目前网络关于分数阶傅里叶变换可靠的代码来源主要有一下几个：
（1）来源一：
M.A. Kutay. fracF: Fast computation of the fractional Fourier transform, 1996.
www.ee.bilkent.edu.tr/~haldun/fracF.m.
（2）来源二：
J. O’Neill. DiscreteTFDs:a collection of matlab files for time-frequency analysis, 1999.
ftp.mathworks.com/pub/contrib/v5/signal/DiscreteTFDs/.
（3）来源三：
Adhemar Bultheel and H´ector E. Mart´ınez Sulbaran.frft:Computation of the Fractional Fourier Transform,2004.
www.cs.kuleuven.ac.be/~nalag/research/software/FRFT/.
（4）来源四：
A. Bultheel.frft2:A two-phase implementation of the fractional Fourier transform,2011.
这里比较推荐的是来源三及其网站。2004年的这篇文章《Computation of the Fractional Fourier Transform》对前面的（1）和（2）进行了详细的对比，分析了两个程序的优劣并进行了改进，（3）的代码较为简洁也比较实用，其对应网站上还有很多相关的代码。
2019-12-21 20:39:49
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% Time-Frequency Toolbox.
% Version 1.0 January 1996
% Copyright (c) 1994-96 by CNRS (France) - RICE University (USA).
%
% Signal Generation Files
%
% sigmerge - Add two signals with given energy ratio in dB.
%
% Choice of the Instantaneous Amplitude
% amexpo1s - Generate one-sided exponential amplitude modulation.
% amexpo2s - Generate bilateral exponential amplitude modulation.
% amgauss - Generate gaussian amplitude modulation.
% amrect - Generate rectangular amplitude modulation.
% amtriang - Generate triangular amplitude modulation.
%
% Choice of the Instantaneous Frequency
% fmconst - Signal with constant frequency modulation.
% fmhyp - Signal with hyperbolic frequency modulation.
% fmlin - Signal with linear frequency modulation.
% fmodany - Signal with arbitrary frequency modulation.
% fmpar - Signal with parabolic frequency modulation.
% fmpower - Signal with power-law frequency modulation.
% fmsin - Signal with sinusoidal frequency modulation.
% gdpower - Signal with a power-law group delay.
%
% Choice of Particular Signals
% altes - Altes signal in time domain.
% anaask - Amplitude Shift Keyed (ASK) signal.
% anabpsk - Binary Phase Shift Keyed (BPSK) signal.
% anafsk - Frequency Shift Keyed (FSK) signal.
% anapulse - Analytic projection of unit amplitude impulse signal.
% anaqpsk - Quaternary Phase Shift Keyed (QPSK) signal.
% anasing - Lipschitz singularity.
% anastep - Analytic projection of unit step signal.
% atoms - Linear combination of elementary Gaussian wave packets.
% dopnoise - Generate complex Doppler random signal.
% doppler - Generate complex Doppler signal.
% klauder - Klauder wavelet in time domain.
% mexhat - Mexican hat wavelet in time domain.
% tftb_window - Window generation (previously window.m).
%
% Addition of Noise
% noisecg - Analytic complex gaussian noise.
% noisecu - Analytic complex uniform noise.
%
% Modification
% s
2019-12-21 20:12:41
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利用分数阶傅里叶变换对线性调频信号进行参数估计，包括中心频率和调频率，在阶次搜索的时候利用了粗搜索和精细搜索的两级搜索方法
2019-12-21 19:43:13
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根据Ozaktas1996年的文章《Digital Computation of the Fractional Fourier Transform》编写的分数阶傅里叶变换程序。
2019-12-21 19:23:58
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本代码利用了分数阶傅里叶变换的方法，通过双随机实现图像加密的功能，并且对分数阶数的敏感度如峰值信噪比和相关系数等进行代码分析，此方法增加了密钥空间且增加了安全性，代码完全可以直接运行。
2019-12-21 18:56:49
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