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

Area of Science:

• Astrophysics and Signal Processing
• Gravitational-wave Astronomy
• Computational Physics

Background:

• Accurate spectral analysis is crucial for detecting faint astrophysical signals.
• Previous methods like the Fast Fourier Transform (FFT) can lack precision or be computationally intensive.
• Logarithmic spectral analysis is vital for phenomena like dark matter searches.

Purpose of the Study:

• To introduce a novel, scalable logarithmic spectral estimation method.
• To achieve computational efficiency comparable to FFT-based algorithms without precision loss.
• To enhance the analysis of gravitational-wave data for dark matter detection.

Main Methods:

• Developed a Constant Q Transform (CQT) algorithm inspired by computer-music analysis.
• Leveraged time-frequency domain symmetries for efficient computation.
• Applied the method to data from the LIGO third observing run.

Main Results:

• Achieved efficient CQT without pre-computation.
• Matched FFT computational efficiency while maintaining precision.
• Boosted signal-to-noise ratio to theoretical maximum in dark matter search.
• Reduced computational costs for spectral analysis.

Conclusions:

• The novel method offers significant improvements for logarithmic spectral analysis.
• It enhances the scientific potential of gravitational-wave dark matter searches.
• The algorithm provides a computationally efficient and precise tool for astrophysical data analysis.