Asymptotic behaviour of FIR filters

The recursive algorithm for the impulse response coefficients of FIR filters with maximally flat specifications was recently developed. Based on a differential equation for the almost equiripple specifications, a similar recursion is derived and presented in this paper. Both backward recursions give an explicit access to the evaluation of asymptotic values to which the impulse response coefficients always converge. Several numerical experiments lead to a general conjecture for the asymptotic behaviour of the impulse response coefficients.