Symplectic Transformations on Wigner Distributions and Time Frequency Signal Design

This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on Wigner distributions and marginalizable time frequency distributions to investigate the change in variance of time and frequency variables from a signal processing perspective. Moreover, operations on signals which leave uncertainty relations unchanged are studied.

Uncertainty Relations for MIMO Ambiguity Functions

In this paper, uncertainty relations for MIMO ambiguity functions are given. Norm inequalities on the MIMO ambiguity functions in terms of signals of concern are studied. A signal dependent lower bound on the support of MIMO ambiguity functions is given via application of a local uncertainty relation. The uncertainty of Lieb and MIMO ambiguity functions are related. Uncertainty relations on MIMO covariance matrix are given in terms of matrix norms.

MIMO Ambiguity Functions and Harmonic Analysis

Multi input multi output (MIMO) systems\' capability of using seperate signals brings many advantages to radar signal processing and time frequency analysis. In this paper, a variety of properties of MIMO ambiguity functions related with representations of Heisenberg group are given. Some of the existing results for SIMO ambiguity functions are generalized to MIMO case. Combined effect of seperate signals is investigated.