Shakhmurov, Veli B.; Zayed, Ahmed I. Fractional Wigner distribution and ambiguity functions. (English) Zbl 1096.94011 Fract. Calc. Appl. Anal. 6, No. 4, 473-490 (2003). 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. Cited in 2 Documents 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 Keywords:fractional Wigner distribution; fractional ambiguity function; fractional modulation and time-frequency shifts; fractional Fourier transform PDFBibTeX XMLCite \textit{V. B. Shakhmurov} and \textit{A. I. Zayed}, Fract. Calc. Appl. Anal. 6, No. 4, 473--490 (2003; Zbl 1096.94011)