Novel uncertainty relations associated with fractional Fourier transform

In this paper the relations between two spreads, betweentwo group delays, and between one spread and one group delay infractional Fourier transform (FRFT) domains, are presented and threetheorems on the uncertainty principle in FRFT domains are alsodeveloped. Theorem 1 gives the bounds of two spreads in two FRFTdomains. Theorem 2 shows the uncertainty relation between two groupdelays in two FRFT domains. Theorem 3 presents the crosseduncertainty relation between one group delay and one spread in twoFRFT domains. The novelty of their results lies in connecting theproducts of different physical measures and giving their physicalinterpretations. The existing uncertainty principle in the FRFT domainis only a special case of theorem 1, and the conventionaluncertainty principle in time-frequency domains is a special case oftheir results. Therefore, three theorems develop the relations oftwo spreads in time-frequency domains into the relations between twospreads, between two group delays, and between one spread and onegroup delay in FRFT domains.