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# Quiz 1 - [O ”5 —’ 0 3L ECE 408 QUIZ#1 20 POINTS[z—...

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Unformatted text preview: [O ' ”5 —’ 0 3L ECE 408 QUIZ #1 20 POINTS . . . [z— The transfer function of an analog ﬁlter IS given by _..___ 2:3 H (s) = 4.65 \$2 +4.6s+31.3 This ﬁlter is transformed to a digital ﬁlter H(z) using impulse invariant transformation (HT). The sampling rate is given by {sampling = 10 Hz. The sampling interval is given by Ts=1 fiampling (a) Find the poles and zeros of H(s) and plot the pole-zero diagram. (b) Plot the magnitude response of the analog ﬁlter, that is, |H(m)|. (0) Plot the phase response of the analog ﬁlter, that is, AH(03). (d) What type (LP, HP, BP, BS) of ﬁlter H(s) is? (e) Find h(t) = L'1[H(s)]. (f) Find h(k) = h(t) evaluated at t "—" kTs. (g) Find H(z). (h) Find the poles and zeros of H(z) and plot the pole-zero diagram. (i) Plot the magnitude response |H(9)| of the digital ﬁlter for 0 S 9 S TC. _,— r. I! ”135ij (i *3? '! +1.3 ’5"??? +373,ch _ ' C’O‘ZE-fjofﬁ’\)\4 MUA r (1 x3 +J mnw) ﬂ ”Lu/E , f , J7 to 7,3 —J<> 3") 1/— ’ ”1‘ Z "s r» 0‘\\(~a L \ J 0 ) 6* whiff} \ M1") = (2 54' ”8e \ r ~ '\ r {JO‘B / Kl,‘é,50 S13“; M -r “WWW ~~~~~ w \ M (-0 144—509) ’\ (ro.;3~jorr‘> / " e, E /" 5, & (”my-w) —‘ (—0.15 ’jo'ﬁs‘ﬁ .4) _\_ (1,7) FjomﬂAUf-L/ * (LB/(JGSEU i-C E 3-“— (21w 5:7"723230 :ﬂ J 5:: f " 6/ “' ~e, % -\-“ e, E Ww———M— _ _\ K — WM ,1 ram/3A 3c SI ,Jorw3 " C 3:, {J “ {J / ,r ’9 L3 -]0r-\$'\ 3011) ,9 L3,: '50"? jo’ 999*EL’QH: ﬂ 6, +6 +3 % @05306 ~i0’3376e, 1' MW" _ (0'13 — ’2— ' a) ...
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