Related papers: Fourier Domain
We present the Fourier Transform of continuous gravitational wave for arbitrary location of detector and source and for any duration of observation time in which both rotational motion of earth about its spin axis and orbital motion around…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
Time of flight cameras may emerge as the 3-D sensor of choice. Today, time of flight sensors use phase-based sampling, where the phase delay between emitted and received, high-frequency signals encodes distance. In this paper, we present a…
Fourier synthesis is one of the foundations of physical optics. Spatial Fourier optics is a basis for understanding optical imaging, microscopy, and holography. In conventional Fourier optics, the complex spatial field distribution in the…
I discuss some practical aspects of the analysis of millisecond time variability X-ray data obtained from accreting neutron stars and black holes. First I give an account of the statistical methods that are at present commonly applied in…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
The time domain is the emerging forefront of astronomical research with new facilities and instruments providing unprecedented amounts of data on the temporal behavior of astrophysical populations. Dealing with the size and complexity of…
The pseudo-spectral method is proposed for following the evolution of density and velocity fluctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity…
Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…
Frequency Map Analysis is a numerical method based on refined Fourier techniques which provides a clear representation of the global dynamics of many multi-dimensional systems, and which is particularly adapted for systems of 3-degrees of…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and…
The temporal evolution of microwave pulses transmitted through random dielectric samples is obtained from the Fourier transform of field spectra. Large fluctuations are found in the local or single channel delay time, which is the first…
Quasi-periodic trajectories with two or more incommensurate frequencies are ubiquitous in nonlinear dynamics, yet the classical Fourier-based time-spectral method is tied to strictly periodic responses. We introduce a torus time-spectral…
E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly…
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly…
Optical turbulence modelling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of…