suitable for high-throughput or real-time operation.

1. Fundamental Pipeline Components and Workflow

Pulse analysis pipelines are built upon several canonical stages, whose sequencing and implementation are determined by the detector modality, noise environment, and scientific objectives:

• Pulse Recognition—Initial segmentation of candidate events, often via thresholding in filtered or derived representations (e.g., see-saw derivative, triggers on baseline or slope, matched-filter outputs).
• Baseline Estimation—Robust subtraction of a local or global time-varying baseline, using constant, moving-average (windowed, e.g., Hann or adaptive), or envelope (moving-max) strategies.
• Noise Characterization—Estimation of noise covariance or power spectral density (PSD) from pre-signal intervals, to inform filter design and statistical weighting.
• Pulse Parameter Estimation—Quantitative extraction of amplitude, arrival time, area, energy, and fit quality. Approaches include direct maxima, least-squares template fitting (in time or frequency domain), and optimal filtering (e.g., Wiener or matched filtering with noise whitening).
• Quality Control and Discrepancy Tests—Statistical evaluation of pulse extractions (e.g., χ², normalized discrepancy measures), removal of artifacts (e.g., isolated spikes, pileup), and application of post-detection corrections (e.g., arrival-time bias, gain drift, saturation).
• Post-processing and Output Compilation—Final construction of the pulse list, reporting key figures of merit for downstream analysis or archival.

This modular decomposition is explicit in high-performance frameworks such as the n_TOF pulse analysis pipeline for neutron time-of-flight detectors (Žugec et al., 2016), the TES x-ray microcalorimeter pulse pipeline (Fowler et al., 2015), and large-scale radio astronomy survey stacks (LOFAR, FAST, CHIME, Astroflow) (Alexov et al., 2010, You et al., 2021, Michilli et al., 2020, Lin et al., 4 Nov 2025).

2. Algorithms for Pulse Detection and Baseline Subtraction

Pulse Recognition

Efficient detection of pulses embedded in nonstationary or correlated noise is realized via derivative-based methods or matched filters. In the n_TOF system (Žugec et al., 2016), a discrete integral-difference derivative is computed

$d_i = \sum_{j=1}^{N} (s_{i+j} - s_{i-j}),$

where $N$ is wider than typical noise but narrower than the shortest pulse, with threshold crossings at $±3.5\sigma_d$ used for candidate window selection. Recursive updates yield $O(P)$ scaling for a waveform of $P$ samples.

Matched or optimal filtering (RICOCHET, TES calorimeters) uses noise-weighted templates or frequency-domain filter transfer functions:

$H(f) = \alpha \frac{S^*(f)}{J(f)},$

where $S(f)$ is the signal template in Fourier space, $J(f)$ the measured PSD, and $\alpha$ ensures unity response (Colas et al., 2021, Fowler et al., 2015). Candidate peaks in the matched-filter output are masked locally to suppress multiple triggers per event.

Baseline Subtraction

Several strategies are used depending on occupancy and drift:

• Constant Baseline: Mean over non-pulse regions; fast but suboptimal for variable backgrounds.
• Weighted Moving Average: Hann or custom windowing with suppression weights for pulse regions. Implemented with auxiliary recursive sums for $O(P)$ scaling (Žugec et al., 2016).
• Envelope (Moving-Maximum): Baseline as local lower envelope; computed via double-ended-queue algorithms for O(P).
• Gamma-Flash Corrections: Known time-locked distortion templates, e.g., in neutron or photon detectors, are subtracted after alignment.

Template pipelines allow dynamic selection or combination of these, enabling adaptation to pileup, high occupancy, or sudden drift.

3. Parameter Estimation, Fitting, and Bias Correction

Amplitude and Arrival Time Extraction

Direct methods (peak max, area integration) are rapid but suboptimal in colored noise or variable templates. Least-squares template matching, as detailed for neutron TOF pulses (Žugec et al., 2016) and bolometric signals in RICOCHET (Colas et al., 2021), minimizes

$$\chi^2(\tau, a) = \sum_f \frac{|D(f) - a\,\mathcal{M}(\tau, f)|^2}{J(f)},$$

yielding optimal amplitude estimates at trial start times, with the global minimum providing the arrival time ($\hat t_0$). In time domain implementations (TES calorimetry), noise covariance matrices are used to construct optimal Wiener or constrained filters, suppressing sensitivity to baseline offsets and arrival-time bias (Fowler et al., 2015).

Arrival Time and Gain Drift Correction

Residual bias in fitted heights as a function of sub-sample arrival time is mitigated through inclusion of derivative templates in the fit matrix, smoothing of filter weights, parabolic lag interpolation, and empirical post-hoc corrections (lookup tables, minimum-entropy sharpening) (Fowler et al., 2015).

Gain drift, as in TES calorimeters, is tracked by correlating fitted pulse heights with baseline shifts and corrected multiplicatively:

$A'_j = A_j \left[1 + \alpha (B_j - B_0)\right],$

with $\alpha$ optimized (e.g., via entropy minimization) to sharpen spectral features (Fowler et al., 2015).

4. Pipeline Performance, Computational Scaling, and Automation

Computational Efficiency

Pulse analysis pipelines for large experiments are optimized for throughput and scalability. Fast implementations leverage:

• Recursive Sums and FFTs: $O(P)$ algorithms for baseline and derivative calculations; $O(n \log n)$ for pulse-template cross-correlation.
• Windowed Processing: Segmentation of data streams (e.g., 1 s blocks, as in RICOCHET) for pipeline parallelization and memory locality (Colas et al., 2021).
• Parallelization: Use of MPI, OpenMP, or CUDA for batch or real-time processing. For example, LOFAR processes 1 hour of data in $\sim$20 min on 8 cores (Alexov et al., 2010); RICOCHET is fully chunk-parallelizable (Colas et al., 2021).
• Data Model Integration: HDF5 chunking, parallel I/O operations, and provenance logging are standard in large survey pipelines (Alexov et al., 2010).

Quality Control and Output

Statistical quality metrics (residual χ², normalized discrepancy $D_q$) are employed for pileup discrimination, fit integrity, and pulse selection. Final outputs include (arrival time, amplitude, area, fit quality), facilitating subsequent physical interpretation (e.g., energy calibration, timing, coincidence).

5. Application Domains and Scientific Impact

Pulse analysis pipelines underpin a wide spectrum of experimental and observational science:

• Astroparticle and Nuclear Physics: n_TOF employs a general pipeline for neutron TOF detectors, with emphasis on computational efficiency and adaptability to arbitrary waveform profiles and pileup (Žugec et al., 2016).
• Calorimetric Physics: TES microcalorimeter pipelines are tailored for high-precision energy recovery, with gain/arrival time corrections critical for realizing intrinsic resolution (Fowler et al., 2015). Exact pulse fitting and data quality steps are essential for sub-eV resolution and pileup-prone environments.
• Cryogenic Rare Event Searches: RICOCHET's modular Python implementation achieves sub-100 eV thresholds and robust event discrimination via template-based methods, supporting rigorous pipeline calibration via simulations and injection studies (Colas et al., 2021).
• Radio Astronomy and High-Throughput Surveys: LOFAR, FAST, and other radio arrays deploy multistage pipelines featuring both real-time (“online”) and batch (“offline”) processing, with dynamic modularity, HDF5 archiving, and rigorous RFI mitigation (Alexov et al., 2010, You et al., 2021).
• Medical/Bio Applications: Photoplethysmographic and optical pulse measurement pipelines (e.g., FusionPPG, Face2PPG) combine robust statistical fusion of spatially-distributed signals with spectral priors to extract arrhythmia-resolved waveforms from video (Amelard et al., 2016, Casado et al., 2022).

The scientific impact is manifested in improved sensitivity (essential for rare event discovery or spectral line extraction), high-resolution timing (critical in time-of-flight or radio transient contexts), and the robustness and reproducibility required for large-scale automated data processing in modern experimental science.

6. Design Trends and Future Directions

Recent developments emphasize:

• Modularity and Adaptability: Pipelines are increasingly abstracted to accommodate new detector technologies and application domains via extensible, parameter-driven architectures (Žugec et al., 2016, Colas et al., 2021).
• Incorporation of AI and Statistical Learning: Classification, parameter optimization, and even dynamic parameter selection are being integrated at various stages, notably in the most recent AI-driven excitation pipelines and high-throughput radio transient pipelines (Kumar et al., 10 Aug 2024).
• Real-Time and Large-Scale Operation: The evolution from bespoke off-line analysis to high-volume, real-time, cluster and GPU-accelerated systems is well established—necessitated by the exponential growth in experimental and observational data rates (Lyon et al., 2018, Lin et al., 4 Nov 2025).
• Transparency and Validation: Open-source codebases, explicit performance benchmarks, thorough documentation of methodological choices, and systematic parameter optimization (e.g., via grid search or injection studies) are now standard (Alexov et al., 2010, Colas et al., 2021).
• Rigorous Statistical Correctness: Pervasive use of simulation-based injection, uncertainty propagation, and entropy- or likelihood-based correction ensures systematic biases are minimized and quantified (Fowler et al., 2015).

Pipelines continue to evolve with advances in hardware, statistical methodology, and the demands of next-generation instruments and multi-messenger astrophysics.

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References:

• “Pulse processing routines for neutron time‐of‐flight data” (Žugec et al., 2016)
• “The Practice of Pulse Processing” (Fowler et al., 2015)
• “Development of data processing and analysis pipeline for the RICOCHET experiment” (Colas et al., 2021)
• “The LOFAR Known Pulsar Data Pipeline” (Alexov et al., 2010)
• “A GPU based single-pulse search pipeline (GSP) with database...” (You et al., 2021)
• “A Processing Pipeline for High Volume Pulsar Data Streams” (Lyon et al., 2018)
• “Face2PPG: An unsupervised pipeline for blood volume pulse extraction from faces” (Casado et al., 2022)
• “A spectral-spatial fusion model for robust blood pulse waveform extraction in photoplethysmographic imaging” (Amelard et al., 2016)
• “Pulse excitation mode selection via AI Pipeline to Fully Automate the WUCT System” (Kumar et al., 10 Aug 2024)
• “ASTROFLOW: A Real-Time End-to-End Pipeline for Radio Single-Pulse Searches” (Lin et al., 4 Nov 2025)