Related papers: The abstruse meets the applicable: Some aspects of…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…
The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with…
Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to many inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called local…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
Recent gravitational wave observations show evidence for the presence of higher harmonics, thus possibly indicating that these waves were generated in the inspiral of compact objects with asymmetric mass ratios. Signals with higher…
The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in…
In this article, we first briefly recall Gabor's communication theory and then Gabor transform and expansion, and also its connection with joint time frequency analysis.
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
This note shows how to align a periodic signal with its the Fourier transform by means of frequency or time scaling. This may be useful in developing new algorithms, e.g. for pitch estimation. This note also convolves the signals and the…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
In this expository note we present an introduction to the Gabor wave front set. As is often the case, this tool in microlocal analysis has been introduced and reinvented in different forms which turn out to be equivalent or intimately…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling…
We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at…
Interpretability is a pressing issue for machine learning. Common approaches to interpretable machine learning constrain interactions between features of the input, rendering the effects of those features on a model's output comprehensible…
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…
Phonetic ambiguity and confusibility are bugbears for any form of bottom-up or data-driven approach to language processing. The question of when an input is ``close enough'' to a target word pervades the entire problem spaces of speech…