The Application Of Fractional Fourier Transform In Signal Analysis

The fractional Fourier transform(FRFT) is an extension and further study on the basis of traditional Fourier transform. It is considered as the traditional Fourier transform to the n-th power, where n is an integer. This new transform has an unique characteristic which separates it from other algorithms. It can transform a function to any intermediate domain between time and frequency. The conception of FRFT was originally proposed by V. Namias. After decades of development, FRFT has achieved great success in the aspects of form definitions, algorithm conducting process, and physical meanings. The completion of the system theory of the fractional Fourier transform provided a strong theoretical base for the future development of its applications in the engineering field. In 1993, Almeida proposed a new physical meaning of the fractional Fourier transform, which indicates this transform can be comprehended as a rotation of frequency. Later on, Ozaktas et al. proposed the discrete algorithm in the application of the fractional Fourier transform in 1996, which further made FRFT become an innovative tool in the field of digital signal processing. In recent years, fractional Fourier transform has been widely used in the underwater acoustic, radar, and other fields of study.This dissertation starts with the definition and the properties of fractional Fourier transform, and studies its discrete numerical calculation method and demonstrates its relationships with other time-frequency analysis algorithms. Common frequency modulation(LFM) signals have been simulated by applying the FRFT theory. The process of applying the FRFT theory analyzing signals has been clearly described through the forms of graphs.FRFT can simultaneously obtain the information of the signal properties in time and frequency. It can also be comprehended as the base resolving of the LFM. In this dissertation, FRFT has been used to analyze the single component Chirp signal. The results of this analysis show that the fractional Fourier transform algorithm can effectively reduce the mutual interference of other components and noise. Additionally, this method is capable of extracting the target component accurately. The simulation results in this dissertation also proves the superiority of this method.