分数傅里叶变换滤波优化算法及滤波器设计

分数傅里叶变换（FrFT, fractional Fourier transform）是经典傅里叶变换的一种表现形式，可理解为在时 频平面中坐标轴系以原点为轴逆时针旋转一定的角度。通过数学推导，对能否利用分数傅里叶变换进行信号滤波，滤波的优化算法如何，以及滤波器有哪些设计结构等问题进行深入的研究，指出分数傅里叶变换适用于非平稳信号滤波。采用Matlab进行了数值仿真实验。实验结果表明：在信号滤波方面，由于傅里叶变换在处理某些数据时有局限性，因此分数傅里叶变换与傅里叶变换相比具有显著的优势。最后给出FrFT滤波器的设计思想。

Optimization algorithm and design of FrFT filter

As Fourier transform is limited in dealing with certain kinds of signals,an improved method of Fourier transform which is called the fractional Fourier transform(FrFT) is put forward.FrFT,a manifestation of the classical Fourier transform,appears to be potentially useful.It depends on a parameter and can be interpreted as a counter-clock-wise rotation of coordinate system taking the original point as an axis by an angle on the time-frequency plane.It is a normal representation of the classical Fourier transform.Through mathematic ratiocination,a conclusion was reached that FrFT is better than Fourier transform in dealing with signal reconstruction.To explain FrFT systemically,the optimization algorithm of FrFT filter was given,then Matlab was used as a tool,which can provide emulator,to test and analyze FrFT's implement effects.At last,all kinds of designs of FrFT-based filters was put forward and explained.