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(tp+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.