Related papers: Generalized Sampling Expansions Associated with Qu…
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
A method for the analysis of the power pattern of phased array antennas (PAs) based on the quantum Fourier transform (QFT) is proposed. The computation of the power pattern given the set of complex excitations of the PA elements is…
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…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR),…
Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant.…
Quantum frequency conversion (QFC) of photonic signals preserves quantum information while simultaneously changing the signal wavelength. A common application of QFC is to translate the wavelength of a signal compatible with the current…
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a…
Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or…
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…
Color in an image is resolved into 3 or 4 color components and 2-Dimages of these components are stored in separate channels. Most of the color image enhancement algorithms are applied channel-by-channel on each image. But such a system of…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In…
In this paper we show that a methodology based on a sampling with the Gaussian function of kind $h\,{e^{ - {{\left( {t/c} \right)}^2}}}/\left( {{c}\sqrt \pi } \right)$, where ${c}$ and $h$ are some constants, leads to the Fourier transform…
The short-time linear canonical transform (STLCT) can be identified as a generalization of the short-time Fourier transform (STFT). It is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty…
The Query Focused Text Summarization (QFTS) task aims at building systems that generate the summary of the text document(s) based on the given query. A key challenge in addressing this task is the lack of large labeled data for training the…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
The paper improves the accuracy of the one-dimensional fractional Fourier transform (FRFT) by leveraging closed Newton-Cotes quadrature rules. Using the weights derived from the Composite Newton-Cotes rules of order QN, we demonstrate that…