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102_1_Review-MT

# 102_1_Review-MT - UCLA DEPARTMENT OF ELECTRICAL ENGINEERING...

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UCLA DEPARTMENT OF ELECTRICAL ENGINEERING Spring 2008 Your Name (LAST, Middle, First):————————————————– EE102: SYSTEMS & SIGNALS SAMPLE MIDTERM EXAMINATION 1

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PART 1 t-Domain Analysis (Do NOT use Laplace Transforms ) (Question 1) (i) Plot the following function: x ( t ) = e - t U ( t - 1 ) + δ ( t + 1 ) (ii) This function is taken to be the input to a system with IPOP relation S : y ( t ) = Z -∞ tU ( σ - t ) x ( σ ) U ( σ ) d σ - ∞ < t < Your problem is to find y ( t ). (iii) S is TV / TI ? C / NC ? (Question 2) The IPOP of system S 1 is: y ( t ) = Z t -∞ x ( τ ) d τ + Z t e t - τ x ( τ ) d τ t ( -∞ , ) The IPOP of system S 2 is: y ( t ) = Z t -∞ e - τ x ( t - τ ) d τ t ( -∞ , ) (i) Find IRFs h 1 ( t , τ ) and h 2 ( t , τ ). (ii) state properties of S 1 and S 2 : TV / TI ? C / NC ? (iii) Find IRF of the cascaded system S 21 : h 21 ( t , τ ). (iv) Is h 12 ( t , τ ) = h 21 ( t , τ )? Why? 2
PART 2 s-Domain Analysis (This is where Laplace Transforms shine ) (Question 3) (i) An LTI Causal system S has output y ( t ) = sin tU ( t ) when the input is x ( t ) = 1 2 ( 1 + t ) U ( t ). Find the system function H ( s

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