Based on the definition and properties
of discrete fractional Fourier transform (DFRFT), we introduced the discrete
Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation
were explored. Also, the condition of equality via Lagrange optimization was
developed, as shows that if the two conjugate variables have constant
amplitudes that are the inverse of the square root of numbers of non-zero
elements, then the uncertainty relations reach their lowest bounds. In
addition, the resolution analysis via the uncertainty is discussed as well.