NSU2009_ETE221 - -2 π, 2 π ] (b) Identify the symmetry of...

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North-South University Midterm 2,Spring 2009 Date: 22nd March,2009 Course: ETE-221/383 Time: 1hr.15min. Marks: 23 Answer all of the following questions. 1. Consider the signals φ 1 ( t ) = 1 and φ 2 ( t ) = 1 - βt 2 , where β is an unknown constant. Let the value of t [0 , 1]. (a) Find the value of β for which the two given signals are mutually orthogonal. (b) Let us try to costruct the signal f ( t ) = 1 - t using the signals φ 1 ( t ) , φ 2 ( t ) i.e. f ( t ) c 1 φ 1 ( t ) + c 2 φ 2 ( t ). What should be the optimal combination so that the error in the construction of f ( t ) is minimized? (c) Establish that the error is orthogonal to the constructed signal. (d) Find the energy lost in the error signal. (2.5+3+2.5+2)=10 2. Consider the periodic signal sgn ( t ) = 2 u ( t ) - 1 which is de±ned over a period of [ - π, π ]. (a) Sketch the signal over the range [
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Unformatted text preview: -2 π, 2 π ] (b) Identify the symmetry of the signal and hence state ( without doing any calculation ) which Fourier coe²cients for this signal must be zero (c) Calculate the non-zero Fourier coe²cients. (1.5+1.5+3)=6 3. Consider a series RC circuit which has a time-dependent voltage as its input which we call x ( t ). The output is identi±ed as the charge on the positive plate of the capacitor. (a) What is the equation relating the input and the output? (b) If the input is given by e jωt , then what is the response function H ( jω ). (c) Thus, if now an input x ( t ) = cos (3 t )-2 sin (2 t ) is applied, what is the corresponding output? (1.5+2.5+3)=7...
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