Having the solution for P(ω), we can now compute the error function E(ω) from

The chebyshev approximation problem is viewed as an optimum design criterion on the sense that the weighted approximation error between the desired frequency response and the actual frequency response is spread evenly across the pass band and evenly across the stop band of the filter minimizing the maximum error. The resulting filter designs have ripples in both pass band and stop band.

Let us consider the design of a low pass filter with the pass band edge frequency ωP and the ripple in the pass band is δ1, then from the general specifications of the chebyshev filter, in the pass band the filter frequency response should satisfy the condition

If the filter has a symmetric unit sample response, then we know that

If the filter has a anti-symmetric unit sample response, then we know that

The weighted approximation error is defined as E(ω) which is given as

If the filter has a anti-symmetric unit sample response, then we know that

FX denotes an array of maximum size 10 that specifies the weight function in each band.

In general, the filter designs that contain more than L+2 alternations or ripples are called as Extra ripple filters.

Let us consider the design of a low pass filter with the stop band edge frequency ωs and the ripple in the stop band is δ2, then from the general specifications of the chebyshev filter, in the stop band the filter frequency response should satisfy the condition