A closed-form discrete fractional gabor expansion

Key Findings & Data:This constant-bandwidth analysis generates a rectangular time-frequency lattice which might lead to poor time-frequency localization for many signals.

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Conclusion & Impact:Completeness and biorthogonality conditions of the new expansion are given.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

We present a discrete fractional Gabor expansion based on the closed form discrete fractional Fourier transform. The traditional Gabor expansion represents a signal as a linear combination of time and frequency shifted basis functions. This constant-bandwidth analysis generates a rectangular time-frequency lattice which might lead to poor time-frequency localization for many signals. Proposed expansion uses a set of basis functions related to the fractional Fourier basis and generate a parallelogram-shaped tiling. Completeness and biorthogonality conditions of the new expansion are given.

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Cite This Article

AKAN, A., ÖNEN, E. (2022). A closed-form discrete fractional gabor expansion. Istanbul University Journal of Electrical and Electronics Engineering, Cilt: 4 - Sayı: 1, 1105–1111. https://ajindex.com/articles/543863

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