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

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Pole Type T MAX W C (rad/s) (dB) 10 Butterworth 60 k MIN (rad/s) 120 k T MIN (dB) -30