Generalized entropic uncertainty principle on fractional Fourier transform

The entropic uncertainty principle is an element in information theory and plays an important role in signal processing. Based on the relations between the original function and the definition of the fractional Fourier transform (FRFT), two novel entropic uncertainty principles in FRFT domains, in which one is Shannon entropy uncertainty principle and the other is Rényi entropy uncertainty principle, are derived, which are associated with the FRFT parameters. In addition, the extended Rényi entropy uncertainty principle for multiple functions and discrete entropy uncertainty principle are explored as well. These inequalities disclose the relations between the bounds and the transform parameters and sampling periods.