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http://dx.doi.org/10.3807/KJOP.2013.24.5.245

A simple Demonstration of the Wiener-Khinchin Theorem using a Digital Oscilloscope and Personal Computer  

Jung, Se-Min (Department of New Material Physics, College of Natural Science, Dong-A University)
Publication Information
Korean Journal of Optics and Photonics / v.24, no.5, 2013 , pp. 245-250 More about this Journal
Abstract
The Wiener-Khinchin theorem, which means that the autocorrelation function of a signal corresponds to the power spectrum of the signal, is very important in signal processing, spectroscopy and telecommunications engineering. However, because of needs for some relatively expensive equipments such as a correlator and the signal processing system, its demonstration in most undergraduate class is not easy so far. Recently, digital oscilloscopes whose functions can be replaced foresaid equipments are marketed with development of digital engineering. In this paper, a simple demonstration of the theorem is given by a digital storage oscilloscope and a personal computer with its theoretical background. The reason that deals again with this theorem which has been introduced in 1930 is that it has been not well informed yet to us and theoretical background of the demonstration is directly introduced from its driving process. Through deriving process of the theorem, some extended physical meanings of the impedance, power, power factor, Wiener spectrum, linear system response and, furthermore, basic idea of the Planck's quantization in the black body theory reveal themselves naturally. Hence it can be referred to lectures in general physics, modern physics, spectroscopy and material characterization experiment.
Keywords
Wiener-Khinchin theorem; Digital oscilloscope; Demonstration; Wiener spectrum;
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  • Reference
1 A. Papoulis, The Fourier Integral and its Applications (McGraw- Hill, NY, USA, 1962), Chapter 1, p. 27.
2 R. A.Gabel and R. A. Roberts, Signals and Linear Systems (John Wiley & Sons, Inc., NY, USA, 1973), Chapter 5, pp. 233-257.
3 L. Levi, Applied Optics (John-Wiley & Sons, Inc., NY, USA, 1968), vol. 1, Chapter 3, pp. 138-140.
4 http://en.wikipedia.org/wiki/Wiener-Khinchin_theorem.
5 http://gmrt.ncra.tifri.res.in/gmrt_hpage/Users/doc/WEBLF/L FRA/node7.html.
6 Agilent, HP54622A User Manual, (Agilent Technology, C.S., 2000), Chapter 5.
7 A. Papoulis, The Fourier Integral and its Applications (McGraw- Hill, NY, USA, 1962), Chapter 5, p. 86.