Quadratic-phase scaled Wigner distribution: convolution and correlation

In this paper, we propose the novel integral transform coined as quadratic-phase scaled Wigner distribution (QSWD) by extending associated with Fourier (QWD) to one inspired definition of fractional bispectrum. A natural magnification effect characterized extra degrees freedom (QPFT) and a factor k on frequency axis enables QSWD have flexibility be used in cross-term reduction. By using machinery operator theory, first establish general properties proposed transform, including conjugate symmetry, non-linearity, shifting, scaling marginal. Then, study main inverse, Moyal’s, convolution correlation. Finally, applications newly defined for detection single-component bi-component linear frequency-modulated (LFM) signal are also performed show advantage theory.