  In this paper we study the nonuniform fast Fourier transform with
nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as
its application. The computation of NNFFT is mainly based on the nonuniform
fast Fourier transform with nonequispaced spatial nodes and equispaced
frequencies (NFFT). The NNFFT employs two compactly supported, continuous
window functions. For fixed nonharmonic bandwidth, it is shown that the error
of the NNFFT with two sinh-type window functions has an exponential decay with
respect to the truncation parameters of the used window functions. As an
important application of the NNFFT, we present the fast sinc transform. The
error of the fast sinc transform is estimated as well.
