In just one decade, gravitational-wave astronomy has gone from the first detection to hundreds of recorded mergers of compact objects. Almost all of these signals, however, are short: they last from fractions of a second to tens of seconds. At the same time, theorists predict the existence of long-duration transient signals, for example from binary primordial black holes of subsolar mass. Such sources could emit in the sensitive band of the LIGO, Virgo, and KAGRA detectors for hours and even years. Searching for these events with traditional methods runs into computational limits, because the number of templates required grows with the duration of the signal.
The authors propose a new way to resample the data that combines two processing stages into one. The key idea: if the signal has a known model of frequency evolution, you can rescale time so that the signal becomes monochromatic. Then, instead of an expensive matched filter for each template, a single fast Fourier transform suffices. The catch is that after resampling the samples become unevenly spaced in the new time coordinate, and the standard FFT no longer applies. Instead of interpolating onto a uniform grid, the authors use the nonuniform fast Fourier transform (NUFFT), which computes the spectrum directly from unevenly spaced samples. This avoids unnecessary operations and speeds up processing.
Benchmarks on a commercial processor showed a speedup of ten to one hundred times compared with traditional stroboscopic resampling. The exact speedup depends on the length of the coherent segment, the sampling rate, and the required accuracy. To demonstrate the method, it was applied to the search for long-duration signals from binary primordial black holes with masses from 0.0005 to 0.1 solar masses. When analyzing the 40–60 Hz band with a coherent segment of 30 seconds, the sensitivity horizon exceeds the distance to the Galactic Center across the entire parameter range studied, and for masses above 0.02 solar masses it reaches the Andromeda Nebula. Tests on signals injected into real LIGO Hanford detector noise confirmed agreement with theoretical predictions.
The work fits into the active push to search for long-duration gravitational signals, alongside studies of gravitational waves from spinning neutron stars and quantum-gravity effects. What sets this work apart is that it offers not a new analysis method but a new computational implementation of an already known approach. This is not a fundamental breakthrough in physics but an engineering improvement that makes practical searches possible in a previously inaccessible region of parameter space.
The method can be extended to other types of long-duration signals, such as those from neutron-star post-merger remnants or ultralight boson clouds around black holes. Optimization for GPUs is possible, which would provide an additional speedup of one to two orders of magnitude. The template bank can also be adapted for different parameter regions, and more accurate signal models can be used.
Faster resampling directly affects the search for primordial black holes, which are candidates for dark matter. The method is also useful for any task that requires processing long-duration, frequency-evolving signals.
The immediate next step is implementing NUFFT on GPUs and evaluating the real-world speedup. After that, a full-scale search on LIGO-Virgo-KAGRA data will be needed.
In gravitational-wave astronomy, the question of whether subsolar-mass primordial black holes exist remains open. This method brings us closer to an answer by making it possible to search for signals from such objects in data from ground-based detectors.
For a system with a chirp mass of 0.0005 solar masses, crossing the 20–2000 Hz band would take about two years. That means the signal would stay in the detector longer than many space missions.