Fractional Wavelet Transform And Its Applications

With the coming of information age, signal which is the carrier of information, and its processing techniques have obtained a rapid development. Signal processing techniques has penetrated into many fields, such as biomedical, geophysics, radio astronomy, mechanical engineering, communication systems and so on. As an important signal processing method, time-frequency analysis has been more and more concerned in recent years. Wavelet transform(WT) and fractional Fourier transform (FRFT) are classic methods in time-frequency analysis. With the continuous development of WT and FRFT, fractional wavelet transform (FRWT) as a new time-frequency analysis method came into being, and it became a focus of frontier signal processing area.In this paper, research on fractional wavelet transform and its applications is made. The main research works can be summarized as follows:(1) The recent research situation of fractional wavelet transform is analyzed. The definition, nature and optical realization of FRWT are summarized. Besides, the method to realize fractional wavelet transform is given. According to the relationship of the fractional wavelet domain and time-frequency domain, FRWT is a time-frequency transform. It can reflect the information in time domain and frequency domain at the same time, and is suitable for non-stationary signal processing.(2) A novel signal de-noising method based on FRWT is proposed. The optimal fractional order of FRWT is obtained by a genetic algorithm according to the SNR of output signals. The noisy signal is transformed into optimal factional wavelet time-frequency domain by an optimal FRWT. Then, the transformed signal is filtered by a narrow band-pass filter. Finally, the signal is reconstructed by an inverse FRWT. De-noising results of noisy Bumps signal and speech signal show that the SNR of output signals can be effectively improved. Results also show that the proposed method can preserve detail information effectively and reduce the noise at the same time.(3) For ensuring the security of digital image information, a novel image scrambling encryption method based on FRWT is proposed. We can encrypt the image by FRWT and scrambling transform. Firstly, factional orders, a series of scaling factors and a scrambling algorithm are chosen. The original image is transformed into factional wavelet time-frequency domain by a FRWT. Then, the transformed image is scrambled by a scrambling algorithm, and the encrypted image is got. Encryption simulations prove its possibility.