Related papers: Partial parameterization of orthogonal wavelet mat…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
We analyze representations of solvable Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive…
We construct a class of representations of the quadratic $R$-matrix algebra given by the reflection equation with the spectral parameter, $$ R{\,}(u-v)\,T^{(1)}(u)\,R{\,}(u+v)\,T^{(2)}(v)= T^{(2)}(v)\,R{\,}(u+v)\,T^{(1)}(u)\,R{\,}(u-v), $$…
We study the matrix factorization problem associated with an SO(2) spinning top by using the algebro-geometric approach. We derive the explicit expressions in terms of Riemann theta functions and discus some related problems including a…
We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized…
Orthogonal Frequency Division Multiplexing (OFDM) systems have been widely used as a communication system. In OFDM systems, there are two main problems. One of them is that OFDM signals have high Peak-to-Average Power Ratio (PAPR). The…
In this work we propose the construction of two-channel wavelet filterbanks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as…
The kinematics of many nonlinear control systems, especially in the robotics field, admit a transitive Lie-group symmetry, which is useful in high performance observer design. The recently proposed equivariant filter (EqF) exploits…
A new approach to distributed cooperative beamforming in relay networks with frequency selective fading is proposed. It is assumed that all the relay nodes are equipped with finite impulse response (FIR) filters and use a filter-and-forward…
In this work we characterize a full Kostant-Toda system in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system we give explicit expressions for…
In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
Orthogonal systems in $\mathrm{L}_2(\mathbb{R})$, once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the differentiation…
This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator.…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Group…
Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…
We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective $C(\mathbb T^n)$-modules. Conversely, we show how cancellation properties for finitely generated projective modules over…
In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the…
We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by…