Related papers: Time Warping and Interpolation Operators for Piece…
We develop a representation of reverse-time migration in terms of Fourier integral operators the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation…
We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…
Recently proposed orthogonal time frequency space (OTFS) modulation has been considered as a promising candidate for accommodating various emerging communication and sensing applications in high-mobility environments. In this paper, we…
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…
We consider the nonlinear inverse problem of learning a transition operator $\mathbf{A}$ from partial observations at different times, in particular from sparse observations of entries of its powers…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
The composition of the Fourier transform in $\mathbb{R}^n$ with a suitable pseudodifferential operator is called a Fourier operator. It is compact in appropriate function spaces. The paper deals with its spectral theory. This is based on…
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and $\tau$-Wigner distributions, using metaplectic operators. However, in order for a metaplectic…
The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need…
Ultra-reliable wireless communication links require the utilization of all diversity sources of a wireless communication channel. Hadani et al. propose a two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal pre-coder…
In the quest to realize analog signal processing using sub-wavelength metasurfaces, in this paper, we demonstrate the first experimental demonstration of programmable time-modulated metasurface processors based on the key properties of…
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…
An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses…
We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the $\mathcal{A}$-\emph{Wigner distribution} defined by $W_{\mathcal A}…
Orthogonal Time Frequency Space (OTFS) modulation is a recently proposed scheme for time-varying narrowband channels in terrestrial radio-frequency communications. Underwater acoustic (UWA) and ultra-wideband (UWB) communication systems, on…
Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…