Higher-Order Derivative Sampling Associated with Fractional Fourier Transform

Abstract

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 $$f^{(l)}(knT)(l=0,1,\ldots ,n-1)$$ or recurrent nonuniform sampling points $$f^{(l)}(n(t_{p}+kNT))(l=0,1,\ldots ,n-1;p=1,2,\ldots ,N)$$ , the related sampling rate is also reduced by n times. The examples and simulations are also performed to verify the derived results.