PROBLEM 2 (15 pts) Consider the dt lti system shown below H(e3) ynI e[nl as sketched below: 2-1 6 Determine and sketch yn] if the magnitude and the phase of H(eju)are given below H(eju)l ∠H(e)
� PROBLEM 2 (15 pts) Consider the DT LTI system shown below: x[n] H(ej�) y[n] The input sequence is � � 5� � x[n] = cos 2 n − 4 as sketched below: �2 x[n] 2 −2 −1 0 1 2 3 4 5 6 n �2 − 2 Determine and sketch y[n] if the magnitude and the phase of H(ej�) are given below: |H(ej�)| �H(ej�) −� � � 1 −� � � 2 −� 2 1 6
Fall 2003 Final exam NAME: gn]= n
Fall 2003: Final Exam NAME: y[n] = y[n] −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 n 7
Work Space for Problem 2
Work Space for Problem 2 8
Fall 2003: Final Exan NAME: PROBLEM 3 (35pts Consider the following system cos wbt cos wct H(w) (t) HG The Fourier transform of r(t), X(w)has real and imaginary parts given below Relxljw)l Mix(ju)l - ab For your convenience, the identical figures above are attached along with the transform tables
Fall 2003: Final Exam NAME: PROBLEM 3 (35pts) Consider the following system: cos �bt cos �ct x(t) × H( ) xc(t) × yc(t) −�b �b 1 H( ) � × H( ) xs(t) × ys(t) + y(t) j� j� j� sin �bt sin �ct The Fourier transform of x(t), X(j�) has real and imaginary parts given below: −�b �b � 1 �e{X( )} −�b �b � 1 −1 j� �m{X( ) j� } For your convenience, the identical figures above are attached along with the transform tables. 9
Part a Provide labeled sketches of the real and imaginary parts of Xs u) Re{X。(ju)} m( w)
� � Part a. Provide labeled sketches of the real and imaginary parts of Xs(j�). �e{Xs(j�)} �m{Xs(j�)} 10