Band-limited signal concentration in time-frequency

This paper studies signal concentration in time-frequency using the general constrained variational method of Franks. We apply this method to formulate the minimum fourth-moment time-duration measure in the time interval [-T/2, T/2] for band-limited signals. An orthonormal basis of band-limited functions with the minimum fourth-moment time-duration measure is obtained. Comparing our optimal band-limited signals with Gabor's function with the minimum second-moment time-duration measure, simulation results show that our function has better properties: 1) faster decaying rate; 2) larger main lobe; and 3) higher energy concentration measure.