Synthesis of recursive digital filters using the FFT

It has been shown that recursive digital filters can be synthesized using the fast Fourier transform. An algorithm for computer implementation has been developed and used in comparing the computation times and noise figures of filters synthesized in this manner with the computation times and noise figures of filters synthesized by recursion. A model has been proposed for analysis of noise in the two-pole filter. Predictions of this model have been found to be in good agreement with noise measurements.