Signal Processing and Linear Systems-B.P.Lathi copy

Signal Processing and Linear Systems-B.P.Lathi copy

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Unformatted text preview: - 10) s + 10 find the system response to the following (everlasting) inputs: (a) ejwt ( b) cos (wt+O) (c) cos t ( d) sin 2t (e) cos lOt ( f) cos lOOt. Comment on the filter response. 7 .2-1 Sketch Bode plots for the following transfer functions: s(s + 100) b (s + 1 0)(8 + 2 0) ( c) (8 + 10)(s + 2 00) ( a) (s + 2 )(8 + 20) ( ) s2(8 + 1 00) (8 + 20)2(8 + 1 000) 7 Frequency Response and Analog Filters 538 t) ~ P roblems 539 y (t) Ole 7 .4-2 D etermine n , t he o rder of a lowpass B utterworth filter, a nd t he c orresponding cutoff frequency W e r equired t o s atisfy t he following lowpass filter specifications. F ind b oth t he values of W e, t he one t hat oversatisfies t he p assband specifications, a nd t he one t hat oversatisfies t he s topband specifications. R epeat P rob. 7.2-1 if 82 ( a) (8 + 1)(82 + 48 7 .3-1 D etermine t he t ransfer function H (s) a nd t he a mplitude response H (jw) for a t hirdorder lowpass B utterworth filter if t he 3 d B cutoff frequency W e = 100. F ind your answer without using Tables 7.1 or 7.2. Verify your answer using either of these Tables. 7 .5-2 7 .2-2 Design a second-order b andpass filter with center frequency W = 10. T he g ain should b e zero a t W = 0 a nd a t W = 0 0. Select poles a t - a ± j 10. Leave your answer in terms of a. E xplain t he influence of a o n t he frequency response. 7 .5-1 F ig. P 7.3-1 Using t he g raphical m ethod o f Sec. 7.4-1, d raw a r ough sketch of t he a mplitude a nd p hase response of L TIC s ystems whose pole-zero plots are shown in Fig. P7.4-2. 7 .4-3 S +Olc 8 + 16) ( b) (s + 1)(s2 + 14.148 (8 + 10) + 100) ( c) 8(8 2 + 14.148 + 100) ( a) a p ~ - 0.5 d B, a s :s; - 20 d B, W p = 100 r ad/s, a nd W s = 200 r ad/s. ( b) G p ~ 0.9885, G s :s; 1 0- 3 , W p = 1000 r ad/s, a nd w . = 2000 r ad/s. ( c) T he g ain a t 3w e is required t o b e no g reater t han - 50 dB. Feedback c an b e used t o increase (or decrease) t he s ystem b andwidth. Consider a s ystem in Fig. P 7.3-1a w ith t ransfer function G(8) = ~. ( a) Show t hat t he 3 d B b andwidth o f this system is W e· ( b) T o increase t he b andwidth o f this system, we use negative feedback w ith H (s) = 9, as d epicted in Fig. P7.3-1b. Show t hat t he 3 dB b andwidth o f t his s ystem is lOwe. ( c) To decrease t he b andwidth of t his s ystem, we use positive feedback w ith H (s) = - 0.9, as i llustrated in Fig. P7.3-1c. Show t hat t he 3 dB b andwidth of this system is 7 .5-3 F ind t he t ransfer function H(8) a nd t he a mplitude r esponse H (jw) for a lowpass B utterworth filter t o s atisfy t he specifications: a p ~ - 3 dB, a s :s; - 14 d B, W p = 1 00,000 r ad/s, a;.nd W s = 1 50,000 ra,?/s. I t i~ d esirable to oversatisfy (if possible) t he r equirement of G s . D etermine t he G p a nd G . o f your design. w c/lO. 7 .6-1 R epeat P rob. 7.5-1 for a Chebyshev filter. Do n ot use Tables. 7 .6-2 Design a lowpass Chebyshev filter t o s atisfy t he specifications: - 22 dB, W p = 100 r ad/s, a nd W s = 200 r ad/s. 7 .6-3 Des...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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