TY - JOUR
T1 - Fractional Zak transform
T2 - Theory and applications
AU - Huang, Gaowa
AU - Zhang, Feng
AU - Giurcăneanu, Ciprian Doru
N1 - Publisher Copyright:
© 2025 Elsevier B.V.
PY - 2026/2
Y1 - 2026/2
N2 - The Zak transform (ZT) emerges as a powerful tool for time–frequency analysis. However, the ZT is inherently limited in its ability to capture local time–frequency features of non-stationary or time-varying signals, due to its nature as a global spectral analysis tool. In this article, we present a comprehensive exploration of the properties, discretization and potential applications of the fractional ZT (FRZT). We begin by elucidating the mathematical foundation of the FRZT, highlighting its ability to capture the time–frequency characteristics of signals with enhanced flexibility. Furthermore, we explore the features of the FRZT, including its basic properties, convolution theorem, and the Weyl–Heisenberg frames associated with FRZT. Additionally, for practical applications where the signals are discrete, we develop two discretization algorithms for the FRZT. Finally, the experiments with simulated chirp signals and potential applications demonstrate the utility of the FRZT in various signal processing tasks through theoretical exposition and practical examples.
AB - The Zak transform (ZT) emerges as a powerful tool for time–frequency analysis. However, the ZT is inherently limited in its ability to capture local time–frequency features of non-stationary or time-varying signals, due to its nature as a global spectral analysis tool. In this article, we present a comprehensive exploration of the properties, discretization and potential applications of the fractional ZT (FRZT). We begin by elucidating the mathematical foundation of the FRZT, highlighting its ability to capture the time–frequency characteristics of signals with enhanced flexibility. Furthermore, we explore the features of the FRZT, including its basic properties, convolution theorem, and the Weyl–Heisenberg frames associated with FRZT. Additionally, for practical applications where the signals are discrete, we develop two discretization algorithms for the FRZT. Finally, the experiments with simulated chirp signals and potential applications demonstrate the utility of the FRZT in various signal processing tasks through theoretical exposition and practical examples.
KW - Fractional Fourier transform
KW - Time–frequency analysis
KW - Zak transform
UR - https://www.scopus.com/pages/publications/105018579539
U2 - 10.1016/j.sigpro.2025.110329
DO - 10.1016/j.sigpro.2025.110329
M3 - Article
AN - SCOPUS:105018579539
SN - 0165-1684
VL - 239
JO - Signal Processing
JF - Signal Processing
M1 - 110329
ER -