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In this paper the relations between two spreads, between
two group delays, and between one spread and one group delay in
fractional Fourier transform (FRFT) domains, are presented and three
theorems on the uncertainty principle in FRFT domains are also
developed. Theorem 1 gives the bounds of two spreads in two FRFT
domains. Theorem 2 shows the uncertainty relation between two group
delays in two FRFT domains. Theorem 3 presents the crossed
uncertainty relation between one group delay and one spread in two
FRFT domains. The novelty of their results lies in connecting the
products of different physical measures and giving their physical
interpretations. The existing uncertainty principle in the FRFT domain
is only a special case of theorem 1, and the conventional
uncertainty principle in time-frequency domains is a special case of
their results. Therefore, three theorems develop the relations of
two spreads in time-frequency domains into the relations between two
spreads, between two group delays, and between one spread and one
group delay in FRFT domains. 相似文献
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