Design of prolate spheroidal wave function pulse based on legendre polynomials

To simplify the hardware complexity of prolate spheroidal wave function(PSWF)implementation, a new design method prolate spheroidal wave function pulse based on normalized Legendre polynomial was proposed.We generated a symmetry matrix according to the pulse parameters, and got the Legendre polynomial coefficients by computing the eigenvectors of the matrix.On this basis, we constructed the required PSWF pulse by the normalized Legendre polynomial approximation method.In the PSWF pulse design procedure, the proposed method can design new PSWF pulses by changing Legendre polynomial coefficients, and it can generate PSWF fastly and accurately with low implementation complexity.