Displaying similar documents to “On discrete Fourier spectrum of a harmonic with random frequency modulation”

On discrete Fourier analysis of amplitude and phase modulated signals

Waldemar Popiński (2012)

Applicationes Mathematicae

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In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal o t , t=0,1,...,n-1, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances...

On the relationships between Fourier-Stieltjes coefficients and spectra of measures

Przemysław Ohrysko, Michał Wojciechowski (2014)

Studia Mathematica

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We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.

Spectrum generating functions for oscillators in Wigner's quantization

Stijn Lievens, Joris Van der Jeugt (2011)

Banach Center Publications

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The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of 𝔬𝔰𝔭(1|2n) generators, and also recall the solution in terms of 𝔤𝔩(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra....

On the spectrum of Robin Laplacian in a planar waveguide

Alex Ferreira Rossini (2019)

Czechoslovak Mathematical Journal

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We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.

An elementary proof of the decomposition of measures on the circle group

Przemysław Ohrysko (2015)

Colloquium Mathematicae

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We give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato, which states that every measure on a compact abelian group G can be decomposed into a sum of two measures with a natural spectrum and a discrete measure.