The logarithmic, Heisenberg's and short-time uncertainty principles associated with fractional Fourier transform

Firstly, based on the relation between the original function and definition of the fractional Fourier transform (FRFT), one novel logarithmic uncertainty principle and one Heisenberg's uncertainty principle in the FRFT domains are derived, which are associated with the FRFT parameter. Secondly, the uncertainty principle for the short-time fractional Fourier transform (STFRFT) is obtained. The novel logarithmic, Heisenberg's and the short-time uncertainty principles connect their bounds with the FRFT parameter, which can help us understand the physical interpretations of the uncertainty principle in nature. This discloses that for these new transforms involving the FRFT parameter the uncertainty principles continue to hold.