Computation and performance of the prolate-spheroidal wave function window in spectral estimation

It has been proven that the prolate-spheroidal wave function (PSWF) window is the optimal high-resolution window in the classical spectral estimation. However, the implementation of the PSWF window is difficult in the past due to the lack of a closed form solution. The numerical computation of the PSWF window using the Legendre function is considered and the performance of this window compared with other windows is discussed. The theoretical analysis and simulation results showed that under the same conditions, the PSWF window which is approximated by using the proposed method is superior to other commonly used windows