分数阶Fourier变换的数值计算

Digital Computation of Fractional Fourier Transform

以分数阶Fourier变换的定义为基础,仿真实现了其数值运算.对于线性调频信号(LFM),分析了调频斜率与分数阶数的关系,进而与匹配滤波器进行了性能比较,并且在低信噪比条件下仿真实现了LFM信号与噪声的分离.仿真结果表明,当分数阶数与调频斜率相匹配时,LFM信号的能量会高度集中.在水声信号处理领域,分数阶Fourier变换的良好的抗多卜勒性能有利于微弱信号检测.

Based on the concept of the fractional fourier transform, its digital computation is given through computer simulation. In terms of linear frequency modulation (LFM) signal, the relation between fractional order and modulation slope is analyzed and the performance comparison with matched filter is given. Moreover, the separation of LFM signal and noise is realized in low signal-to-noise ratio through simulation. Simulation results indicate that the energy of LFM signal will be collected effectively when the fractional order is matching with its modulation slope. In weak signals detection of underwater acoustic domain, we can get high anti-Doppler performance using the Fractional fourier transform algorithm.