Beyond FINDCHIRP: Breaking the memory wall and optimal FFTs for Gravitational-Wave Matched-Filter Searches with Ratio-Filter Dechirping

TL;DR

This paper tackles the memory bandwidth bottleneck in FFT-based gravitational-wave matched-filter searches by introducing Ratio-Filter Dechirping, a reorganized computation that replaces memory-bound FFTs with cache-efficient, short FIR convolutions using a coarse reference template. The approach enables a two-stage filtering process, where a reference SNR is produced with a coarse template and a compact FIR ratio filter reconstructs the final SNR for target templates, dramatically improving data locality. Key contributions include a two-stage hierarchical search bank, chi-squared optimized FIR ratio templates with robust morphologies, and empirical results showing an eightfold improvement in core filtering throughput with strong potential for >10× gains in low-latency analyses, along with a clear path to hardware acceleration on GPUs. The method substantially expands the feasible search space to dense, high-dimensional parameter regions (e.g., eccentricity, precession, subsolar-mass components) and provides a natural bridge to stochastic and hybrid pipelines, ultimately enabling faster and more sensitive gravitational-wave detections and earlier multi-messenger alerts.

Abstract

A primary bottleneck in modern FFT-based matched-filter searches for gravitational waves from compact binary coalescences is not raw processor throughput, but available memory bandwidth. Standard frequency-domain implementations, such as the FINDCHIRP algorithm, rely on streaming long template waveforms and data from main memory, which leads to significant processor stalling when template durations exceed cache capacities. In this work, we introduce \textit{Ratio-Filter Dechirping} as a solution, an algorithmic restructuring of the matched filter that transforms the operation from a memory-bound Fast Fourier Transform (FFT) into a cache-efficient, compute-bound Finite Impulse Response (FIR) convolution. By utilizing a reference template to remove common orbital phase evolution, we produce slowly changing frequency-domain ratios that can be accurately implemented as short FIR filters. This method delivers a measured speedup of $8\times$ for the core filtering loop used in offline searches and should enable $>10\times$ for low-latency analysis. We find that this approach generalizes to a variety of searches that include physical features such as finite size effects, eccentricity, and precession. By dramatically reducing the computational cost of matched filtering, this approach enables the expansion of searches into dense or high-dimensional parameter spaces, such as those for eccentric or subsolar-mass signals, that are already limited by available computing budgets. Furthermore, this framework provides a natural path for hardware acceleration on GPU architectures.

Figures (5)

• Figure 1: The sample rate throughput of the Fourier transform as a function of FFT size benchmarked on a representative cluster node (Haswell architecture) when the machine is fully utilized (orange) and when it is otherwise unoccupied (blue). The expected scaling just accounting for arithmetic operations is shown (green dotted). We see that the FFT performance scales initially with the expected computational cost; at larger sizes memory access becomes the bottleneck so the performance degrades. The current operating point of typical GW searches is shown (red) along with the target operating point of our new algorithm (yellow). An $8\times$ performance improvement is possible if the final algorithm is FFT dominated. Similar scaling is also found on a variety of x86 CPU architectures.
• Figure 2: Schematic representation of the two-step Ratio-Filter Dechirping process. The detector data (top) is first matched-filtered against a coarse reference template to produce a reference SNR time series (middle). This latter step can be thought of as a combined filtering stage which both overwhitens and heterodynes the data. For visual clarity, only the real part of the otherwise complex filter output is shown. This time series is then convolved with a short FIR ratio filter to reconstruct the final SNR for a specific target template (bottom). The contribution to the data of an embedded simulated binary neutron star signal is highlighted in orange in both the top and middle panels. The original BNS signal which is $\sim 170s$ in duration is efficiently compressed to a region of only a fraction of a second after the heterodyning stage. As can be seen, the final SNR result is nearly identical to the original reference SNR calculated using a single-stage matched filter. The improvement in computational performance occurs because the application of the FIR ratio filter can be done separately on much shorter segments of data (e.g. O(1s) as opposed to O(100s).
• Figure 3: Visualization of the hierarchical template bank structure in the component mass parameter space for a slice of the BNS region ($\mathcal{M} \in [1.2, 1.3] M_\odot$). The large black points represent the coarse reference bank (minimal match $\sim 0.5$), while the dense colored points represent the standard search bank (minimal match $0.965$). The color of each target template indicates its association with the nearest reference neighbor, ensuring the resulting ratio waveform corresponds to a short, computationally efficient FIR filter.
• Figure 4: The distribution of FIR ratio filter size in terms of the number of taps required for a target match to the original target signal of 0.99 (blue), 0.999 (orange), or 0.9999 (green) for a representative BNS template bank. The full template bank is designed for a minimal match of 0.965, while the coarse bank is chosen so that it is $\sim150\times$ smaller in size than the full bank. The waveform is sampled at a rate of 2048 Hz. The short tap size means that small blocks can be used in a standard overlap-add matched filtering analyses, e.g. $2^{11-12}$ points or 1-2s, while still ensuring that the majority of output is uncorrupted by filter wraparound. As expected, the tap size distribution shifts to larger values with increasing match target, however, we observe that it only grows logarithmically with the mismatch, making it feasible to reach high accuracy where required.
• Figure 5: Frequency-domain representation of the ratio $\tilde{h}(f)/\tilde{h}_{\text{ref}}(f)$ for three distinct physical deviations from a common reference template (a $5.4 M_\odot - 1.4 M_\odot$ NSBH system). The real part of the ratio is shown. The target waveforms introduce a shift in chirp mass (green), orbital eccentricity (blue), and spin precession (orange). Despite the match between the reference and target being $<0.6$, a designed 251-tap FIR filter (dashed grey lines) achieves a match of $>0.999$ to the target signal.