Related papers: Finite Impulse Response Filters for Simplicial Com…
To any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig's discrete Morse complex and abutting to the matching complex of X. This construction leads to the definition of several homology theories,…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
A novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_p; with p an odd prime, is described and studied. The new functions are proved to satisfy good auto-correlation,…
This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the…
Infinite impulse response filters are an essential building block of many time-varying audio systems, such as audio effects and synthesisers. However, their recursive structure impedes end-to-end training of these systems using automatic…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
Many real-world systems can be represented as graphs where the different entities in the system are presented by nodes and their interactions by edges. An important task in studying large datasets with graphical structure is graph…
We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on persistent homology. We achieve this control through the use of an interleaving…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of…
This paper presents the design and implementation of three System on Chip (SoC) cores, which implement the Digital Signal Processing (DSP) functions: Finite Impulse Response (FIR) filter, Infinite Impulse Response (IIR) filter and Fast…
Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energy on the higher frequencies. These filters are sub-ideal…
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing…
Experimental observation of Doppler-free signals for weak transitions can be greatly facilitated by an estimate for their expected amplitudes. We derive an analytical model which allows the Doppler-free amplitude to be estimated for small…
This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FF-Wavelets) including FF-Haar and FF-Daubechies are derived. Non-orthogonal FF-wavelets such as B-spline over GF(p) are also…
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
This paper proposes a novel feature called spectrum congruency for describing edges in images. The spectrum congruency is a generalization of the phase congruency, which depicts how much each Fourier components of the image are congruent in…