The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its poten...The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.60232010 and 60572094)the Teaching and Research Award for 0utstanding Young Teachers in Higher Education Institutions of M0E,P.R.C.the Ministerial Foundation of China(Grant No.6140445).
文摘The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
文摘由于太阳辐射的随机性很大，同时考虑到传统方法建立的单一最小二乘支持向量机（least square support vector machine，LSSVM）模型精度不高，该文提出一种基于经验模态分解（empirical mode decomposition,EMD）局部均值分解（local mean decomposttion，LMD）和与机器学习方法LSSVM联合的逐时太阳辐照度预测模型。先利用信号处理算法EMD及LMD将时间顺序数据分解成一系列相对平稳的分量序列，冉对各子序列分别建立LSSVM预测模型，最后将各子序列预测结果进行叠加得到最终预测值。仿真结果表明，该模型取得比单一模型更好的预测效果，均方根误差精度可提高24．59％。
