Simplified computation of useful functions in linear canonical transform

Mawardi Bahri

doi:10.62918/hjma.v3i2.40

Authors

Mawardi Bahri Universitas Hasanuddin

DOI:

https://doi.org/10.62918/hjma.v3i2.40

Keywords:

linear canonical transform, Gaussian function, Fourier transform

Abstract

The linear canonical transform is an extension of the usual Fourier transform because the Fourier transform is a special form of the linear canonical transform. It also is a valuable tool in signal analysis. Many essential properties of the Fourier transform can be transferred in the linear canonical Fourier domain with some changes. In this research paper, we first introduce the interesting connection between the linear canonical transform and Fourier transform. It is shown that the relation can be developed to efficiently evaluate Gaussian function in the linear canonical transform domain. Some examples of the Gaussian function in the linear canonical domain are also presented to illustrate the result.

References

M. Bahri, R. Ashino, An Inequality for Linear Canonical Transform, In: S. L. Peng, M. Favorskaya, H. C. Chao (Eds.), Sensor Networks and Signal Processing, Smart Innovation, Systems and Technologies, vol 176. Springer, Singapore, 2021.

D. Bing, T. Ran, W. Yue, Convolution theorems for the linear canonical transform and their application, Sci. China Inf. Sci. 49(5) (2006) 592--603.

P. Dang, G. T. Deng, T. Qian, A tighter uncertainty principle for linear canonical transform in terms of phase derivative, IEEE Trans. Signal Process. 61(21) (2013) 5153--5164.

L. Debnath, F. A. Shah, Wavelet transforms and their applications, Springer Nature, Switzerland, 2020.

Q. Feng, B. Z. Li, Convolution and correlation theorems for the two-dimensional linear canonical transform and its applications, IET Sig. Process. 10(2) (2016) 125--132.

N. Goel, K. Singh, R. Saxena, Multiplicative filtering in the linear canonical transform domain, IET Sig. Process.10(2)} (2016) 173--181.

Y. Guo, B. Z. Li, Blind image watermarking method based on linear canonical transform and QR decomposition, IET Sig. Process. 10(10) (2016) 773--786.

J. J. Healy, P. O'Grady, J. T. Sheridan, Simulating paraxial optical systems using the linear canonical transform: properties, issues and applications, Proc. SPIE 7072, Optics and Photonics for Information Processing II, 70720E, 2008.

Z. J. Huang, S. Cheng, L. H. Gong, N. R. Zhou, Nonlinear optical multi-image encryption scheme with two-dimensional linear canonical transform, Opt. Lasers Engg. 124 (2020) 105821.

D. Wei, Filter bank reconstruction of band-limited signals from multichannel samples associated with the LCT, IET Sig. Process 11(3) (2016) 320--331.

D. Wei, H. Hu, Sparse discrete linear canonical transform and its application, Signal Process. 183 (2021) 108046.

D. Wei, H. M. Hu, Sparse discrete linear canonical transform and its applications, Signal Process. 183 (2021) 108046.

D. Wei, Q. Ran, Y. Li, A convolution and convolution theorem for the linear canonical transform and its application, Circuits Syst. Sig. Process. 31(1) (2012) 301--312.

D. Wei, Q. Ran, Y. Li, New convolution theorem for the linear canonical transform and its translation invariance property, Optik-Int. J. Light Electron. Opt. 123(16) (2012) 1478--1481.