USE PYTHON ONLY! Read all instructions below very carefully. I will downvote if done incorrectly.

Write python code to create a low$-$pass filter based on the minimization of a quadratic function of the filter subject to a constraint. do not use the remez algorithm or any other algorithm.

Then plot the frequency response of that low$-$pass filter with varying lengths of $51,101,$ and $201($basically three low$-$pass filters$)$ in the transition band and portions of the pass and the stop bands so as the number of filter point increases, the response more closely approximates the ideal response. plot all three graphs on the same plot and use dotted lines to show the transition band. keep the grid off. also label all three filter lengths and color code them.

The goal of the problem is to re$-$create figure $4\mathrm{.}2$ exactly as it is shown in the image attached to this question with the low$-$pass filter created by the minimization of a quadractic function of the filter subject to a constraint.