Consider the second-order band pass filter shown in Figure.
a. Derive expressions for L and C in terms of the resonant frequency ω0 and quality factor Qs.
b. Write the KVL equation for the circuit and use it to develop a digital filter that mimics the action of the RLC filter. Use the results of part (a) to write the coefficients in terms of the resonant frequency ω0, circuit quality factor Qs, and sampling interval T.
(Hint: The circuit equation contains an integral, so differentiate with respect to time to obtain a pure differential equation.)
