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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 23, Issue 3


A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

Navdeep Goel
  • Corresponding author
  • Electronics and Communication Engineering Section, Yadavindra College of Engineering Punjabi University Guru Kashi Campus, Talwandi Sabo-151302, Punjab, India
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Kulbir Singh
  • Department of Electronics and Communication Engineering Thapar University, Patiala-147001, Punjab, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-09-30 | DOI: https://doi.org/10.2478/amcs-2013-0051


The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution and product theorem in the LCT domain derived by a representation transformation in quantum mechanics, which seems a convenient and concise method. It is compared with the existing convolution theorem for the LCT and is found to be a better and befitting proposition. Further, an application of filtering is presented by using the derived results.

Keywords : linear canonical transform; convolution and product theorem; quantum mechanical representation

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About the article

Navdeep Goel

Navdeep Goel completed his B.E. in electronics and telecommunication engineering in 2002 at BNCOE, Pusad (Amravati University), Maharastra, India, his M.Tech. in electronics and communication engineering at Punjab Technical University, Jalandhar (Punjab), and is pursuing a Ph.D. at Thapar University, Patiala (Punjab). He has worked as a scientist/engineer (SC) in the Vikram Sarabhai Space Centre, Indian Space Research Organization (ISRO), Thiruvananthapuram. He has been teaching since 2004 and is presently working as an assistant professor (ECE) in the Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, Bathinda, Punjab.

Kulbir Singh

Kulbir Singh was born in Batala, Punjab, India. He completed his B.Tech. degree in 1997 at PTU, Jalandhar. He received his M.E. and Ph.D. degrees from Thapar University, Patiala, in 2000 and 2006, respectively. He is currently working as an associate professor in the Department of Electronics and Communication Engineering, Thapar University, Patiala. He has published more than 55 research papers in national and international journals/conference proceedings. He is a recipient of the Best Paper Award of the IETE Journal of Education for the year 2008. His research interests include signal processing, image processing, DSP processors based design and fractional transforms.

Published Online: 2013-09-30

Published in Print: 2013-09-01

Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 23, Issue 3, Pages 685–695, ISSN (Online) 2083-8492, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/amcs-2013-0051.

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