Quadratic phase S-Transform: Properties and uncertainty principles

Abstract

In this paper, a novel quadratic phase S-transform (QPST) is proposed, by generalizing the S-transform (ST) with five parameters a, b, c,d and e. QPST displays the time and quadratic phase domain-frequency information jointly in the time-frequency plane. Firstly, we define the novel QPST and give its relation with quadratic phase Fourier transform (QPFT). Secondly, several important properties of newly defined QPST, such as conjugation, translation, modulation, orthogonality relation and reconstruction formula are derived. Finally, we formulate several classes of uncertainty inequalities, such as the Heisenberg uncertainty inequality and logarithmic uncertainty inequality.

Keywords

• 42C40
• 81S30
• 11R52
• 44A35