root-mean-square (RMS) bandwidth constraint. A num- ber of bandwidth measures for time-limited waveforms have been proposed in the literature [4]. Perhaps the most popular measures are the root-mean-square (RMS) and the fractional out-of-band-energy (FOBE) bandwidth measures. In this paper, we concentrate on the RMS bandwidth (we have obtained similar results for FOBE bandwidth [5]) introduced by Gabor [6] and used subse- quently in (e.g., [71-[141X