分数阶傅里叶变换是近十多年来备受关注的一种新型信号处理工具，它是傅里叶变换的广义形式，适合于进行非平稳信号处理。短时分数阶傅里叶变换使用旋转的时频分辨单元分析信号，能够进行变尺度时频分析。分数阶傅里叶域滤波器组则能够实现分数阶傅里叶域多分辨率分析。因此，本项目将分数阶傅里叶域滤波器组、自适应滤波和短时加窗结合起来，系统地研究分数阶傅里叶域子带分解及其自适应滤波，以及以短时分数阶傅里叶变换为核心的时频分析理论。具体内容包括：分数阶傅里叶域过采样滤波器组、分数阶傅里叶域子带分解、基于分数阶傅里叶域子带分解的自适应滤波、短时分数阶傅里叶域变尺度分析等。通过本项目研究，可以进一步完善分数阶傅里叶变换理论体系，丰富自适应滤波和时频分析方法和手段，所得成果在波束形成、雷达目标检测与识别、变换域通信、信道盲均衡、自适应信道估计、增强数字水印系统的安全性及抗各种恶意攻击的稳健性等方面具备广阔的应用前景。

The fractional Fourier transform has been a novel signal processing tool and attracted a lot of attention in recent ten years. As the generalization of Fourier transform, the fractional Fourier transform is adaptive for nonstationary signal processing. The short-time fractional Fourier transform analyzes the signal by means of the rotating time-frequency unit, and can achieve the time-frequency analysis with variable scale. In addition, filter bank can obtain the multi-resolution analysis in the fractional Fourier domain. Thus, this project combines filter bank in the fractional Fourier domain, adaptive filtering, and window function. And the adaptive filtering based on subband decomposition in the fractional Fourier domain is studied systematically, as well as the time-frequency analysis focused on the short-time fractional Fourier transform. The detailed content of this project includes: oversampled filter banks in the fractional Fourier domain, subband decomposition in the fractional Fourier domain, adaptive filtering based on subband decomposition in the fractional Fourier domain, short-time fractional Fourier analysis with variable scale, and etc. Through this project, the theory system of fractional Fourier transform will be enriched further, as well as the methods of adaptive filtering and time-frequency analysis. The research production has the broad application prospect in such fields as beam forming, radar target detection and recognition, transform domain communication, blind channel equalization, adaptive channel estimation, enhancing the security of digital watermarking, and so on.