The Applications And Study Of Fractional Fourier Transform In Signal Detecting And Image Processing

As a new method of time-frequency analysis, Fractional Fourier Transform (FRFT), is a generalized form of traditional Fourier Transform (FT). It is very suitable for non-stationary signal processing, especially the chirp signal (linear frequency modulation signal). Due to the good time-frequency domain features, FRFT is introduced to the image processing field to make up for the inadequacy of FT analysis, such as image filtering, restoration, digital watermarking and image encryption etc.On the basis of studying the FRFT theory, digital computation and its relationship with image, the main aim of this paper is to study the applications of FRFT, which includes the following three aspects:After studying the method of FRFT used to detect a single chirp signal and the FRFT separation technology, an algorithm based on Integral Quadratic Phase Function (IQPF) and FRFT of multipath chirp signal detection and estimation is proposed, with the estimation precision improved effectively.A new method based on the variety of FRFT, multi-scale of wavelet decomposition and pseudo-randomness of chaotic sequences for encrypting image is proposed, which can improve encryption effect and efficiency at the same time.After the analysis of the image energy, amplitude and phase distribution in the fractional domain, a new image enhancement algorithm based on FRFT and homomorphic filter is proposed, which improve the image quality effectively.In addition to the above applications, FRFT can also be applied into other aspects, such as edge detection, pattern recognition, etc. With the further development of time-frequency analysis theory and technology of FRFT, FRFT will have further development in the field of image processing.