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
介绍了噪声背景中正弦信号频率估计的方差下限,对利用FFT主瓣内两条幅度最大谱线进行插值的频率估计方法(R ife-Jane方法和Q u inn方法)以及利用FFT相位进行频率插值的方法(分段FFT相位差法和重叠FFT相位差法)的方差进行了理论分析,推导...介绍了噪声背景中正弦信号频率估计的方差下限,对利用FFT主瓣内两条幅度最大谱线进行插值的频率估计方法(R ife-Jane方法和Q u inn方法)以及利用FFT相位进行频率插值的方法(分段FFT相位差法和重叠FFT相位差法)的方差进行了理论分析,推导了Q u inn方法的频率估计方差计算公式,提出了通过滤波进一步提高分段FFT相位差法的频率估计精度的方法。通过计算机M on te C arlo模拟实验对上述各种方法的频率估计精度以及加窗函数的影响进行了分析并与理论下限进行了比较,指出了每种方法所能达到的估计精度。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.
文摘介绍了噪声背景中正弦信号频率估计的方差下限,对利用FFT主瓣内两条幅度最大谱线进行插值的频率估计方法(R ife-Jane方法和Q u inn方法)以及利用FFT相位进行频率插值的方法(分段FFT相位差法和重叠FFT相位差法)的方差进行了理论分析,推导了Q u inn方法的频率估计方差计算公式,提出了通过滤波进一步提高分段FFT相位差法的频率估计精度的方法。通过计算机M on te C arlo模拟实验对上述各种方法的频率估计精度以及加窗函数的影响进行了分析并与理论下限进行了比较,指出了每种方法所能达到的估计精度。
