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

Navdeep Goel; Kulbir Singh

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 3, page 685-695
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Navdeep Goel, and Kulbir Singh. "A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics." International Journal of Applied Mathematics and Computer Science 23.3 (2013): 685-695. <http://eudml.org/doc/262405>.

@article{NavdeepGoel2013,
abstract = {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.},
author = {Navdeep Goel, Kulbir Singh},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {linear canonical transform; convolution and product theorem; quantum mechanical representation},
language = {eng},
number = {3},
pages = {685-695},
title = {A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics},
url = {http://eudml.org/doc/262405},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Navdeep Goel
AU - Kulbir Singh
TI - A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 3
SP - 685
EP - 695
AB - 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.
LA - eng
KW - linear canonical transform; convolution and product theorem; quantum mechanical representation
UR - http://eudml.org/doc/262405
ER -

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