Related papers: On Performance of Sparse Fast Fourier Transform Al…
A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…
Amplitude encoding of real-world data on quantum computers is often the workflow bottleneck: direct amplitude encoding scales poorly with input size and can offset any speedups in subsequent processing. Fourier-based sparse amplitude…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
Filtering of digital signals is accomplished on an Excel spreadsheet using fast Fourier transform (FFT) convolution in which the kernel is either a Gaussian or a cosine modulated Gaussian. Pedagogical examples of low-pass and band-pass…
Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing…
Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier…
This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…
This research work focuses on the design of a high-resolution fast Fourier transform (FFT) /inverse fast Fourier transform (IFFT) processors for constraints analysis purpose. Amongst the major setbacks associated with such high resolution,…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
The fast Fourier transform (FFT) is a primitive kernel in numerous fields of science and engineering. OpenFFT is an open-source parallel package for 3-D FFTs, built on a communication-optimal domain decomposition method for achieving…
Raster images can have a range of various distortions connected to their raster structure. Upsampling them might in effect substantially yield the raster structure of the original image, known as aliasing. The upsampling itself may…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is…