Analytical kernels for efficient constant Q transforms in dark matter searches with LIGO

We introduce a novel scalable logarithmic spectral estimation method based on insights from computer-music analysis, allowing us to perform an efficient constant Q transform with no need for pre-computing. By leveraging symmetries between the time and frequency domains, this method matches the computational efficiency of FFT-based algorithms without, unlike such algorithms, compromising precision. We apply our algorithm to data from LIGO's third observing run, using the results to enhance a previous search for scalar dark matter which relied on FFT-based approximations. Our results show that we can simultaneously boost the signal-to-noise ratio up to the theoretical maximum and reduce computational costs. With potential for further refinements, this method is already capable of boosting the scientific potential of any logarithmic spectral analysis with limited computational budget, which includes all future dark matter searches with gravitational-wave detectors.