Question $5$:

a$)$ Given the lowpass filter characteristic plots as shown, specify what each of these IIR filter types are? $($Choose: Butterworth, Chebyshev I, Chebyshev II$,$ Elliptical$)$

$($i$)$

$($ii$)$

$($iii$)$

$($iv$)$

b$)$ In a DSP signal communication system design, a requirement exists to design an Infinite Impulse Response $($IIR$)$ digital highpass filter with a Chebyshev characteristic to meet the following specifications:

$-$ Passband frequency

$-$ Stopband frequency

$-$ Passband ripple

$-$ Stopband attenuation

$-$ Sampling frequency

$4\mathrm{.}2$ kHz

$1\mathrm{.}6$ kHz

$0\mathrm{.}5$ dB

$30$ dB

$10$ kHz

$($at the passband frequency $4200$ Hz $)($at the stopband frequency $1600$ Hz $)$

$($Use the information provided in Annex$-2$ to answer this Question $5$b$.)$

$($i$)$ Determine the digital passband $\backslash (\backslash$omega$\_\{$d p$\}\backslash )$ and stopband $\backslash (\backslash$omega$\_\{$d s$\}\backslash )$ edge frequencies in rad$/$s and then calculate the equivalent pre$-$warped analog prototype filter passband $\backslash (\backslash$omega$\_\{$a p$\}\backslash )$ and stopband frequencies $\backslash (\backslash$omega$\_\{$a s$\}\backslash ).$