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Digital signal processing is a valuable practical skill for the contemporary physicist, yet in physics curricula its central concepts are often introduced either in method courses in a highly abstract and mathematics-oriented manner or in…
Pulsar detection and timing experiments are applications where adaptive filters seem eminently suitable tools for radio-frequency-interference (RFI) mitigation. We describe a novel variant which works well in field trials of pulsar…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
A discrete auditory transform (DAT) from sound signal to spectrum is presented and shown to be invertible in closed form. The transform preserves energy, and its spectrum is smoother than that of the discrete Fourier transform (DFT)…
Dispersive Fourier transform (TS-DFT) technique opens a fascinating pathway to explore the ultrafast non-repetitive even, which has been employed to study the build-up process of mode-locked lasers. Here the whole evolution dynamics (from…
We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…
The nonlinear Schr\"odinger equation (NSE) is well-known to model an ideal fiber-optic communication channel. Even though the NSE is a nonlinear evolution equation, it can be solved analytically using a nonlinear Fourier transform (NFT).…
The one-dimensional PDE model of the wave equation with a state feedback controller at its boundary, which describes wave dynamics of a wide-range of controlled mechanical systems, has exponentially stable solutions. However, it is known…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version…
The fundamentals of Fourier Transform are presented, with analytical solutions derived for Continuous Fourier Transform (CFT) of truncated signals, to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFT were…
A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain…
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…
In this research we address the problem of capturing recurring concepts in a data stream environment. Recurrence capture enables the re-use of previously learned classifiers without the need for re-learning while providing for better…
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…
An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Decision-focused learning (DFL) has emerged as a powerful end-to-end alternative to conventional predict-then-optimize (PTO) pipelines by directly optimizing predictive models through downstream decision losses. Existing DFL frameworks are…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…