Related papers: The Complex-Step Integral Transform
This letter introduces a real valued summation known as Complex Conjugate Pair Sum (CCPS). The space spanned by CCPS and its one circular downshift is called {\em Complex Conjugate Subspace (CCS)}. For a given positive integer $N\geq3$,…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
This paper considers wave-based imaging through a heterogeneous (random) scattering medium. The goal is to estimate the support of the reflectivity function of a remote scene from measurements of the backscattered wave field. The proposed…
We propose a method of complex-amplitude Fourier single-pixel imaging (CFSI) with coherent structured illumination to acquire both the amplitude and phase of an object. In the proposed method, an object is illustrated by a series of…
In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
High-order numerical methods enhance Transformer performance in tasks like NLP and CV, but introduce a performance-efficiency trade-off due to increased computational overhead. Our analysis reveals that conventional efficiency techniques,…
Coherent surface scattering imaging (CSSI) is an emerging experimental technique uniquely suited to probing the structure of thin nanostructures. In these experiments, a specimen is placed on a substrate, and a series of X-ray diffraction…
We propose a method for analyzing two-dimensional symmetry protected topological (SPT) wavefunctions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the…
The paper proposes a synchropahsor estimation (SE) algorithm that leverages the use of a delayed in-quadrature complex signal to mitigate the self-interference of the fundamental tone. The estimator, which uses a three-point IpDFT combined…
Integrated Gradients (IG) is a widely adopted feature attribution method that satisfies desirable axiomatic properties. However, the choice of integration path significantly affects the quality of attributions, and the standard…
In recent years, the continuous wavelet transform (CWT) has been employed as a spectral feature extractor for acoustic recognition tasks in conjunction with machine learning and deep learning models. However, applying the CWT to each…
Hyperspectral image super-resolution has attained widespread prominence to enhance the spatial resolution of hyperspectral images. However, convolution-based methods have encountered challenges in harnessing the global spatial-spectral…
The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their…
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…
Optical imaging plays a critical role in advancing our understanding of three dimensional dynamics of biological systems. Coherent imaging (CI) methods exploit spatial phase information, encoded through propagation of coherent signal light…
While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform,…
We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its…