Related papers: Continuous Angular Power Spectrum Recovery From Ch…

Given a reciprocal/palindromic polynomial of even degree, we show that the gamma vector is essentially given by an inverted Chebyshev polynomial basis expansion. As an immediate consequence, we characterize real-rootedness of a linear…

Beam alignment is key in enabling millimeter wave and terahertz radios to achieve their capacity. Due to the use of large arrays in these systems, the common exhaustive beam scanning results in a substantial training overhead. Prior work…

The Fluid Antenna System (FAS) overcomes the spatial degree-of-freedom limitations of conventional static antenna arrays in wireless communications.This capability critically depends on acquiring full Channel State Information across all…

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…

We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the…

A distributed algorithm for least mean square (LMS) can be used in distributed signal estimation and in distributed training for multivariate regression models. The convergence speed of an algorithm is a critical factor because a faster…

For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…

Clipping is one of the simplest peak-to-average power ratio (PAPR) reduction schemes for orthogonal frequency division multiplexing (OFDM). Deliberately clipping the transmission signal degrades system performance, and clipping mitigation…

We propose learnable polyphase sampling (LPS), a pair of learnable down/upsampling layers that enable truly shift-invariant and equivariant convolutional networks. LPS can be trained end-to-end from data and generalizes existing handcrafted…

Field theoretical renormalization group methods are applied to the Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf…

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point source. Its solution consists of a set of discrete modes radiating into the upper…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

In this paper, we investigate the AMLI-cycle method and make two contributions. First, we revisit the AMLI-cycle using the Chebyshev polynomials and establish a theory for its uniform convergence, assuming the two-grid method converges…

Chebyshev expansion coefficients can be computed efficiently by using the FFT, and for smooth functions the resulting approximation is close to optimal, with computations that are numerically stable. Given sufficiently accurate function…

Quantum networking continues to encode information in polarization states due to ease and precision. The variable environmental polarization transformations induced by deployed fiber need correction for deployed quantum networking. Here we…

Non-regular sampling can reduce aliasing at the expense of noise. Recently, it has been shown that non-regular sampling can be carried out using a conventional regular imaging sensor when the surface of its individual pixels is partially…

We seek to improve the data efficiency of neural networks and present novel implementations of parameterized piece-wise polynomial activation functions. The parameters are the y-coordinates of n+1 Chebyshev nodes per hidden unit and…

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…

In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…