Two Aspects of the Donoho-Stark Uncertainty Principle

We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical Donoho-Stark estimate in two different aspects: a better general lower bound and a lower bound in dependence on the signal itself.Comment: 20 page

Windowed-Wigner Representations, Interferences and Operators

2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.“Windowed-Wigner” representations, denoted by Wig and Wig_ , were introduced in [2] in connection with uncertainty principles and interferences problems. In this paper we present a more precise analysis of their behavior obtaining an estimate of the L2-norm of interferences of couples of “model” signals. We further define a suitable functional framework for the associated operators and show that they form a class of pseudodifferential operators which define a natural “path” between the multiplication, Weyl and Fourier multipliers operators

Cohen class of time-frequency representations and operators: boundedness and uncertainty principles

This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered. For these operators, which include all usual quantizations, we prove a boundedness result in the $L^p$ functional setting and a form of uncertainty principle analogous to that for localization operators.Comment: 21 pages, 1 figur

Generalized Spectrograms and t -Wigner Transforms

We consider in this paper Wigner type representations Wig t depending on a parameter t ∈ [0,1] as defined in [2]. We prove that the Cohen class can be characterized in terms of the convolution of such Wig t with a tempered distribution. We introduce furthermore a class of "quadratic representations" Sp t based on the t-Wigner, as an extension of the two window Spectrogram (see [2]). We give basic properties of Sp t as subclasses of the general Cohen class.Nosotros consideramos en este artículo representaciones de tipoWigner Wig t dependiendo de um parámetro t ∈ [0,1] como definido en [2]. Probamos que la clase Cohen puede ser caracterizada en terminos de la convolución de tales Wig t con una distribución temperada. Introducimos también la clase de "representaciones cuadraticas" Sp t basado en el t-Wigner, como una extensión de dos ventanas espectrograma (ver [2]). Nosotros damos propiedades básicas de Sp t como subclases de la clase Cohen