Time-Frequency Localization optimization of PR FMT: Case of an overlapping factor equal to 2

•Time-Frequency Localization (TFL) is a key indicator for transmission systems.•Short OFDM pulses are preferred in many communication applications: 5G, power lines.•An overlapping factor equal to 2 only adds limited complexity and latency.•Perfect Reconstruction (PR) leads to a reduced size of the TFL optimization problem.•Furthermore, compact representations (CRs) make the optimization problem tractable. In this paper, we analyze the Perfect Reconstruction (PR) 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 nevertheless 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, different types of compact representation are proposed to efficiently optimize the TFL criterion and a simple and general construction algorithm is also provided for the computation of the PR FMT prototype filter coefficients. Numerical results and graphical displays illustrate the good behavior of our proposed design methods in terms of TFL performance and computational complexity. Finally, various FMT prototype filters are compared with regard to their resilience to symbol timing offset.