1、1Chapter 2 Problems Solution nhnxny1 a224 ny12 2-1 0 1 2 3 4 n 22 b12nynhnxny 22 c13nynhnxny2.1 312nnnnx 1212nnnhCompute and plot each of thefollowing convolutions: 422212412nnnnn2Chapter 2 Problems Solution 445kyx k hk4N 14 140kyx k hk 0 , n5h n 4N 2.5 elsewhere 0, 90 1, nnx elsewhere 0, 0 1, Nnnh
2、014 , 54 yynhnxnyDetermine the value of N.140 , k9hk3Chapter 2 Problems Solution2.7 A linear system S has the relationship kngkxnyk2between its input and output ny nx 4nunung a 1x nn 12ky nkg nk 26u nu n b 2x nn 22ky nkg nk 48u nu n(c) S is time-varying.2g n4g n4Chapter 2 Problems Solution d x nu n
3、kngkunyk24220knuknuk 10684 624nunununununununu 2y nu nu n 21u nnn5Chapter 2 Problems Solution2.10 Suppose that elsewhere 0, 10 1, ttx 10 , /aatxth thtxty dttyd(a) Determine(b) If contains only three discontinuities,what is the value of a?011t txSolution ： th0a1t tya0 a 1 1+a t6Chapter 2 Problems Sol
4、ution0 a 1 1+a t1-1 dttydIf a=1， contains only threediscontinuities. dttyd2.11 Let 53tututx tuetht 3(a) Compute thtxty(b) Compute thdttdxtg/(c) How is related to ty tg7Chapter 2 Problems Solution01txt3t5t ueh303t5ttx 03 1t 3 t, 0ty 530503 2ttt detyt33 03133 te 505 3tt detytt33 5 33353ttee ueh303t5tt
5、x8Chapter 2 Problems Solution thdttdxtg/ b tuettt 353535333tuetuett dttdytg/ c9Chapter 2 Problems Solution2.12 Let ktkttuety3Show that for tAety30tDetermine the value of A. 3tky te u ttk 33tkky teu tk 03 0t3tkky te 3301 0t31tktky teeee 311Ae1k 03 30ktut102.20. Evaluate the following integrals: 1cosc
6、os a00ttdtttu 032sin b50dttt du2cos1 c155 dtttut12cos16410 2cos10ttChapter 2 Problems Solution11Chapter 2 Problems Solution2.22 ? a thtxtytuethtuetxtt dtueuetuetuetyttt ty tueetu tetytt t0 t, 0 deett0t 0 t t t tede 0 tdeet0 t 12Chapter 2 Problems Solution20123 txttsin th2011t(c)one period of thtxtht
7、x1321211thth dht0 t22t0 |cos1sin 00ttd 2cos11tutut13Chapter 2 Problems Solution 533cos12311cos12tututtututtyOr 5 t 0 5t3 cos12- 3t1 cos12 1 t 0 ttty14Chapter 2 Problems Solution2.23 txtT0TT2T211011t thDetermine and sketch for the following value of T: thtxty(a) T=4 (b) T=2 (c) T=3/2 (d) T=1 kkTttx k
8、kkTththkTtty15Chapter 2 Problems Solution1 ty(a) T=4-5 -4 -3 -1 0 1 3 5 t (d) T=1 ty10 t 1 ty-3 -1 0 1 3 t (b) T=21 ty0 t (c) T=3/216Chapter 2 Problems Solution2.40 (a) an LTI system: dxetytt2 What is the impulse response for this system? th(b) Determine the response of tx1021 txt dxtuetyt22th 22tue
9、tht dxtuetyt2(a) thtxthtxty1 b2111thth17Chapter 2 Problems Solution dueth t212 4 11 141tuetuetytt2.46 Consider an LTI system S and a signal 123tuetxt tytxand tuetydttdxt23If Determine the impulse response of S. th 2 121tuetht2 t t2 2de18Chapter 2 Problems Solution 121633tetuedttdxttSolution ： tuethe
10、t2312 1233tetxdttdx 123 3Sthetydttdx tuetydttdxt23 121123tueethtthe impulse response19Chapter 2 Problems Solution ththtxtx00 2 a2.47 An LTI system with impulse response th0 tytx000 2 t 1 ty0In each of these cases,determinewhether or not we have enough Information to determine the output ty tyty020 2
11、 t 2 ty ththtxtxtx000 2 b 200tytyty0 2 4 t 1 ty20Chapter 2 Problems Solution 1 2 c00ththtxtx 10tyty0 1 2 t 1 ty ththtxtx00 dWe have not enough information to determine the output ththtxtx00 e dthxthtxty0000 dthx00 dthxty000 0tyty-2 0 t 1 ty21Chapter 2 Problems Solution ththtxtx00 f tyty0 0 2 t 2/1 t
12、y2/12.24 nh2 nh1 nh2 ny nx 22nununh nhn5012 3145641710811 nh nh1 1nnnx(a) Find the impulse response(b) Find the response of the overall system to the input22Chapter 2 Problems Solution 2222nununununhnh 0,1,2n , 1 , 2 , 122nhnh xhxhxhxh221/ 26543221/48111051xxxxxxxx 0,1,2,3,4n , 1 , 2 , 3 , 3 , 11nh4322331xxxx nhnhnhnh221(a) nh2 nh1 nh2 ny nx23 11nhnhnynnnx(b) 5,60,1,2,3,4,n , 1, 3, 4, 3, 1 , 5 , 4 , 1nyChapter 2 Problems Solution
