Designing a Frequency$-$Selective Filter

The circuit shown in the figure below is part of an audio signal receiver device. The portion of this circuit that is enclosed in the red box is a frequency$-$selective circuit that passes or rejects frequencies based on the values selected for its components. In this project, you will design this frequency selective circuit by choosing the values of its components that will enable it to strongly reject one frequency $f_r()kHz)$ and strongly pass another frequency $),$ with intermediate response for other frequencies. Thus, this circuit is a combination of a bandpass and a band reject filter.

Part $1$: Theoretical Analysis

Calculate your selected $f_r$ and $f_p.$

Derive the transfer function of the filter: $H(s).$ Show your work.

Derive the magnitude and phase expressions: $|H(j)|$ and $(j).$ Show your work.

Calculate the missing values of $C_x$ and $C_y.$ Show your work.