Fourier-hermite communications; where Fourier meets Hermite

A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency localization. Its robustness against time-frequency shifts is assessed and compared to Hermite and Fourier basis signals. The Fourier-Hermite signal set is particularly designed for communications in spectrum-scarce environments.