It was well known in both mathematics and engineering that the optimal response would exhibit an equiripple behavior and that the number of ripples could be counted using the Chebyshev approximation. Several attempts to produce a design program for the optimal Chebyshev FIR filter were undertaken in the period between 1962 and 1971. Despite the numerous attempts, most did not succeed, usually due to problems in the algorithmic implementation or problem formulation. Otto Herrmann, for example, proposed a method for designing equiripple filters with restricted band edges. This method obtained an equiripple frequency response with the maximum number of ripples by solving a set of nonlinear equations. Another method introduced at the time implemented an optimal Chebyshev approximation, but the algorithm was limited to the design of relatively low-order filters.