Research Article

Coupled Fractional Ambiguity Function

Volume: 4 Number: 1 June 30, 2026
Istanbul Journal of Mathematics Cover
Istanbul Journal of Mathematics
PDF Download

Coupled Fractional Ambiguity Function

Abstract

The ambiguity function is a vital analytical instrument for characterizing radar waveform attributes, such as time-delay and Doppler resolutions. This paper introduces the coupled fractional ambiguity function (CFrAF), a novel generalization that extends the utility of the classical ambiguity function. We present a theoretical framework for the CFrAF, deriving its fundamental properties such as time-frequency shifts, Moyal’s identity, and the inversion formula. As a consequence of Moyal’s identity, we also establish the maximum and volume properties of the proposed function.

Keywords

References

  1. Almeida, L. B., 1994, The fractional Fourier transform and time-frequency representations, IEEE Trans. Signal Process. 42, 3084–3091. google scholar
  2. Gao W.B., Li B.Z., 2021, Convolution theorem involving 𝑛-dimensional windowed fractional Fourier transform, Sci China Inf Sci. 64, 169302. google scholar
  3. Kamalakkannan, R., Roopkumar, R., 2020, Multidimensional fractional Fourier transform and generalized fractional convolution, Integral Transforms Spec. Funct. 31, 152–165. google scholar
  4. Kamalakkannan, R., Roopkumar, R., Zayed, A., 2021, Short time coupled fractional Fourier transform and the uncertainty principle, Fract. Calc. Appl. Anal. 24, 667–688. google scholar
  5. Kamalakkannan, R., Roopkumar, R., Zayed, A., 2022, On the extension of the coupled fractional Fourier transform and its properties, Integral Transforms Spec. Funct. 33, 65-80. google scholar
  6. Kaur, N.; Gupta, B.; Verma, A.K., 2023, Multidimensional fractional wavelet transforms and uncertainty principles, J. Comput. Appl. Math. 430, 115250. google scholar
  7. Kerr, F.H., 1988, Namias’ fractional Fourier transforms on 𝐿2 and applications to differential equations, J. Math. Anal. Appl. 136, 404–418. google scholar
  8. McBride, A. C., Kerr, F. H., 1987, On Namias’s fractional Fourier transforms, IMA J. Appl. Math. 39, 159–175. google scholar

Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Publication Date

June 30, 2026

Submission Date

October 20, 2025

Acceptance Date

March 30, 2026

Published in Issue

Year 2026 Volume: 4 Number: 1

DOI

https://doi.org/10.26650/ijmath.2026.00031

IZ

https://izlik.org/JA27NM53KY

Cite

RIS / Bibtex
APA
Sandıkçı, A. (2026). Coupled Fractional Ambiguity Function. Istanbul Journal of Mathematics, 4(1), 1-7. https://doi.org/10.26650/ijmath.2026.00031
AMA
1.Sandıkçı A. Coupled Fractional Ambiguity Function. Istanbul Journal of Mathematics. 2026;4(1):1-7. doi:10.26650/ijmath.2026.00031
Chicago
Sandıkçı, Ayşe. 2026. “Coupled Fractional Ambiguity Function”. Istanbul Journal of Mathematics 4 (1): 1-7. https://doi.org/10.26650/ijmath.2026.00031.
EndNote
Sandıkçı A (June 1, 2026) Coupled Fractional Ambiguity Function. Istanbul Journal of Mathematics 4 1 1–7.
IEEE
[1]A. Sandıkçı, “Coupled Fractional Ambiguity Function”, Istanbul Journal of Mathematics, vol. 4, no. 1, pp. 1–7, June 2026, doi: 10.26650/ijmath.2026.00031.
ISNAD
Sandıkçı, Ayşe. “Coupled Fractional Ambiguity Function”. Istanbul Journal of Mathematics 4/1 (June 1, 2026): 1-7. https://doi.org/10.26650/ijmath.2026.00031.
JAMA
1.Sandıkçı A. Coupled Fractional Ambiguity Function. Istanbul Journal of Mathematics. 2026;4:1–7.
MLA
Sandıkçı, Ayşe. “Coupled Fractional Ambiguity Function”. Istanbul Journal of Mathematics, vol. 4, no. 1, June 2026, pp. 1-7, doi:10.26650/ijmath.2026.00031.
Vancouver
1.Ayşe Sandıkçı. Coupled Fractional Ambiguity Function. Istanbul Journal of Mathematics. 2026 Jun. 1;4(1):1-7. doi:10.26650/ijmath.2026.00031