Assess quality of a bandpass filter without human intervention

Question

I wanted to know if there is a way to assess the quality of a bandpass filter created by the Remez exchange algorithm. I am using the Remez algorithm to determine the best bandpass filter at a number of different sample frequencies and numbers of coefficients and was wondering if there some easy way to assess the quality of the bandpass filter created without just looking at it's frequency response?

I want to be able to iteratively explore the parameter space and return the sample frequency and number of coefficients that produce the best band-pass filter. I am aware that there is not an objective "best" filter, by "best" I mean the filter that best matches a certain specification.

Answer 1

The Remez exchange algorithm not only returns the optimal filter coefficients but also the approximation error $\delta$. This error determines the maximum amplitude error in the pass bands and in the stop bands. The actual amplitude error in band $i$ is given by $\delta/W_i$, where $W_i$ is the error weight in band $i$.

If the algorithm converges, then you know for sure that the maximum errors $\delta/W_i$ occur at the band edges of band $i$. And you know the band edges because they are part of the specs.