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Paper details
Number 3 - September 2013
Volume 23 - 2013
A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics
Navdeep Goel, Kulbir Singh
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.
Keywords
linear canonical transform, convolution and product theorem, quantum mechanical representation