Mind the step: On the frequency-domain analysis of gravitational-wave memory waveforms

Abstract

Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on finite time intervals. In order to reduce artifacts in the Fourier transform, it is common to use recipes that involve windowing and padding with constant values. Here we discuss how to regularize the Fourier transform in a straightforward way by splitting the signal into a given sigmoid function that can be Fourier transformed in closed form, and a residual which does depend on the details of the gravitational-wave signal and has to be Fourier transformed numerically, but does not contain a persistent component. We provide a detailed discussion of how to map between continuous and discrete Fourier transforms of signals that contain a persistent component. We apply this approach to discuss the frequency-domain phenomenology of the $(\ell =2,m=0)$ spherical harmonic mode, which contains both a memory and an oscillatory ringdown component.

16 pages, 14 figures, published in PRD under the title "Frequency-domain analysis of gravitational-wave memory waveforms"

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Cited by in corpus (6)

• GW231123: a Binary Black Hole Merger with Total Mass 190-265 $M_{\odot }$
• Adding equatorial-asymmetric effects for spin-precessing binaries into the SEOBNRv5PHM waveform model
• Real modes and null memory contributions in effective-one-body models
• Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset
• Accelerating the time-domain LISA response model with central finite differences and hybridization techniques
• Waveform model for the $(\ell =2,m=0)$ spherical harmonic and the displacement memory contribution from precessing binary black holes