An Efficient Approach for Discrete Gabor Expansion

A real discrete Gabor expansion (RDGE) for finite and infinite sequences is defined in this paper. By using the similar method applied to the complex discrete Gabor expansion (CDGE), a significant computation of the RDGE can be saved when compared to the computation of the widely used CDGE. And the RDGE is more convenient to be implemented by both software and hardware due to its real operations. In addition, the RDGE has a very simple relationship with the CDGE so that the CDGE coefficients can be easily obtained from the RDGE coefficients. As a result a direct replacement of the existing CDGE by the proposed RDGE is possible.