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光谱分析采样数据重建原始信号
引用本文:宋一中,董祥军,赵志敏.光谱分析采样数据重建原始信号[J].光谱学与光谱分析,2008,28(7):1492-1495.
作者姓名:宋一中  董祥军  赵志敏
作者单位:1. 南京航空航天大学理学院,江苏,南京,210016;德州学院物理系,山东,德州,253000
2. 山东轻工业学院信息科学与技术学院,山东,济南,250353
3. 南京航空航天大学理学院,江苏,南京,210016
基金项目:中国博士后科学基金 , 江苏省博士后科学基金
摘    要:用光谱分析方法分析信号的采样与恢复。用三个改进的升余弦脉冲构造对称的限带频谱F(ω),经理论推导获得时域信号f(t)。采用梳状函数δT(t)对f(t)采样,调节T值,获得Shannon采样。应用快速傅里叶变换,计算采样的频谱Fd(ω),比较计算频谱Fd(ω)与限带频谱F(ω)的差别,讨论由采样频谱Fd(ω)重建f(t)的方法。结果发现:计算频谱Fd(ω)与限带频谱F(ω)非常相似,由采样数据可以在时域直接重建原始信号,而由频谱数据经快速逆傅里叶变换,同样能准确重建原始信号。因此,信号存储,既可以存储其采样信号,也可以存储采样信号的数字频谱。

关 键 词:快速傅里叶变换  采样定理  恢复  频域  数字信号处理

Tracking the Process Reconstructing Original Signal with Sampled Data by Spectroscopy
SONG Yi-zhong,DONG Xiang-jun,ZHAO Zhi-min.Tracking the Process Reconstructing Original Signal with Sampled Data by Spectroscopy[J].Spectroscopy and Spectral Analysis,2008,28(7):1492-1495.
Authors:SONG Yi-zhong  DONG Xiang-jun  ZHAO Zhi-min
Institution:School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. yizhongsong@126.com
Abstract:With spectroscopy, the principle and process of sampling and reconstructing a continuous-time signal are discussed. A symmetrical frequency-finite spectrum function F (omega) is constructed with three modified rise-cosine pulses. Its corresponding time-domain signal f(t) is worked out theoretically. f(t) is sampled with a comb function deltaT (t). By modifying the value of T, Shannon sampling signal is obtained. With Fast Fourier Transform (FFT), the frequency spectrum F(d) (omega) of the sampling signal is figured out. The calculated F(d) (omega) is compared with the constructed F(omega). The processes to reconstruct f(t) with the sampling signal and its digital frequency spectrum F(d) (omega) are discussed. As the result, there is little difference between the calculated F(d) (omega) and the constructed F (omega). The original signal can accurately be reconstructed with the sampling data in time domain, so can with the frequency spectrum F(d) (omega) by FFT. As soon as signal storage is concerned, we can store the sampling data or its digital frequency spectrum.
Keywords:Fast fourier transform  Sampling theorem  Reconstruction  Frequency domain  Digital signal processing
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