PROBLEM 2 (15 pts) Consider the dT lti system shown below: H(eu) The input sequence is r[n]=cos(o as sketched below an 23 6 Determine and sketch yn if the magnitude and the phase of H(eju) are given below: ∠H(e) 2 6
Fall 2003: Final Exam NAME n v n ee xIn\>co FT.4心Ak+ aM waing te te X(ev):e S(w-7. 22)+e Siw, 2+ 2uQ) Y(em)=lxlen)(H(e")I 4 Xle)+X Her) +2 8W-;2)e 20):nSw,号,2A) f cee ofte Mle). 5T Slw-+ 2u8)-T'slw,2+2uA)>yIn=m i n
Work Space for Problem 2
Fall 2003: Final exam NAME PROBLEM 3 (35pts) Consider the following system cos wbt cost ae(t) ge(t) HGw) HGu) a(t) y(t) H(w) sin wbt sin wct The Fourier transform of r(t), XGu)has real and imaginary parts given below Re(xGu)) SmX(w) -wb For your convenience, the identical figures above are attached along with the transform tables
Part a. Provide labeled sketches of the real and imaginary parts of Xs (jw) Re(xs w)) 3m{X。(ju)}