Fast algorithms for 1-D & 2-D real-valued discrete Gabor transforms

By replacing the complex-valued Gabor basis functions of the complex-valued discrete Gabor transforms (CDGTs) with real-valued Gabor basis functions, we propose fast algorithms for 1-D and 2-D real-valued discrete Gabor transforms (RDGTs) in this paper. The RDGT algorithms provide a simpler method than the CDGT algorithms to calculate the transform (or Gabor) coefficients of a signal or an image from finite summations and to reconstruct the original signal or image exactly from the computed transform coefficients. The similarity between the RDGTs and the discrete Hartley transforms (DHTs) enables the RDGTs to utilize the fast DHT algorithms for fast computation. Moreover, the RDGTs have a simple relationship with the CDGTs such that the CDGT coefficients can be directly computed from the RDGT coefficients.