Explanation
The picture above on the right displays the various extremal frequencies for the plot shown. The extremal frequencies are the maximum and minimum points in the stop and pass bands. The stop band ripple is the lower portion of ripples on the bottom right of the plot and the pass band ripple is the upper portion of the ripples on the top left of the plot. The dashed lines going across the plot indicate the δ or maximum error. Given the positions of the extremal frequencies, there is a formula for the optimum δ or optimum error. Since we do not know the optimum δ or the exact positions of the extrema on the first attempt, we iterate. Effectively, we assume the positions of the extrema initially, and calculate δ. We then re-estimate and move the extrema and recalculate δ, or the error. We repeat this process until δ stops changing. The algorithm will cause the δ error to converge, generally within ten to twelve iterations.
Read more about this topic: Parks-Mc Clellan Filter Design Algorithm
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