Time–frequency analysis of chirped femtosecond pulses using Wigner distribution function

2002 ◽  
Vol 74 (S1) ◽  
pp. s231-s236 ◽  
Author(s):  
K.-H. Hong ◽  
J.-H. Kim ◽  
Y.H. Kang ◽  
C.H. Nam
Keyword(s):  
Distribution Function ◽  
Frequency Analysis ◽  
Wigner Distribution ◽  
Femtosecond Pulses ◽  
Wigner Distribution Function ◽  
Time Frequency Analysis ◽  
Time Frequency

scholarly journals Linear perturbations of the Wigner distribution and the Cohen class

2019 ◽  
Vol 18 (03) ◽  
pp. 385-422 ◽  
Author(s):  
Elena Cordero ◽  
S. Ivan Trapasso
Keyword(s):  
Phase Space ◽  
Frequency Analysis ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Linear Perturbations ◽  
Cohen Class ◽  
Invertible Matrices

The Wigner distribution is a milestone of Time–frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kinds of modifications have been proposed. This contribution fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As a main result, we provide a characterization for the Cohen’s class [L. Cohen, Generalized phase-space distribution functions, J. Math. Phys. 7 (1996) 781–786; Time–frequency Analysis (Prentice Hall, New Jersey, 1995)]. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.

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