离散信号和图象的实数形式Gabor变换

定义了用于有限序列和图象表示的实数形式离散Ｇａｂｏｒ变换（ＲＤＧＴ）这种通过将复数形式离散Ｇａｂｏｒ变换（ＣＤＧＴ）的复数Ｇａｂｏｒ基本函数替换成实数Ｇａｂｏｒ基本函数而进行的实数变换，在算法复杂性上与ＣＤＧＴ相比，明显降低，并且由于ＲＤＧＴ与离散Ｈａｒｔｌｅｙ变换（ＤＨＴ）有着相似的形式，从而使得ＲＤＧＴ能够利用快速的ＤＨＴ加速变换，另外，ＲＤＧＴ系数与ＣＤＧＴ系数的实部和虚部之间有着非常简单的

Real Discrete Gabor Transform for Finite Discrete Signal and Image Representation

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.