Sensing and Imaging

, 20:8 | Cite as

A Mathematical Analysis Method of the Relationship Between DFT Magnitude and Periodic Feature of a Signal

  • Ronggang Huang
  • Yiguang LiuEmail author
  • Xuelei Shi
  • Yunan Zheng
  • Ying Wang
  • Bei Zhai
Original Paper
Part of the following topical collections:
  1. Recent Developments in Sensing and Imaging


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.


DFT magnitude index Fold number Periodic feature Unit of image frequency 



The authors would like to thank Lee et al. [8] for the rotation symmetry test images. This work is supported by NSFC under Grants 61860206007 and 61571313, by National Key Research and Development Program under Grant 2016YFB0801101, by Sichuan Province under Grant 18GJHZ0138, by Sichuan University and Lu-Zhou city under 2016CDLZ-G02-SCU.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Computer ScienceSichuan UniversityChengduChina
  2. 2.The Third People’s Hospital of Chengdu CityChengduChina

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