Spectrum Characteristic Analysis of Linear Frequency-Modulated Signals in the Fractional Fourier Domain

Linear frequency-modulated signal is a kind of typical non-stationary signal and is used widely in the fields of radar, sonar, communications and so on. The fractional Fourier transform is a new kind of time-frequency transform and has become a good tool of the detection and parameter estimation of the linear frequency-modulated signal because of its unique properties. Especially, as a linear transform, the fractional Fourier transform can avoid the cross-terms interference in multi-component linear frequency-modulated signals processing. However, the multi-component linear frequency-modulated signals also have the problems of the mutual effects among the signals in the fractional Fourier domain. In order to solve the problems, it is very necessary to study the spectrum distribution characteristics of the linear frequency-modulated signal in the fractional Fourier domain. First, in this paper, based on the definition of the fractional Fourier transform and the relationship between the fractional Fourier transform and time-frequency distribution, the spectrum distribution characteristics of linear frequency-modulated signal is analyzed in the fractional Fourier domain, and the relationship between the spectrum distribution of linear frequency-modulated signal and the fractional rotation angle α is also analyzed. Second, based on the algorithm of digital computation of the fractional Fourier transform, the digital fractional spectrum distribution characteristics of the linear frequency-modulated signal are analyzed, and the approximate expression of the linear frequency-modulated signal’s energy spectrum in the fractional Fourier transform is deduced. Finally, using the fractional spectrum distribution characteristics of the linear frequency-modulated signal, the peaks shifting of the multi-component linear frequency-modulated signals is studied in the fractional Fourier domain, and the reason and conditions of the peaks shifting are given. This paper establishes the foundation to analyze the quantitative relationship of mutual effects among multi-component linear frequency-modulated signals in the fractional Fourier domain, and it also offers an important reference to improve the ability of the fractional Fourier transform to process the multi-component linear frequency-modulated signals.