Shift-invariance of short-time Fourier transform in fractional Fourier domains

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.