Closed-Form Expressions of Optimal Short PR FMT Prototype Filters

The Filtered MultiTone (FMT) modulation can be seen as a simple extension of the OFDM modulation. Indeed, it can be efficiently realized as a Discrete Fourier Transform (DFT)-based transceiver. However, to avoid a significant increase of its computational complexity the FMT has to be implemented with short prototype filters. In this paper we propose explicit expressions to compute such short prototype filters. The corresponding closed-form expressions of the prototype filter coefficients are obtained for two different optimization criteria: out-of-band energy and time-frequency localization. In both cases it is shown that these quasi-optimal results correspond to linear-phase prototype filters.