Efficient processing of nonstationary signals requires time-varying approach. An interesting research area within this approach is time-varying filtering. Since there is a certain amount of freedom in the definition of timevarying spectra, several definitions and solutions for the time-varying filtering have been proposed so far. Here we will consider the Wigner distribution based time-varying ...

Abstract. Consider an N × N hermitian random matrix with independent entries, not necessarily Gaussian, a so called Wigner matrix. It has been conjectured that the local spacing distribution, i.e. the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is, in the limit as N → ∞, the same as that of hermitian random matrices from GUE. We prove this con...

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field prop...

We have studied statistical properties of the values of the Wigner function W (x) of 1D quantum maps on compact 2D phase space of finite area V . For this purpose we have defined a Wigner function probability distribution P (w) = (1/V ) ∫ δ(w − W (x))dx, which has, by definition, fixed first and second moment. In particular, we concentrate on relaxation of time evolving quantum state in terms o...

Timbre morphing is a technique of music sound synthesis which combines existing sounds (timbres) to form a new sound. Musical timbre is defined as the temporal development of harmonics within a sound. We implement the Wigner time-frequency distribution as our representation of the temporal variation of harmonics. Similarity between input signals provides a basis for generating the Wigner distri...

A new approach has been proposed for improving the performance of the Wigner–Ville distribution. This approach is based on signal decomposition and modified magnitude group delay function. Signal decomposition achieved by perfect reconstruction filter bank reduces significantly the existence of crossterms. The Gibbs ripple effect is due to truncation of the Wigner–Ville distribution kernel. The...

A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial wave-particle duality. Quantum particles are seen as localized and indivisible concentrations of energy and/or mass, their probability amplitude in phase space ...