DCT-based Real-valued Discrete Gabor Transform And Gabor Representation For Radar Signals

Gabor transform, as a joint time-frequency signal analysis tools, can overcome the disadvantage that Fourier transform can not accurately describe how the frequency contents of a signal change with time. As early as 1946, Dennis Gabor proposed the traditional Gabor transform, in which time-shift Gauss functions are added to the Fourier transform to compose the elementary functions of the Gabor transform, and then, a signal can be expanded into a set of the elementary functions in joint time-frequency domain. However, the applications of traditional Gabor transform were limited due to the difficulties in computing the biorthogonal analysis window functions and the Gabor coefficients.To improve the traditional Gabor transform, Liang Tao et al. proposed the real-valued discrete Gabor transforms (RDGTs) based on discrete Hartley transform (DHT) and discrete cosine transform (DCT), in which the computations of the Gabor coefficients, the signal reconstruction and biorthogonal analysis window functions involve only the real-valued operations, and the RDGTs can utilize the fast algorithms of DCT and DHT to accelerate the computations. Compared to the traditional complex-valued Gabor transform, the RDGTs greatly reduce the computation load. So the RDGTs can be easily implemented in computer hardware and software and have wide applications.This paper firstly reviews the theory of Gabor transform, and then, discusses the DCT-based RDGT and its application in the Gabor representation for radar signals. The main contributions of the thesis are summarized as follows:The DCT-based RDGT is applied in the moving target detection (MTD) system of a radar receiver, and a fast algorithm for the Gabor representation for radar signals is proposed. The simulation results show that the proposed algorithm is capable of separating echoes of the objects with different doppler frequencies, various arrival times, and additive white noises.