examIII_f99 - EXAMINATION III EE 350 Continuous Time Linear...

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Unformatted text preview: EXAMINATION III EE 350 Continuous Time Linear Systems November 22, 1999 Name (Print): ID. number : Section number : Do not turn this page unit xou are told to do so Test form A ham 1. You have 2 hours (120 min. total) to complete this exam. 2. This is a closed book exam. You are allowed one sheet of 8.5” x 11” of paper for notes as mentioned in the syllabus. labeling the page with the question number; for example, “Question 4.2) Continued”. NO credit will be given to solution that does not meet this requirement. 4. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted and a grade of ZERO will be assigned. Problem 1: (25 Points) - Question 1.1 (5 Points) Find the fundamental frequency mo of the signal f(t) = sum-2; + 3’5) + 2cm?) + 4. Question 1.2 (10 Points)Determine the exponential Fourier series of the signal f (t). State all nonzero values of D". Question 1.3 (10 Points) Consider a LTIC system whose frequency response function is 1 H(“’)=2+jw‘ Find the zero-state output y(t) of this system due to the input f (t) = %+E°° 2 sin(mr/ 2) cos(21mt) 71:1 H Problem 2: (25 Points) Question 2.1 (12 Points) Sketch the magnitude and phase spectra of the compact trigonometric Fourier series of the function f (t) = —3 + sin (t + g) + fines (gt) + sin (gt). Use the graphs provided in Figures 1 and 2. Figure 1: A blank graph for plotting On for problem 2.1. Figure 2: A blank graph for plotting 0,1 for problem 2.1. Question 2.2 (13 Points) A certain periodic signal has the compact trigonometric Fourier series on 2 _ f(t)=5+5nz=]_—1\/—+l_§—GFCOS (2nt-tan 1(4n)). The power of the signal f (t) is Pf = 29.974. What percentage of the signal’s power is contained in the second and higher harmonics? Problem 3: (25 Points) Question 3.1 (15 Points) Find the signal f (t) whose spectrum is given by F (w) z e_%lw| 1 using direct calculation of the inverse Fourier transform. Question 3.2 (10 Points) A certain signal, f (t), has the spectrum shown in Figure 3. Sketch the Fourier transform of the signal 9 (t) = gr (2:) e73” using the graph provided in Figure 4. Figure 3: The spectrum of f (t) for problem 3.2. Cum} Figure 4: A blaqk graph for sketching the spectrum, G (u). Problem 4: (25 Points) Consider a DSB-SC AM system in Figure 5. cod 0),!) local «cluster Demodulator Figure 5: Amplitude modulation scheme (DSB—SC) The spectrum 3(a)) of 3(t) is shown in Figure 6. Figure 6: The spectrum S(w) of the signal s(t) 10 Question 4.1 (10 Points) What is the bandwidth of m(t) in Hz.? Sketch the amplitude spectrum of the input m(t) in the graph provided in Figure 7. Label your plot properly. |M( m)l Figure 7: The graph for sketching the amplitude spectrum |M(w)| 11 Question 4.2 (10 Points) Sketch the amplitude Spectrum |E(w)| of the signal e(t) using the graph provided in Figure . Label your plot properly. lElmN Figure 8: The graph for sketching the amplitude spectrum |E(w)| Question 4.3 (5 Points) What is the minimum cutoff frequency (rad/sec) of the ideal lowpass filter so that the massage m(t) is recovered without distortion? 12 ...
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