Q$3)$ Design a second$-$order anti$-$aliasing lowpass filter which is a Butterworth type,

a$)$ determine the values of circuit elements if we want the filter to have a cutoff frequency of $800$ Hz $.$

b$)$ determine the percentage of aliasing level at the frequency of $400$ Hz $,$ assuming that the sampling rate is $4000$ Hz $.$

Q$4)$ A DSP system is given with the following specifications:

Design requirements:

Sampling rate $22,000Hz$;

Maximum allowable gain variation from $0$ to $4000Hz=2dB$;

$40$ dB rejection at the frequency of $18,000Hz$; and

Butterworth filter assumed

Determine the cutoff frequency and order for the anti$-$image filter

Answer: Fc $=4624Hz,n=3$