Related papers: Multi-dimensional graph fractional Fourier transfo…
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…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
Most codec designs rely on the mean squared error (MSE) as a fidelity metric in rate-distortion optimization, which allows to choose the optimal parameters in the transform domain but may fail to reflect perceptual quality. Alternative…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…
Fourier optics, the principle of using Fourier Transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and has been widely applied to optical information processing, imaging, holography etc.…
Source wavelet estimation is the key in seismic signal processing for resolving subsurface structural properties. Homomorphic deconvolution using cepstrum analysis has been an effective method for wavelet estimation for decades. In general,…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from…
Though Fourier Transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
Information from an image occurs over multiple and distinct spatial scales. Image pyramid multiresolution representations are a useful data structure for image analysis and manipulation over a spectrum of spatial scales. This paper employs…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
Low-light remote sensing images generally feature high resolution and high spatial complexity, with continuously distributed surface features in space. This continuity in scenes leads to extensive long-range correlations in spatial domains…