On discrete Fourier analysis of amplitude and phase modulated signals

Waldemar Popiński

Displaying similar documents to “On discrete Fourier analysis of amplitude and phase modulated signals”

On discrete Fourier spectrum of a harmonic with random frequency modulation

Waldemar Popiński (2013)

Applicationes Mathematicae

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Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., n-1 by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as n → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations...

Fermi Golden Rule, Feshbach Method and embedded point spectrum

Jan Dereziński (1998-1999)

Séminaire Équations aux dérivées partielles

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A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jak $\overset{ˇ}{s}$ ić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.

Spectrum of L

W. Marek, K. Rasmussen

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CONTENTS0. Motivation, results to be used in the sequel ................51. Slicing $L_{α}$ ’s ..........................................................102. Hereditarily countable, definable elements ................133. Spectrum of L.............................................................154. The width of elements of spectrum ............................195. Non-uniform strong definability ..................................266. Solution to a problem of Wilmers................................327....

Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

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Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , $S p (A, B) = S p (A) \times S p (B)$ , where Sp denotes the joint Taylor spectrum.

Dunkl-Gabor transform and time-frequency concentration

Saifallah Ghobber (2015)

Czechoslovak Mathematical Journal

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The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg’s uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks’ uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with...

Resonant delocalization for random Schrödinger operators on tree graphs

Michael Aizenman, Simone Warzel (2013)

Journal of the European Mathematical Society

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We analyse the spectral phase diagram of Schrödinger operators $T + λ V$ on regular tree graphs, with $T$ the graph adjacency operator and $V$ a random potential given by $i i d$ random variables. The main result is a criterion for the emergence of absolutely continuous $(a c)$ spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials $a c$ spectrum appears at arbitrarily weak disorder $(λ ≪ 1)$ in an energy regime which extends beyond the spectrum of $\sim T$ ....

Local spectrum and local spectral radius of an operator at a fixed vector

Janko Bračič, Vladimír Müller (2009)

Studia Mathematica

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Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with $σ_{T} (e) = σ_{δ} (T)$ , respectively $r_{T} (e) = r (T)$ , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.

Ascent spectrum and essential ascent spectrum

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri (2008)

Studia Mathematica

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We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{a s c}^{e} (T + F) = σ_{a s c}^{e} (T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued...

On the uncertainty inequality as applied to discrete signals.

Venkatesh, Y.V., Raja, S.Kumar, Vidyasagar, G. (2006)

International Journal of Mathematics and Mathematical Sciences

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The third order spectrum of the p-biharmonic operator with weight

Khalil Ben Haddouch, Najib Tsouli, Zakaria El Allali (2014)

Applicationes Mathematicae

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We show that the spectrum of $Δ ²_{p} u + {2 β \cdot \nabla (| Δ u |}^{p - 2} {Δ u) + | β | ² | Δ u |}^{p - 2} Δ u = α m {| u |}^{p - 2} u$ , where $β \in ℝ^{N}$ , under Navier boundary conditions, contains at least one sequence of eigensurfaces.

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f (σ_{W} (T)) \cup z \in ℂ : | z | = 1$ is connected, where $σ_{W} (T)$ denotes the Weyl spectrum of T.

Spectra of extended double cover graphs

Zhibo Chen (2004)

Czechoslovak Mathematical Journal

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The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph $G$ with vertex set $V = {v_{1}, v_{2}, \dots, v_{n}}$ , the extended double cover of $G$ , denoted $G^{*}$ , is the bipartite graph with bipartition $(X, Y)$ where $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y = {y_{1}, y_{2}, \dots, y_{n}}$ , in which $x_{i}$ and $y_{j}$ are adjacent iff $i = j$ or $v_{i}$ and $v_{j}$ are adjacent in $G$ . In this paper we obtain formulas for the characteristic polynomial and the spectrum of $G^{*}$ in terms of the corresponding information of $G$ . Three formulas are derived for the number of spanning trees...

Some examples of cocycles with simple continuous singular spectrum

K. Frączek (2001)

Studia Mathematica

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We study spectral properties of Anzai skew products $T_{φ} : ² \to ²$ defined by $T_{φ} (z, ω) = (e^{2 π i α} z, φ (z) ω)$ , where α is irrational and φ: → is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of $T_{φ}$ on the orthocomplement of the space of functions depending only on the first variable is a “typical” property in the above-mentioned class of cocycles, if α admits a sufficiently...

Consistency of the LSE in Linear regression with stationary noise

Guy Cohen, Michael Lin, Arkady Tempelman (2004)

Colloquium Mathematicae

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We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also $L_{p}$ -consistency when the noise is strict sense stationary...

A spectral mapping theorem for Banach modules

H. Seferoğlu (2003)

Studia Mathematica

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Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then $σ (T_{μ}) = \bar{μ ̂ (s p (X))}$ for each measure μ in reg(M(G)), where $T_{μ}$ denotes the operator in B(X) defined by $T_{μ} x = μ \circ x$ , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal $I_{X} = f \in L ¹ (G) | T_{f} = 0$ , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains...

Rearrangement of coefficients of Fourier series on $S U_{2}$

Giancarlo Travaglini (1987)

Colloquium Mathematicae

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