In this paper

we define 1-D and 2-D real discrete Gabor transforms (RDGT) for finite discrete signal and image representation. By replacing the complex Gabor basis functions of the complex discrete Gabor transform (CDGT) with real Gabor basis functions

a significant computation of the RDGT can be saved as compared with the computation of the CDGT. The similarity between the RDGT and the discrete Hartley transform (DHT) allows the RDGT to utilize the fast DHT algorithms for fast computation. In addition

not only does the RDGT have a simple relationship with the CDGT such that the CDGT coefficients can be directly computed from the RDGT coefficients

but the RDGT coefficients also have the same properties as the CDGT coefficients. Some simulation results are given at the end of this paper.