PhD Seminar: Jorge Valencia Gómez, Estudiant del Programa de Doctorat de Física — Mind the step: On the frequency-domain analysis of gravitational-wave memory waveforms

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 artefacts 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. I apply this approach to discuss the frequency domain phenomenology of the (2, 0) spherical harmonic mode, which contains both a memory and an oscillatory ringdown component.