A#16_Solutions

A#16_Solutions - Assignment #16 — Solutions —— 13.1...

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Unformatted text preview: Assignment #16 — Solutions —— 13.1 ECSE-2410 Signals & Sysiems u Fall 2006 Tue 11/07/06 1(30). A Buttcrworth lowpass ﬁlter of order n m 1 is given by H (s) = 1 . 5 + 1 (a) Find the transfer function H 3;,(3) of the corresponding bandpass ﬁlter with center frequency of one and a passband of 0.1. num:[0.1 O]; den=[10.1 1]; w={0.5:.01:1.5]; [mag,phase]zbode(num,den,w); s a s 2 5 a z p10t(wnmag); 0' g g g «in; .... u .. "E .............. .E- ............. a; ............. "g..." % 0 .................................................................................. .................................................................. .. ‘1 :3 0 , ............................................................ .. ans 2 ..............:....--nun-“L.nu.nunu5ununun- "nun-nu": I a u u u a Isl-I‘DAIA:I anu"n..{.u..........n..§...............: ............ .. E 0 I w1.0512 t lehllhl' O. : >> 1/09512 i 0' ‘ ; ans 3 I 0.1 ............. .. 1.0513 (5.5 0.6 0.7 0.8 09511105" 1.2 1.3 1.4 1.5 Frequency (rad/sec.) Assignment #16 — Solutions w 19.2 ECSE-2410 Signals & Systems - Fail 2006 Tue 11/07/06 20.0). Verify the following properties for a general nth order Butterworth lowpass ﬁlter (a) Ifn is odd, then H(s) has a pole at S m ~wc. ~ 2 3 £23”? mg} 23% g, \$‘Hﬁ3 m SE»: :4ng Awe. gee-i; i; e; g}? ., g£ Wage wag“ 5e.” Rigger .k é {EL I % Wﬁ'ég § W my? gem ﬁn émﬁeg {mfg ad? fw' Assignment #16 — Soiutions ~ 9.3 ECSE~2410 Signals & Systems - Fall 2006 Tue E1/07/06 3(10). Show that H(s) = oforder n = 5, ggkm y? 51g mi g}, Bﬁgé; gﬁacgaamawwfma Assignment #16 — Solutions —— p.4 ECSE-24IO Signals & Systems ‘ Fali 2006 Tue 11/07/06 4(10). Find H(s) of a third erder Butterworéh iowpass ﬁlter with a bandwidth of 5 Hz. Note Hz ! Assignment #16 —~ Solutions — [3.5 ECSE—2410 Signals & Systems - F211} 2006 Tue 11/07/06 I 5(30). Consider a Butterworth lowpass ﬁIier of order n = 3 ,i.e., H (s) = ~3——-3——-—m~ . S + 23 + 23 +1 (a) Derive an expression for the impuise response, Mt). i. #6:}; 4: a 2:. £9? ﬂaw“ gaze‘ﬁzgei @+g3{§3+§es} gas»: gz+g=§w§ \e a. ‘ . r é+i 4% M m g :2 §§+£ éﬁagiege em: ,3 ea gage; m em: ,,. mg i i _ 41\$ . \$1 Q95; gem w [email protected]> £55 wefé Q smfﬁﬁw h a? é m“ 31 :: awe?) ~=- e; Luff) megﬁm ﬂ. \ ﬁi’ g @{éﬁﬁ g:- §< egg; )m3§- Kgitﬁégﬁg’ﬁ 1 2- )e i Assignment #16 m Solutions — p.6 ECSE-24IO Signals & Systems — Fall 2006 Tue 11/07/06 1 5(30). Consider a Butterworth Iowpass ﬁlter of order n w 3 ,i.e., HQ?) 2 W . S + 25 + 23 «M (b) Use MATLAB to plot Mr) :15“ F4333, i Ampiitude Time (sec) Anaiytical Solution Time(sec) 659% W wa “‘1 W' clear all numxﬁ}; tm[0:.02:10]; hxexp(~t)~(2/sqrt(3)).*exp(—O.5,*t).*cos(0.5.*sqrt(3)*t+(pi/6)); denm[1 2 2 I]; subp1'0t(2,1,1); impulse(num,den); grid subp10t(2, 1 ,2);grid; p10t(t,h) grid titleCAnalytical SOEution'); ylabelCAmpIitude');x1abei(‘Time(sec)‘) ...
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This homework help was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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A#16_Solutions - Assignment #16 — Solutions —— 13.1...

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