Tracking the Process Reconstructing Original Signal with Sampled Data by Spectroscopy
SONG Yi-zhong1,2,DONG Xiang-jun3,ZHAO Zhi-min1
1. School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2. Department of Physics, Dezhou University, Dezhou 253000, China 3. School of Information Science and Technology, Shandong Institute of Light Industry, Ji’nan 250353, China
Abstract：With spectroscopy, the principle and process of sampling and reconstructing a continuous-time signal are discussed. A symmetrical frequency-finite spectrum function F(ω) 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 δT(t). By modifying the value of T, Shannon sampling signal is obtained. With Fast Fourier Transform(FFT), the frequency spectrum Fd(ω) of the sampling signal is figured out. The calculated Fd(ω) is compared with the constructed F(ω). The processes to reconstruct f(t) with the sampling signal and its digital frequency spectrum Fd(ω) are discussed. As the result, there is little difference between the calculated Fd(ω) and the constructed F(ω). The original signal can accurately be reconstructed with the sampling data in time domain, so can with the frequency spectrum Fd(ω) by FFT. As soon as signal storage is concerned, we can store the sampling data or its digital frequency spectrum.
Key words：Fast fourier transform;Sampling theorem;Reconstruction;Frequency domain;Digital signal processing
宋一中1, 2,董祥军3,赵志敏1. 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(07): 1492-1495.
SONG Yi-zhong1,2,DONG Xiang-jun3,ZHAO Zhi-min1. Tracking the Process Reconstructing Original Signal with Sampled Data by Spectroscopy. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2008, 28(07): 1492-1495.
［1］ Alan V Oppenheim, Alan S Willsky, Hamid Nawab S. Signals and Systems(Second edition). Beijing：Publishing House of Electronics Industry, 2003. ［2］ Andrew S. Tanenbaum ed, XIONG Gui-xi. et al. Computer Network. Beijing：Tsinghua University Press, 1998. ［3］ SONG Yi-zhong, HU Guo-ying, HE An-zhi(宋一中, 胡国英, 贺安之). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2006, 26(12)：2364. ［4］ SONG Yi-zhong, SUN Tao, HU Guo-ying, et al(宋一中, 孙 涛, 胡国英, 等). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2006, 26(8)：1411. ［5］ SONG Yi-zhong, YANG Xiang-jun, LIU Xue-mei, et al(宋一中, 阳向军, 刘学梅, 等). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2006, 26(10)：1918. ［6］ Jerry A J. The Shannon Sampling Theorem—Its Various Extension and Applications：a Tutorial Review, Proc. IEEE, 1977，65：1565. ［7］ ZHENG Jun-li, YING Qi-hang, YANG Wei-li(郑君里, 应启珩, 杨为理). Signals and Systems(信号与系统). Beijing：Higher Education Press(北京：高等教育出版社), 2000. ［8］ CHENG Pei-qing(程佩青). Digital Signal Precessing Tutorial(数字信号处理教程). Beijing：Tsinghua University Press(北京：清华大学出版社), 2003.
