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P2 50 PTS A certain system is described by the transfer function (p): Y() yt GO) 48 p2 + 7p + 12 The input signal u(t) = f(t) is the Full-Wave Rectified sinusoid shown in the figure below with Even Fourier Series representation An * Full Wwe Rectified Sim -TOT 27 Let A Tasse కందు మ Al Write the DC and first 3 harmonic terms (n=1,2,3) u(t) = 1 -cos(21) - cos(4e) - cos(61). B) Fill in the Frequency Response table below to compute the DC and first 3 harmonic terms of y(t). Must show your calculations for credit. The Bode Diagram of GC) is included to assist in veritying your calculations, Recall that: 1GC) (dB) = 20 108:0G(*) w 0 2 0 1 2 3 G) 4 148-/2.58 -0.24-1168 -049 -0.86 IG 4 (12.04dB) 2.999.48 dB) 1.7(46 dB) 0.99 (-0,07 dB) 2G) OF -60.26 -98.13 - 119.7 6 Calculations: G(2) 12-704 -1.48 -12.582.984(-60.26) G4) *-0.24 - 1.68 = 1.74-98.13) 48 606) - =-0.49 -0.86 - 0.994-119.7") 12-6+42

B) Complete the table below: must show your calculations for credit, then write y(t) explicitly. U - Phasor Representation of the harmonic of u(t) and Y - Phasor Representation of the milharmonic of y(t) HINT: -Acos(ast + ) = A.cos(wt + +180) + 0 3 ON 1 GO)(1) = 420 2 1 3<180 602) (180) 2 2 4 2 15 2180° 2 2180-) - 2 982C-60.26) (-180-) - 1.99 2119.74 604) 2180) 1.72-98.13") 2180º = 0.23 (81.879 2 G(6) 54180° = 0.99 (-119.75 180" = 0. 056 (60. 3) 15 3 6 352180") y(t) = 4 +1.99cos(26 + 119.74) + 0.23cos(4t + 81.87") + 0.0566cos(6t+ 60.3) + (A)