相关论文: On harmonic analysis of vector-valued signals
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the…
A signed graph is a graph with edges marked positive and negative; it is unbalanced if some cycle has negative sign product. We introduce the concept of vector valued switching function in signed graphs, which extends the concept of…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
In this work we extend analytic signal theory to the multidimensional case when oscillations are observed in the $d$ orthogonal directions. First it is shown how to obtain separate phase-shifted components and how to combine them into…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a submanifold M of a Riemannian manifold (with corners) that…
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
In this paper, we introduce a new concept, namely $\epsilon$-arithmetics, for real vectors of any fixed dimension. The basic idea is to use vectors of rational values (called rational vectors) to approximate vectors of real values of the…
Classical Graph Signal Processing (GSP) provides a robust framework for analyzing signals on irregular domains, utilizing the graph Fourier transform as a cornerstone for spectral analysis and filtering. However, as data structures grow in…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
An arbitrary derivative of a Vandermonde form in $N$ variables is given as $[n_1\cdots n_N]$, where the $i$-th variable is differentiated $N-n_i-1$ times, $1\le n_i\le N-1$. A simple decoding table is introduced to evaluate it by…
In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion…
A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…