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| Discussion about the Existence Condition of Signal Fourier Transform |
| Wang Dao-xian Duan Xiao-hui Yang Guang-lin |
| School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China |
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Abstract For any given signal, determining the existence of its Fourier transform has remained an unsolved problem. This raises many concerns in the teaching of signal analysis courses, and also in many engineering applications. This paper presents an analysis of the problem. By comparing the characteristics of the ramp signal,s Fourier transform with that of the Fourier transforms of common energy signals and power signals, the author points out some problems regarding the Fourier transform of the ramp signal. This analysis shows that ramp signal does not satisfy the Fourier integral theorem, thus invalidating the Fourier transformation of ramp signal. Finally, the author further proves this assertion through simulation analysis, and summarizes the general rules of some common signal,s Fourier transform.
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Received: 27 February 2013
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Corresponding Authors:
Wang Dao-xian
E-mail: wdx@pku.edu.cn
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2013, Vol. 35 
