Plenary Lecture
Prof. Ayse Sandikci
Ondokuz Mayıs Üniversitesi, Turkey
Title: A Theoretical Framework on the Properties and Operator Characteristics of the Coupled Fractional -Wigner Transform
Abstract: This study introduces the Coupled Fractional -Wigner Transform as a generalized mathematical
framework aimed at examining the energy distribution of signals through both parametric and
angular perspectives. By integrating the time-domain flexibility of the -parameter with the
angular rotation capabilities of fractional domains within a coupled kernel structure, the
proposed operator establishes a comprehensive analytical foundation for characterizing non-
stationary signals. Within the scope of this research, the analytical underpinnings of this novel
transform are rigorously constructed, and its mathematical consistency is substantiated through
extensive theoretical proofs. In this context, the shift properties in the time and frequency
domains are first addressed, deriving the complex projections of signal modulations and
translations under the coupled fractional kernel. The validity of Moyal’s identity, which
characterizes energy conservation and inner-product space relationships, is proven for this new
transform, theoretically verifying how the operator distributes signal energy across fractional
planes. Furthermore, by analyzing the invertibility conditions of the defined transform, an
inversion formula is presented in mathematical integrity, ensuring the precise reconstruction of
the signal from the fractional parameters and coefficients back to the time domain. All these
theoretical findings demonstrate that the coupled fractional Wigner transform is not merely a
conceptual extension but a robust analytical tool offering high degrees of freedom for the
analysis of complex waveforms.
Bio: Ayse Sandikci received her M.Sc. (2004) and Ph.D. (2007) from the Ondokuz Mayis
University, Turkey. She is an Associate Professor at the Ondokuz Mayis University, Turkey,
since 2017. Her research interest is Functional Analysis. In particular, her interests are
Harmonic analysis, time-frequency analysis, Gabor analysis, fractional Fourier transform. She
is author of several publications on international journals. She is the co-author of the book in
Turkish 'Advanced Calculus' . She has been a speaker at 45 conferences. She is active in joint
research projects. She is a reviewer for some international journals.