Related papers: On discrete cosine transform
Convolutional neural networks are based on a huge number of trained weights. Consequently, they are often data-greedy, sensitive to overtraining, and learn slowly. We follow the line of research in which filters of convolutional neural…
The Causal Dynamical Triangulation (CDT) approach to quantum gravity is a lattice approximation to the gravitational path integral. Developed by Ambj\o{}rn, Jurkiewicz and Loll, it has yielded some important results, notably the emergence…
In this Letter we present discrete wave turbulence (DWT) as a counterpart of classical statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the size of clusters, i.e. it includes, but is not reduced to,…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and…
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the…
Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical…
The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary…
Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum…
This chapter reviews the fundamentals of continuous and discrete Linear Time-Invariant (LTI) systems with Single Input-Single Output (SISO). We start from the general notions of signals and systems, the signal representation problem and the…
Data transformation (DT) is a process that transfers the original data into a form which supports a particular classification algorithm and helps to analyze the data for a special purpose. To improve the prediction performance we…
A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…
We propose and demonstrate a computational imaging technique that uses structured illumination based on a two-dimensional discrete cosine transform to perform imaging with a single-pixel detector. A scene is illuminated by a projector with…
Digital Twin (DT) has gained great interest as an innovative technology in Industry 4.0 that enables advanced modeling, simulation, and optimization of service and manufacturing systems. This article provides an extensive review of the…
In this paper we present a novel class of compact orthomode transducers which use digital calibration to synthesize the desired polarization vectors while maintaining high isolation and minimizing mass and volume. These digital orthomode…
The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is…
We propose a practical approach to JPEG image decoding, utilizing a local implicit neural representation with continuous cosine formulation. The JPEG algorithm significantly quantizes discrete cosine transform (DCT) spectra to achieve a…
A general method for recovering missing DCT coefficients in DCT-transformed images is presented in this work. We model the DCT coefficients recovery problem as an optimization problem and recover all missing DCT coefficients via linear…
With the rapid advancements in digital imaging systems and networking, low-cost hand-held image capture devices equipped with network connectivity are becoming ubiquitous. This ease of digital image capture and sharing is also accompanied…
In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new confining method for ultracold atoms on optical lattices, based on off-diagonal confinement (ODC). This method was shown to have distinct advantages over the…