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.