光谱学与光谱分析 |
|
|
|
|
|
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.
|
Received: 2007-05-10
Accepted: 2007-08-20
|
|
Corresponding Authors:
SONG Yi-zhong
E-mail: yizhongsong@126.com
|
|
[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.
|
[1] |
ZHANG Tian-yao1, 2, LI Bo-yang1, LI Xing-yue1, LI Ying1, WU Xian-hao1, ZHAO Xiao-yan1, ZHANG Zhao-hui1*. Refractive Index Measurement Using Continuous Wave Terahertz
Frequency-Domain Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(02): 495-502. |
[2] |
LIU Qiang1, LIU Shao-bo1, 2, LU Xue-song1, 2*, FAN Jun-jia1, 2, TIAN Hua1, 2, MA Xing-zhi1, 2, GUI Li-li1, 2. Research Progress in the Application of Raman Spectroscopy in Petroleum Geology[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2022, 42(09): 2679-2688. |
[3] |
WAN Liu-jie1, 2, ZHEN Chao3, QIU Zong-jia1, LI Kang1, MA Feng-xiang3, HAN Dong1, 2, ZHANG Guo-qiang1, 2*. Research of High Precision Photoacoustic Second Harmonic Detection Technology Based on FFT Filter[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2020, 40(10): 2996-3001. |
[4] |
SHANG Hou-fei1, DU Zhen-hui2, 3, GAO Nan1, 3*, LI Jin-yi4, XIAO Yan-jun1, MENG Zhao-zong1, ZHANG Zong-hua1. Parameter Analysis of Tunable Diode Laser Absorption Spectroscopy Based on Spectral Frequency Characteristics[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2019, 39(11): 3359-3364. |
[5] |
LI Jiang-tao1, HU Wen-yan1, ZHAO Long-lian1, 2*, LI Jun-hui1, 2. Study of the Accuracy of Apple Internal Lesion Detection Based on Frequency Domain Diffuse Optical Tomography[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2019, 39(09): 2836-2841. |
[6] |
CAO Can1, 2, ZHANG Zhao-hui1, 2*, ZHAO Xiao-yan1, 2, ZHANG Han2, 3, ZHANG Tian-yao1, 2, YU Yang1, 2. Review of Terahertz Time Domain and Frequency Domain Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2018, 38(09): 2688-2699. |
[7] |
SUN Gui-fen1, QIN Xian-lin1*, YIN Ling-yu1, LIU Shu-chao1, LI Zeng-yuan1, CHEN Xiao-zhong2, ZHONG Xiang-qing2. Changes Analysis of Post-Fire Vegetation Spectrum and Index Based on Time Series GF-1 WFV Images[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2018, 38(02): 511-517. |
[8] |
HU Wen-yan1,3, WANG Yu-heng1,3, ZHANG Xiao-shuan2, LI Jun-hui1,3, WANG Zhong-yi1,3, ZHAO Long-lian1,3*. Determination and 3D Reconstruction of Optical Parameters of Biological Tissue Based on Frequency-Domain Near-Infrared Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2017, 37(05): 1374-1379. |
[9] |
HU Wen-yan1,3, LIU Hui1,3, WANG Yu-heng1,3, LI Jun-hui1,3, ZHANG Xiao-shuan2, WANG Zhong-yi1,3, ZHAO Long-lian1,3*. Study for the Photon Propagation Properties in Biological Tissue Based on Frequency-Domain Near-Infrared Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2017, 37(04): 1074-1080. |
[10] |
PENG Yu1, MI Kai1, QIN Ya1, QING Feng-ting1, LIU Wei-chen1, XUE Da-yuan1, LIU Xue-hua2* . Spectral Reflectance Characteristics of Dominant Plant Species at Different Eco-Restoring Stages in the Semi-Arid Grassland[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2014, 34(11): 3090-3094. |
[11] |
LI Zhi2, WANG Sheng-hao1,2*, ZHAO Yong1, WANG Xiang-feng3, LI Yao-zheng4 . Model Research of Electric Coal Calorific Value Based on Near Infrared Frequency Domain Self-Adaption Analysis Method[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2014, 34(10): 2792-2798. |
[12] |
ZHANG Min-juan3, WANG Zhao-ba1, 2, WANG Zhi-bin3, LI Xiao3, LI Shi-wei3, LI Jin-hua3 . The Technology of Fast Spectral Reconstruction in the Longer Optical Path Difference PEM-FTS [J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2014, 34(07): 2010-2014. |
[13] |
YANG Xue1,3,4, LI Xue-you2,3*, LI Jia-guo1*, MA Jun4, ZHANG Li2, YANG Jan1, DU Quan-ye2. Research on Fast Fourier Transforms Algorithm of Huge Remote Sensing Image Technology with GPU and Partitioning Technolog[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2014, 34(02): 498-504. |
[14] |
LI Gang, ZHOU Mei, WANG Hui-quan, XIONG Chan, LIN Ling* . Contrastive Study on Dynamic Spectrum Extraction Method[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2012, 32(05): 1324-1328. |
[15] |
Lü Jin-guang1,2, LIANG Jing-qiu1*, LIANG Zhong-zhu1, FU Jian-guo1,2. Study on Uniformity of Optical Field in Static Fourier Transform Spectrometer[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2012, 32(01): 259-263. |
|
|
|
|