Three inequalities for quadratic-phase Fourier transform

Mawardi Bahri

doi:10.62918/hjma.v2i1.18

Authors

Mawardi Bahri Universitas Hasanuddin

DOI:

https://doi.org/10.62918/hjma.v2i1.18

Keywords:

One-dimensional Fourier transform, Parseval formula, One-dimensional quadratic-phase Fourier transform

Abstract

In this work, we introduce the one-dimensional quadratic-phase Fourier transform. The relation between one-dimensional quadratic-phase Fourier transform and one-dimensional Fourier transform is discussed in detail. We finally propose several versions of the inequalites related to one-dimensional quadratic-phase Fourier transform.

References

L. B. Almeida, The fractional Fourier transform and time-frequency representations, IEEE Transactions on Signal Processing, vol. 42 (1994), no. 11, 3084-3091.

M. Bahri, S. A. A. Karim, Fractional Fourier transform: main properties and inequalities. Mathematics, 11 (5) (2023), 1234.

M. Bahri, S. A. A. Karim, Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform, Mathematics, 11(5) (2023), 1235.

R. Bracewell, The Fourier Transform and its Applications, McGraw Hill, Boston, MA, 2000.

Bultheel, A. Martínez, H. A. Shattered, Survey of the Fractional Fourier Transform, Report TW337, Department of Computer Science, Katholieke Universiteit Leuven: Leuven, Belgium, 2002.

L. P. Castro, M. R. Haque, M. M. Murshed, S. Saitoh, N. M. Tuan, Quadratic Fourier transform, Ann. Funct. Anal., 5 (2014), 10-23.

L. P. Castro, L. T. Minh, N. M. Tuan, New convolution for quadratic-phase Fourier integral operators and their application, Mediterr. J. Math., 15 (2018), 13.

X. Guanlei, W. Xiaotong, X. Xiaogang, The logarithmic, Heisenberg's and short-time uncertainty principles associated with fractional Fourier transform. Signal Processing, 89 (2009), 339-343.

S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA, 2001.

J. Shi, X. Liu, N. Zhang, On uncertainty principle for signal concentrations with fractional Fourier transform, Signal Processing, 92 (2012), 2830–2836.

S. Shinde, V. M. Gadre, An uncertainty principle for real signals in the fractional Fourier transform domain, IEEE Trans. Signal Processing, 49 (2001), 2545-2548.