Multi-Gaussian Window Based Real-value Discrete Gabor Transform And Expansion

As the Gabor transform can in the time domain and frequency domain simultaneously to obtain better localized information, information processing has been recognized as signal and image representation in one of the best. Gabor transformation in recent decades, research around the main window of the dual solution method, Gabor transform computing speed, time-frequency resolution of the problem.Thesis first introduces the theory of time-frequency analysis, a brief description of the traditional Gabor transform theory development process. As a non-orthogonal Gabor transform window function, and therefore can not simply solve the Gabor coefficients of the inner product of the way through to get to Gabor transform coefficients become very complex, thereby affecting the Gabor transform in real-time applications in engineering. Over the last decade, many scholars at home and abroad made a lot of computing Gabor coefficients of the method, but these calculations are based on complex numbers, Gabor transform coefficients in order to reduce the computational complexity, Professor Tao Liang proposed a theory of real-valued discrete Gabor transform and solve the Gabor coefficients of computational complexity problem.Traditional Gabor transform using a separate window function lead to a constant bandwidth, with a fixed time-frequency resolution. We can not guarantee time-resolved and frequency resolution while achieving the best result and a separate window function constant bandwidth. Paper discusses the multi-Gaussian window applied to the real-valued discrete Gabor transform, and can also be formed by the different bandwidth Gabor grid, which has a high time-frequency resolution, both the physical reality of the value of the discrete Gabor transform algorithm speed advantages, but also a good solution to the problem of time-frequency resolution, promising evolutionary spectrum of computing a new method, it can well handle non-stationary random signals.