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The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
Density functional theory (DFT) is the de facto approach for predicting self-consistent-field electronic structures of ground-state configurations of complex atoms, molecules, and solids and providing their property data for materials…
This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier…
Non-stationary forced oscillations (FOs) have been observed in power system operations. However, most detection methods assume that the frequency of FOs is stationary. In this paper, we present a methodology for the analysis of…
A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to non-linear static density response functions in quantum many-body systems. Within this framework, explicit expressions…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…
In the presence of additive Gaussian noise, the statistics of the nonlinear Fourier transform (NFT) of a pulse are not yet completely known in closed form. In this paper, we propose a novel approach to study this problem. Our contributions…
The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…
Optoacoustic imaging technologies require fast and accurate signal pre-processing algorithms to enable widespread deployment in clinical and home-care settings. However, they still rely on the Discrete Fourier Transform (DFT) as the default…
When considering two or more time series of functions or curves, for instance those derived from densely observed intraday stock price data of several companies, the empirical cross-covariance operator is of fundamental importance due to…
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function \phi(X)---specifically,…
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…
- In this paper we present a method to compute the coefficients of the fractional Fourier transform (FrFT) on a quantum computer using quantum gates of polynomial complexity of the order O(n^3). The FrFt, a generalization of the DFT, has…
Channel estimation is one of the most important parts in current mobile communication systems. Among the huge contributions in channel estimation studies, the discrete Fourier transform (DFT)-based channel estimation has attracted lots of…
Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field. While the method was originally applied to linear impulse response…
Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…