Related papers: A Linearized Approach to Radial-Velocity Extractio…
High-precision radial velocity (RV) measurements are crucial for exoplanet detection and characterisation. Efforts to achieve ~10 cm/s precision have been made over the recent decades, with significant advancements in instrumentation, data…
Radio Frequency Interference (RFI) increasingly contaminates the radio astronomy spectrum, often exceeding astronomical signal amplitudes by 50-70 dB. Reliable detection and mitigation are therefore essential for studies of faint transient…
For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…
The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
Photonic Doppler Velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the standard approach to PDV analysis, a short-time Fourier transform (STFT) is used…
We address the problem of recovering a signal (up to global phase) from its short-time Fourier transform (STFT) magnitude measurements. This problem arises in several applications, including optical imaging and speech processing. In this…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
The synchrosqueezing transform (SST) has been developed as a powerful EMD-like tool for instantaneous frequency (IF) estimation and component separation of non-stationary multicomponent signals. Recently, a direct method of the…
This chapter describes briefly the key aspects behind the derivation of precise radial velocities. I start by defining radial velocity precision in the context of astrophysics in general and exoplanet searches in particular. Next I discuss…
Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat.…
The Fourier Transform method is a popular tool to derive the rotational velocities of stars from their spectral line profiles. However, its domain of validity does not include line-profile variables with time-dependent profiles. We…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
The data analysis of space-based gravitational wave detectors like Taiji faces significant challenges from non-stationary noise, which compromises the efficacy of traditional frequency-domain analysis. This work proposes a unified framework…
The standing waves existed in radio telescope data are primarily due to reflections among the instruments, which significantly impact the spectrum quality of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Eliminating…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
Fourier transform spectroscopy (FTS) has been widely used in a variety of fields in research, industry, and medicine due to its high signal-to-noise ratio, simultaneous acquisition of signals in a broad spectrum, and versatility for…