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Fall 2000

# Fall 2000 - Hd(W = D(w)e-jw with match the Ideallowpass...

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ESE 337 Exarn IV Fall, 2000 Name ID no. 1. (a) Consider the CT signal x(t) = 2 sin 2t + cos lOOt. The signal is to be processed digitally using the sampling period T = 0.02. Design a DT first-order-digit.al filter with bandwidth ~ in..the Nyquist freqmm..c...y 1 " h h' h f &,PJ' r.a.&ge to e Immate t e Ig - requency component. (b) Compute the steady state response of the output of the filter you designed. Ci- Dr p-~ ~~ I~ P1 .~ (J ·r l ! _ ~ . ~ II (J):: J -- t?- - 2 ;-~ Jt; ~a ~ ' tjM-d !p:v'; a. :;:. iJ, 1f' ) (111) :;: .2 ~ ()jl'J4 n.. ..,.. PIn:2 n... HrJ) - i p I e + .. --- po ----- ! '

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2. Design a type I FIR filter of order 2 to L8.

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Unformatted text preview: Hd(W) = D(w)e-jw with match the Ideallowpass filter D{w) = { 1 at w = 0, 1, 1.5 1.1[. ° • ': LJ fI(~.J~) := ,4-{w} f:-. ..J O:S;w:S;l 1.5 :s; w :s; 7f i+(wr:.:: d [dlj 1" d {( J e-co 4J 3. Transform the Butterworth analog prototype filter 1 G (s) ---::------S2 + l.4s + 1 to andpass filterith passband edge frequencies Wpl = 20 rad / s and W pu = 30. ......... 2.. .5 ~).pKJ(J ____ .:o. .-. . __ ~ 10 S '"l-f I /f:Y1:J S :r 't -f I XJ'? J '-. .. 36"""" ;-;;, x /o:i ( , '--;-t-) . .. / fJ1J y"" ! ' 4. Design a digital high pass filter with passband edge frequency wp 2.8 from the analog prototype filter in Problem 3....
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