Real discrete Gabor expansion for finite and infinite sequences

A real discrete Gabor expansion (RDGE) for finite and infinite sequences is defined in this paper. By replacing the complex Gabor basis functions of the complex discrete Gabor expansion (CDGE) with real Gabor basis functions, a significant computation of the RDGE can be saved as compared with the computation of the CDGE. The similarity between the RDGE and the discrete Hartley transform (DHT) allows the RDGE to utilize the fast DHT algorithms for fast computation. In addition, the RDGE has a simple relationship with the CDGE such that the CDGE coefficients can be directly computed from the RDGE coefficients. Some simulation results are given at the end of this paper