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Fractional Wigner distribution and ambiguity functions. (English) Zbl 1096.94011

Summary: The Wigner distribution function is a time-frequency representation of a signal. In this work we introduce a class of fractional (weighted) Wigner distributions (FWD) using the kernel of the fractional Fourier transform (FFT) as a modulation factor. The fractional modulation depends on an angular parameter \(\alpha\) and can be interpreted as a rotation by an angle \(\alpha\) in the time-frequency plane. We also introduce a fractional ambiguity function and fractional time-frequency shifts. In addition, an uncertainty principle for the fractional Fourier transform is also derived. These results improve and generalize some of the previous time-frequency distributions derived in the literature.

MSC:

94A14 Modulation and demodulation in information and communication theory
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A30 Multiple integral transforms
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