Further results on signal concentration in time-frequency

This paper formulates a novel class of signals which are concentrated simultaneously in time and frequency. Two concentration measures studied are second-moment and fourth-moment bandwidth measures in frequency subject to 1 - γ proportion of the energy inside the time interval [-T/2, T/2] for some nominal small γ. We employ the general constrained variational method of Franks to determine the integral equations for the optimal signals. Simulation results show that the optimal functions with minimum fourth-moment weighting have more energy in the main lobe and quicker decaying tails than Gabor half sinusoids.