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The development of a discrete transform for the Wigner distribution and ambiguity function
A theoretical basis for the development of the discrete Wigner distribution and ambiguity function is presented that is based on the temporal and spectral properties of the two-dimensional Wigner kernel function. This two-dimensional description is helpful in visualizing the various functions and shows that the increase in the number of points required
Mark A. Poletti
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Efficient computation of the discrete Wigner distribution function through a new iterative algorithm
This paper presents a new iterative method to speed up the DWDF computation. At present it has been considered from a computational point of view as a 1-D section of the Wigner kernel (WK)N point FTs. We purpose a new way to compute the DWDF based on the symmetry properties of the WK and the cosine function.
I. del Puerto +4 more
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ELIMINATION OF CROSS TERMS OF THE DISCRETE WIGNER DISTRIBUTION USING MULTIWAVELETS
Su Feng, Changwen Qu, He You
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About SIC POVMs and discrete Wigner distributions
Journal of Optics B: Quantum and Semiclassical Optics, 2005A set of d2 vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is distinguished by its high degree of symmetry. Measures of this kind are called symmetric informationally complete, or SIC POVMs for short, and could be applied ...
Colin, Samuel +3 more
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On the existence of discrete Wigner distributions
IEEE Signal Processing Letters, 1999Among the myriad of time-frequency distributions, the Wigner distribution stands alone in satisfying many desirable mathematical properties. Attempts to extend definitions of the Wigner distribution to discrete signals have not been completely successful.
J.C. O'Neill, P. Flandrin, W.J. Williams
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Discrete time and frequency Wigner-Ville distribution: Moyal's formula and aliasing
IEEE Signal Processing Letters, 2005In this letter, we propose a new definition of the discrete time and frequency Wigner-Ville distribution. The proposed distribution not only displays a readable representation (small aliasing) but also exhibits unitarity and is easy to compute. We compare the time-frequency representation associated with this proposed definition with other existing ...
Chassande-Mottin, Eric, Pai, Archana
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Wigner distribution in linear canonical domains: properties and discretization
2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), 2019In our previous work, we introduced a kind of closed-form linear canonical transform (LCT) based Wigner distribution (WD), namely, the closed-form instantaneous cross-correlation function type of WD (CICFWD), and discussed its applications in non-stationary signal separation and detection. However, some related theoretical foundations are still unknown.
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A contribution to the unaliased discrete-time Wigner distribution
The Journal of the Acoustical Society of America, 1993This paper presents a new closed form analytical definition of the unaliased discrete-time Wigner distribution (DTWD), which arises naturally from its continuous-time counterpart, and is straightforwardly implementable for digital signal processing. This DTWD possesses properties that resemble those of the continuous time case.
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