HW1_soln_set_1

HW1_soln_set_1 - 1.20(a Given Therefore(b We know that r(t...

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Unformatted text preview: 1.20. (a) Given Therefore, (b) We know that r(t) - dzt + y(t) -- dst r(t) : e-izt -| y(t) : s-i\t Since the system is linea,r, rr (r) : f,{a" * e-izt', + yt(r) = itrt' * e-itt1 ,{t): cos(2t) a yr(t) : cos(3t) | - . t , \ s - i . i z t I s i s - i z t *z$): cos [rtt - ;) ) = z Using the linearity property, we may once again write I -.6' 1 *r$): ){"-iA" +"i"-izt) + yr(r) : r{u-iast +de-?3') - cos(3t - 1) Therefore, ,{t) - cos(2(t - Llz)) 1 yr(t) : cos(3t - t) 1.21. The signals a,re sketched in Figure 51.21. *(zt+t) f*+t+r(+)lut+) Figure 51.21 7.22. The signals are sketched in Figure 51.22. 7.23. The even and odd pa,rts are sketched in Figare 51.23. 10 *Ln-+7 {"l.utnd = x[h'l (e) o l z , \ (f) =Ut o l (cl U-l Figure 5t,22 (c) Figure 51.23 x.ftn+0- t {rhl + f erltrxt"l rtGn-r)'J 1 1 \/' o) (c) Figure 5L.24 1.24. The even and odd parts are sketched in Figure s1.24. L.25. (a) Periodic, perio d - Zn l(4) : r 12' (b) Periodic, Perio d : 2r l(r) : 2. (c) r(t) : [1 + cos(4t -Zn13)]12. Periodic, period :2rl@) - r/2' (d) r(t) : cos(4nt)12....
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This note was uploaded on 10/15/2008 for the course EEE 203 taught by Professor Chakrabarti during the Fall '07 term at ASU.

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HW1_soln_set_1 - 1.20(a Given Therefore(b We know that r(t...

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