Abstract
In this study, we developed a logical and complete mathematical analysis of the relationship between the discrete Fourier transform (DFT) magnitude and periodic feature of a signal. The physical meaning of the DFT magnitude index corresponds to the periodic signal feature; further analysis makes clear the relationship among DFT magnitude, magnitude index, and number of samples. The proposed analysis method also elucidates the relationship between alternating current magnitude index and frequency, by the way, the unit of image frequency will be given. The proposed analysis method is suitable for the machine vision and image processing in general.
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