Optimal Multiband Pulse Shaping and Improved Power Spectrum Estimation Using Stopbands Information

In this letter, we derive formulas for optimal discrete-time pulse shaping for communications in multiband channels. Furthermore, we propose a technique for extending a short signal segment for the purpose of power spectral estimation using the available information about the signal stopbands. The later technique can be also used for minimizing the energy leakage into stopbands of a signal, e.g., as in windowing for orthogonal frequency division modulation (OFDM). Simulation results show that when the pulse duration is long enough, the stopband energy can be practically reduced to zero using the proposed technique. The proposed power spectral estimation technique can improve the resolution and reduce the energy leakage from signal passbands into adjacent stopbands. Moreover, it can reduce the out-of-band power leakage significantly when used for windowing in OFDM.