102_1_Spring09-102-MT-Q1-Sols

102_1_Spring09-102-MT-Q1-Sols - Put FIRST Letter of LAST...

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Put FIRST Letter of LAST Name in the Corner −→−→−→%% L U C L A DEPARTMENT OF ELECTRICAL ENGINEERING Your Name (LAST , Middle, First): LEVAN, NMI, Nhan (Fill in the following lines — if applicable) NAME OF FRIEND ON YOUR LEFT: Laplace NAME OF FRIEND ON YOUR RIGHT: Fourier Tuesday, May 05: 8:00 - 9:50 am MIDTERM EXAMINATION: Q-1-Solutions Instructions: (i) Closed Book, Calculators, Cell Phones and IPods Are NOT Allowed A Two-Sided Sheet (8.5 x 11.0) of Notes Is Allowed (ii) Please use LOOSE Papers and Write On ONE Side Only — otherwise -5 pts/(two-sided) sheet (iii) Please Put The First Letter of Your LAST NAME In The Upper Right Hand Corner of This Page (iv) Staple These Examination Papers With Your Papers PLEASE MAKE SURE THAT YOU HAVE 4 PAGES OF THESE EXAMINATION PAPERS NUMBER OF YOUR SUBMITTED PAGES: [ 5 ] 1
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QUETION 1 (40%) (Parts (i), (ii), and (iii) are standing-alone) (i) (10%) Let h ( t,τ ) be the IRF of a L system S . If h ( t,τ ) = h ( t τ ) , −∞ ≤ t, τ ≤ ∞ , then S is TI. True or False? Why? Conversely, if S is TI then h ( t,τ ) = h ( t τ ) , −∞ ≤ t, τ ≤ ∞ . True or False? Why? SOLS. Given that S is L and h ( t,τ ) = h ( t τ ) , −∞ ≤ t, τ ≤ ∞ , Then by BT: x ( t ) [ S ] y ( t ) = Z −∞ h ( t τ ) x ( τ ) From which we ±nd y ( t A ) = Z −∞ h ( t A τ ) x ( τ ) ( ) Then consider x ( t A ) [ S ] = Z −∞ h ( t τ ) x ( τ A ) := z ( t ) (set t τ = σ ) z ( t ) = Z −∞ h ( t A
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This note was uploaded on 03/29/2011 for the course ELECTRICAL EE102 taught by Professor Levan during the Spring '09 term at UCLA.

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102_1_Spring09-102-MT-Q1-Sols - Put FIRST Letter of LAST...

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