Real Gabor Transform Theory and Applications

Author: Tao Liang / Gu Juanjuan
Publisher:
Publish Date: 2005-08-01
Features: The main contents of this book include: 1. Reviewing the theoretical methods of traditional complex-valued Gabor transform; 2. Proposing the basic theory and fast algorithms of one-dimensional and two-dimensional real-valued discrete Gabor transform; 3. To effectively and quickly compute the real-valued discrete Gabor transform, block-time recursive algorithms for solving the coefficients of one-dimensional real-valued discrete Gabor transform under critical sampling and oversampling conditions, as well as block-time recursive algorithms for reconstructing the original signal from the transform coefficients, were studied. The implementation methods of these two algorithms using parallel lattice structures were investigated, and the computational complexity and superiority of the algorithms were discussed and compared. At the same time, the time-recursive characteristics of two-dimensional RDGT were studied, as well as the method of rapidly implementing two-dimensional time-recursive RDGT using a double-layer parallel lattice structure; 4. Some application studies of real-valued discrete Gabor transform, including Gabor representation algorithms for transient signals, NMR FID signal enhancement algorithms based on oversampled real-valued discrete Gabor transform, and linear time-varying system representation and approximation methods based on real-valued discrete Gabor transform. Experimental results verify the superiority and effectiveness of real-valued discrete Gabor transform in applications, demonstrating the practical value of real-valued discrete Gabor transform.