Shift-invariance of short-time Fourier transform in fractional Fourier domains |
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Authors: | Lutfiye Durak |
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Institution: | Department of Electronics and Communications Engineering, Yildiz Technical University, Besiktas, Istanbul 34349, Turkey |
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Abstract: | Fractional Fourier domains form a continuum of domains making arbitrary angles with the time or frequency domains on the time-frequency plane. Signal representations in these domains are related to the fractional Fourier transform (FrFT). In this paper, a new proof on the shift-invariance of linear time-frequency distributions on fractional Fourier domains is given. We show that short-time Fourier transform (STFT) is the unique linear distribution satisfying magnitude-wise shift-invariance in the fractional Fourier domains. The magnitude-wise shift-invariance property in arbitrary fractional Fourier domains distinguishes STFT among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution as shown by numerical examples. |
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Keywords: | Fractional Fourier domains Fractional Fourier transform Linear time-frequency representations Short-time Fourier transform Generalized shift-invariance property |
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