Related papers: Compact Support Biorthogonal Wavelet Filterbanks f…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
In this paper, we consider nonsubsampled graph filter banks (NSGFBs) to process data on a graph in a distributed manner. Given an analysis filter bank with small bandwidth, we propose algebraic and optimization methods of constructing…
Spectral graph signal processing is traditionally built on self-adjoint Laplacians, where orthogonal eigenbases yield an energy-preserving Fourier transform and a variational frequency ordering via a real Dirichlet form. Directed networks…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and…
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an…
Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…
Filter bank multiple access (FBMA) without subbands orthogonality has been proposed as a new candidate waveform to better meet the requirements of future wireless communication systems and scenarios. It has the ability to process directly…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. To approximate the auditory frequency resolution in the signal chain, some applications rely on perceptually motivated FBs, the gammatone FB…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
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…
Perfect reconstruction filter banks can be used to generate a variety of wavelet bases. Using IIR linear phase filters one can obtain symmetry properties for the wavelet and scaling functions. In this paper we describe all possible IIR…
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
In many applications such as wireless communications and subband adaptive filtering, we need to design non-uniform filter banks (NUFB), which may lead to better performances and reduced hardware complexity when compared to uniform filter…