Research on Three Convolutions Related Issues in Signal Processing

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 269)


Convolution computing is an important section in signal processing and it has many applications in the real life, such as medical signal analysis, image and video processing, linear system simulation, communication analysis, electronics, automation and so on. There are there types of convolution algorithms and they are linear convolution, periodic convolution and circular convolution, which are the key points and difficult points in signal processing, because these three concepts are abstract for students to understand and master. In this paper, we will explain the definition of these three convolutions; analyze the relationship between them, especially study deeply on the equalization conditions of these convolutions’ transformation.


Signal processing Linear convolution Periodic convolution Circular convolution 



This work is supported by a grant from the Fundamental Research Funds for the Central Universities (No. 1112KYQN40, No. 1112KYZY49, No. 0910KYZY55) and Cultural heritage protection science and technology project of Cultural relics bureau (No.20110135). Our gratitude is extended to the anonymous reviewers for their valuable comments and professional contributions to the improvement of this paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Information Engineering in Minzu University of ChinaBeijingChina
  2. 2.Research Institute of Information Technology in Tsinghua UniversityBeijingChina

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