Problem $4$

You are to design a highpass filter with these specifications: The passband gain is $20$ dB relative to the input; the stopband attenuation is $-40$ dB relative to the input; the $-3$ dB cutoff frequency is $1000rad{s}^{-1}$; and the upper stopband edge is at $200rad{s}^{-1}.$

Butterworth and Chebyshev polynomials are on the back of the tear$-$off sheet.

$($a$)$ Design the transfer function for a Butterworth filter meeting the specifications.

$($b$)$ Design the transfer function for a Chebyshev filter meeting the specifications.