Higher-Order Derivative Sampling Associated with Fractional Fourier Transform

The uniform and recurrent nonuniform higher-order derivative sampling problems associated with the fractional Fourier transform are investigated in this paper. The reconstruction formulas of a bandlimited signal from the uniform and recurrent nonuniform derivative sampling points are obtained. It is shown that if a bandlimited function f(t) has n- 1 order derivative in fractional Fourier transform domain, then f(t) is determined by its uniform sampling points f^(l)(knT) (l= 0 , 1 , … , n- 1) or recurrent nonuniform sampling points f^(l)(n(t_p+ kNT)) (l= 0 , 1 , … , n- 1 ; p= 1 , 2 , … , N) , the related sampling rate is also reduced by n times. The examples and simulations are also performed to verify the derived results.