Construct the lowest order, high-pass transfer functions that meet the following filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at \(\omega=\omega_{\mathrm{C}}\) and \(\omega_{\text {MIN }}\). Use MATLAB to validate that your transfer function meets the design specifications.

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Pole Type You Decide @ C T MAX (rad/s) (dB) 100 k 10 @ MIN (rad/s) 20 k T MIN (dB) -50