In this paper, we define 1-D and 2D real-valued discrete Gabor transforms (RDGTs) fordiscrete signal and image representation. By replacing the complex-valued Gabor basis functions of thecomplex-valued discrete Gabor transform (CDGT)with real-valued Gabor basis functions, a significantcomputation of the RDGT can be saved as comparedwith 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, the RDGThas a simple relationship with the CDGT such thatthe CDGT coefficients can be directly computed fromthe RDGT coefficients. Some simulation results aregiven at the end of this paper.