Synthesis of high rejection filters with the Fourier transform method

Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10(-4). Two new spectral functions are proposed for use in the Fourier transforms. An empirical procedure which is much faster than refinement is described for optimization of the spectral performance. The method and optimization are illustrated numerically for several different spectral shapes.