Short-time quadratic-phase Fourier transform

The quadratic-phase Fourier transform (QPFT) is a recent addition to the class of integral transforms which embodies several signal processing tools ranging from the classical Fourier to the much contemporary special affine Fourier transforms. However, the QPFT is inadequate for localizing the quadratic-phase spectrum of non-transient signals, as such, it is imperative to introduce a unique localized transform coined as the short-time quadratic-phase Fourier transform, which can effectively localize the quadratic-phase spectrum of such signals. The preliminary analysis encompasses the study of fundamental properties of the proposed short-time quadratic-phase Fourier transform in quadratic-phase Fourier domain including the Parseval's theorem, inversion formula and complete characterization of the range. Subsequently, we formulate several classes of uncertainty inequalities such as the Heisenberg-type, Nazarov-type, Leib-type and the logarithmic uncertainty inequalities.

Automated summary

The short-time quadratic-phase Fourier transform is introduced to effectively localize the quadratic-phase spectrum of non-transient signals. The preliminary analysis in the quadratic-phase Fourier domain studies the fundamental properties of this transform and formulates various uncertainty inequalities.