A New Class of Linear Canonical Wavelet Transform

[1] Debnath, L., Bhatta, D., Integral transforms and their applications, Boca Raton: CRC press, 2014.

[2] Almeida, L.B., The fractional Fourier transform and time-frequency representations, IEEE Transactions on Signal Processing, 42(11), 1994, 3084-3091.

[3] Wei, C., Zunwei, F., Loukas, G., Yue, W., Fractional Fourier transforms on Lp and applications, Applied and Computational Harmonic Analysis, 55, 2021, 71-96.

[4] Zayed, A.I., Fractional Fourier transform of generalized functions, Integral Transforms and Special Functions, 7, 1998, 299-312.

[5] Moshinsky, M., Quesne, C., Linear canonical transformations and their unitary representations, Journal of Mathematical Physics, 12(8), 1971, 1772-1780.

[6] Sharma, K.K., Joshi, S.D., Signal separation using linear canonical and fractional Fourier transforms, Optics Communications, 265, 2006, 454-460.

[7] Wei, D., Li, Y., Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain, IET Signal Processing, 8(6), 2014, 647-657.

[8] Barshan, B., Kutay, M.A., Ozaktas, H.M., Optimal filtering with linear canonical transformations, Optics Communications, 135, 1997, 32-36.

[9] Gao, W.B., Li, B.Z., The octonion linear canonical transform: Definition and properties, Signal Processing, 188, 2021, 108233.

[10] Healy, J.J., Kutay, M.A., Ozaktas, H.M., Sheridan, J.T., Linear canonical transforms: Theory and applications, New York: Springer, 2015.

[11] Debnath, L., Shah, F.A., Wavelet transforms and their applications, Springer, 2002.

[12] Dai, H., Zheng, Z., Wang, W., A new fractional wavelet transform, Communications in Nonlinear Science and Numerical Simulation, 44, 2017, 19-36.

[13] Kou, K.I., Xu, R.H., Windowed linear canonical transform and its applications, Signal Processing, 92, 2012, 179-188.

[14] Srivastava, H.M., Shah, F.A., Garg, T.K., Lone, W.Z., Qadri, H.L., Non-separable linear canonical wavelet transform, Symmetry, 13, 2021, 2182.

[15] Wei, D., Li, Y.M., Generalized wavelet transform based on the convolution operator in the linear canonical transform domain, Optik, 125, 2014, 4491-4496.

[16] Guo, Y., Li, B.Z., The linear canonical wavelet transform on some function spaces, International Journal of Wavelets, Multiresolution and Information Processing, 16, 2018, 1850010.

[17] Shi, J., Zhang, N.T., Liu, X.P., A novel fractional wavelet transform and its applications, Science China Information Sciences, 55, 2012, 1270-1279.

[18] Prasad, A., Manna, S., Mahato, A., Singh, V.K., The generalized continuous wavelet transform associated with the fractional Fourier transform, Journal of Computational and Applied Mathematics, 259, 2014, 660-671.

[19] Folland, G.B., Sitaram, A., The uncertainty principle: a mathematical survey, Journal of Fourier Analysis and Applications, 3, 1997, 207-238.

[20] Shapiro, H.S., Uncertainty principles for bases in L^2 (R), in: Proceedings of the Conference on Harmonic Analysis and Number Theory, CIRM, Marseille-Luminy, October 16-21, 2005.

[21] Jaming, P., Powell, A.M., Uncertainty principles for orthonormal sequences, Journal of Functional Analysis, 243, 2007, 611-630.

[22] Malinnikova, E., Orthonormal sequences in L^2 (R^d) and time frequency localization, Journal of Fourier Analysis and Applications, 16, 2010, 983-1006.

[23] Lamouchi, H., Omri, S., Time-frequency localization for the short time Fourier transform, Integral Transforms and Special Functions, 27, 2016, 43-54.

[24] Hamadi, N.B., Lamouchi, H., Shapiro’s uncertainty principle and localization operators associated to the continuous wavelet transform, Journal of Pseudo-Differential Operators and Applications, 8, 2017, 35-53.

[25] Hamadi, N.B., Omri, S., Uncertainty principles for the continuous wavelet transform in the Hankel setting, Applicable Analysis, 97, 2018, 513-527.

[26] Hamadi, N.B., Hafirassou, Z., Herch, H., Uncertainty principles for the Hankel-Stockwell transform, Journal of Pseudo-Differential Operators and Applications, 11, 2020, 543–564.

[27] Nefzi, B., Shapiro and local uncertainty principles for the multivariate continuous shearlet transform, Integral Transforms and Special Functions, 32, 2021, 154-173.

[28] Hleili, K., Windowed linear canonical transform and its applications to the time-frequency analysis, Journal of Pseudo-Differential Operators and Applications, 13, 2022, 1-26.

[29] Wilczok, E., New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform, Documenta Mathematica, 5, 2000, 201-226.

[30] Verma, A.K., Gupta, B., A note on continuous fractional wavelet transform in R^n, International Journal of Wavelets, Multiresolution and Information Processing, 20, 2021, 2150050.

[31] Bahri, M., Ashino, R., Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space, International Journal of Wavelets, Multiresolution and Information Processing, 15, 2017, 1750050.

[32] Shah, F.A., Tantary, A.Y., Non-isotropic angular Stockwell transform and the associated uncertainty principles, Applicable Analysis, 100, 2019, 1-25.

[33] Huo, H., Sun, W., Xiao, L., Uncertainty principles associated with the offset linear canonical transform, Mathematical Methods in the Applied Sciences, 42, 2019, 466-474.

[34] Deng, B., Tao, R., Wang, Y., Convolution theorems for the linear canonical transform and their applications, Science in China Series F: Information Sciences, 49, 2006, 592-603.

[35] Daubechies, I., Ten lectures on wavelets, Philadelphia: SIAM, 1992.

[36] Donoho, D.L., Stark, P.B., Uncertainty principles and signal recovery, SIAM Journal on Applied Mathematics, 49, 1989, 906-931.

[37] Gröchenig, K., Foundations of time-frequency analysis, Springer Science & Business Media, 2001.

[38] Kou, K.I., Xu, R.H., Zhang, Y.H., Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform, Mathematical Methods in the Applied Sciences, 35, 2012, 2122-2132.

[39] Saitoh, S., Theory of reproducing kernels and its applications, Harlow: Longman Scientific & Technical, 1988.