Time-Frequency Localization Optimization of PR FMT: Case of an Overlapping Factor Equal to 2

In this paper, we analyze the perfect reconstruction property of Filtered MultiTone (FMT) systems with overlapping factor equal to 2. If small overlapping factors are not common for FMT systems that originally targeted nearly perfect subchannels isolation, we show that they can provide pretty good results when the optimization is carried out with the Time-Frequency Localization (TFL) criterion. Furthermore, it appears that the TFL criterion can ease the treatment of the PR equations. In this respect, our study exhibits nearly optimal TFL results and also leads to a simple and interesting closed form expression for the PR FMT prototype filter coefficients. Numerical results and illustrations are also provided showing the good behavior of our proposed design method in terms of TFL performance and computational complexity