Fractional bispectrum transform: definition and properties

Abstract

A signal with discrete frequency components has a zero bispectrum if no addition or subtraction of any of the frequencies equals one of the frequency components. The authors introduce the fractional bispectrum (FBS) transform in which for signals with zero bispectrum the FBS could be non-zero. It is shown that FBS has the same property as the bispectrum for signals with a Gaussian probability density function (PDF). The FBS of a zero mean signal with a Gaussian PDF is zero. Therefore, it can be used to significantly reduce the Gaussian noise.

Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

“…found in the definition of fractional bi-spectrum [29], which is parameterized by a constant k ∈  þ to introduced a scaled version of the conventional WD. Later Dar and Bhat [30] introduced the scaled version of Ambiguity function and Wigner distribution in the linear canonical transform domain.…”