$1.$ A passive RL low pass filter requires a cutoff frequency of $20$ kHz $.$ You have an available inductor of $100$ mH $.$ Please define the required resistor in $\backslash (\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash ).$

$2.$ A Fourier series is represented using the trigonometric form with Cosine and Sine terms. The coefficient a$3=4,$ and the coefficient b$3=3.$ If we use the complex exponential form, what is the magnitude of the coefficient c$3?$ Hint: Use Table $13-3$ in the Fourier section notes.

$3.$ You must design a "Filter Bank" That takes an incoming signal and provides three separate outputs: a Low$-$Band Pass, a Middle Band Pass, and a High$-$Band Pass. The cutoff frequencies are $100$ KHz for the low pass, $1$ MHz for the high pass, and between $100$ KHz to $1$ MHz for the bandpass. You can choose any RC$.$ RL or RLC circuits that are appropriate for the design.