20092ee102_1_S09-102-HW-1

20092ee102_1_S09-102-HW-1 - ) is output. Is S : TI or TV? C...

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Spring 2009: Put First Letter of LAST Name in the corner →→%% ( Otherwise Your HW Will 1 Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– HW: # 1 A LATE HW IS INDEED A NON-HW! Posted: April 2 Hand In To NNMIL April 9 Attach This Sheet To Your HW Notations := means “equal be de±nition” x [ a, b ) means a x < b 1. Calculate: I := Z −∞ e t U ( t + 1) t U ( t 1) dt I ( t ) = Z −∞ [ δ ( t τ ) e ( t τ ) ] U ( t τ ) e τ U ( τ ) 2. Consider the following di²erential equation — together with the initial conditions: 4 dy ( t ) dt + y ( t ) = dx ( t ) dt , t > 0 y (0) = 0 = x (0) (i) Solve for y ( · ) in terms of x ( · ). (ii) Calculate y ( · ) given that x ( t ) = te t , t 0 1 intentionally 1

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(iii) If y ( t ) and x ( t ) in part (i) are OP and IP respectively of a system S . Show whether S is L or NL. 3. A system S is described by the following IPOP description: y ( · ) = T [ x ( · )] , y ( t ) = Z −∞ τ U ( τ t ) x ( τ ) dτ, t > −∞ where x ( · ) is input and y ( ·
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Unformatted text preview: ) is output. Is S : TI or TV? C or NC? 4. Compute: I ( t ) := Z ∞ −∞ ( t − τ ) e − ( t − τ ) U ( t − τ ) U ( τ + 2) dτ, t > − 2 5. Given the following IPOP description of a system S : y ( t ) = T [ x ( t )] , y ( t ) = x ( t ) U ( t − 2) − Z t 2 e − t e τ x ( τ ) dτ, t > 2 (i) Rewrite y ( t ) as y ( t ) = Z ∞ −∞ [ ? ] dτ where [ ? ] is TBD (To Be Determined) — by You. (ii) Which of the following properties: L, NL, TI, TV, C, NC, are appli-cable to S . 6. A system admits the IPOP description: y ( · ) = T [ x ( · )] , y ( t ) = Z ∞ −∞ e − 2( t − σ ) U ( t − σ ) x ( σ ) dσ, t ∈ ( −∞ , ∞ ) Find y ( t ) given that: x ( t ) = e − t , t ≥ = e t , t < THE END HAPPY HOMEWORKING ! 2...
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This note was uploaded on 06/04/2009 for the course EE ee102 taught by Professor Levan during the Spring '09 term at UCLA.

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20092ee102_1_S09-102-HW-1 - ) is output. Is S : TI or TV? C...

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