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1、 Chapter 3 Problem SolutionHomework: 3.1 3.13 3.15 3.34 3.35 3.43* Chapter 3 Problem Solution3.1 jaaaa4 , 213318T kkktkAtx01cos40 tjtjtjtjjejeeetx4343444422jajaaa4 , 4 , 21331 243cos84cos4tttx Chapter 3 Problem Solution3.13 Consider a continuous-time LTI system 4sinjH 8t4 14t0 1 tx4 80T00a0k 40k 04/
2、44sin0kkjkH 000tjkkkejkHaty Chapter 3 Problem Solution3.15100 0100 1 jH txty/TtxS 6 , For what values of k is guaranteed that ?0ka12 60/T kkabtxty8 08 1 0kkjkH8 0kbk8 0 kak Chapter 3 Problem Solution3.34 Consider a continuous-time LTI system Find the Fourier series representation of the output for e
3、ach of the following inputs : 4 teth ty nttxn (a) nttxnn1 (b)(c) is the periodic wave depicted in Figure P3.34 tx1 tx -2 -1 0 1 2 t2/1 Chapter 3 Problem Solution2248 jH1 2 (a)k0a tjkkkebty 2 2jkHabkk22168k 2T (b)0 jkea2121 k tjkkkejkHaty00 even is k 0odd is k 1odd is k 168even is k 02kbk tjkkkebty C
4、hapter 3 Problem Solution21 0a0k 2/sin412sin k kkkka 2jkHabkkkak22168 2 1T (c)0 3.35otherwise 0250 1 jH txty/TtxS 7 , For what values of k is guaranteed that ?0ka Chapter 3 Problem Solution14 70/T kkabtxty18 018 1 0kkjkH18 0kbk18 0 kak Chapter 3 Problem Solution3.43 tjkkkeatx0even isk , 0kaodd harmo
5、nic tx 2/Ttxtx is odd harmonic tx(a) is odd harmonic sketch and find its 2T , 1t0for ttx txodd isk , 0ka is even harmonic tx(c) Could T be the fundamental period for such a signal? 0, 0 111aa(d) If one of two things happens,T is fundamental period. mon no have l andk , 0, 0 2lkaaka tx Chapter 3 Prob
6、lem Solution 010Tax t dtT 100 , tttT/2xtx t 21/2xtxtT 12r txtxtF/211j TXjXje 0/21011jkTkaXjkeT 0 k is evenka /2x tx tT (a) (i) 200 , tT/2ttTxtx t is odd harmonic x t1jke k is even0 Chapter 3 Problem Solution(ii) even isk 0ka /2x tx tT00/2jkt Tjktkkkka ea e 0 1 jktjkkkaee 0ka /20 x tx tT /2x tx tT k
7、is even0 k is odd101234211 txt0 01jktkkabe Chapter 3 Problem Solution10123421 tx1tSolution 1 111txtxtx FS1kxtb1jkkkabe 00 1t10123421 kcdttdxFS1t/2sin/212jkjkkkceek kkcbjk 2 0 k is even12 k is oddkajkjk Chapter 3 Problem Solution022j ntnna e Let 2kn 0jktkkx ta e (c) T/2Fundamental period022jntnna e 0
8、 , k is oddka Chapter 3 Problem Solution(d) 111 0,0aaSuppose T is not fundamental period 1/ M is integerTT M10M00jktjmMtkmkma eb e 11 0,0aa M1T is fundamental period. 2 0,0 ,k and l have no common factors.klaa Chapter 3 Problem SolutionSuppose T is not fundamental period 1/ M is integerTT M10M00jktjmMtkmkma eb e 12 , m Mkm Ml1M T is fundamental period.10123421 kbdttdxFSt3.43 (b) Solution 2kkkdcbkjkkajkec12110123421t tx2 kkcddttdx2FS2kajk222jkcjkcakkk txtxdttdx21 Chapter 3 Problem Solution