102_1_102-MT-SOLS

102_1_102-MT-SOLS - UCLA DEPARTMENT OF ELECTRICAL...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UCLA DEPARTMENT OF ELECTRICAL ENGINEERING Winter 2008 Your Name (LAST, Middle, First): LEVAN n.m.i. Nhan (Fill in the following lines — if applicable) NAME OF BEST FRIEND ON YOUR LEFT : NAME OF BEST FRIEND ON YOUR RIGHT : EE102: SYSTEMS & SIGNALS February 6, 2008 MIDTERM EXAMINATION SOLUTIONS Instructions: (i) Closed Book, Calculators Are NOT Allowed (ii) Please bring your own LOOSE papers. Write On ONE Side Only (-5 points for each two-sided page) (iii) Staple These Examination Papers With Your Papers — using your own stapler (iv) Questions are equally weighted 1 QUESTION 1 t-Domain Analysis (Do NOT use Laplace Transforms ) (i) The IPOP relation of a SISO system S is: x ( t )-→ [ S ]-→ y ( t ) y ( t ) = t-∞ x ( τ ) d τ + ∞ t e t e- τ x ( τ ) d τ , t ∈ (-∞ , ∞ ) Find the IRF h ( t , τ ) of S , then state all properties of the system (no proof is required). Find the USR (Unit Step Response) g ( t ) of S . —————————————- SOLS (i) y ( t ) = t-∞ x ( τ ) d τ + ∞ t e t e- τ x ( τ ) d τ , = ∞-∞ [ U ( t- τ ) + e ( t- τ ) U (- ( t- τ ) ) ] x ( τ ) d τ ∴ h ( t- τ ) = U ( t- τ ) + e ( t- τ ) U (- ( t- τ ) ) (by BT) ∴ h ( t ) = U ( t ) + e t U (- t ) S : L, TI, NC By definition: g ( t ) = t-∞ U ( τ ) d τ + ∞ t e t e- τ U ( τ ) d τ , = t 1 d τ + e t ∞ t e- τ U ( τ ) d τ t 1 d τ = t U ( t ) e t ∞ t e- τ U ( τ ) d τ = e t ∞ e- τ 1 d τ = e t , for t < = e t ∞ t e- τ 1 d τ = 1 , for t ≥ 2 Finally g ( t ) = ( 1 + t ) U ( t ) + e t U (- t ) —————————————– (ii) Compute the OP y ( t ) of S given that its input x ( t ) is x ( t ) = U ( t- 4 ) , t ∈ (-∞ , ∞ ) —————————————-...
View Full Document

This homework help was uploaded on 04/01/2008 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

Page1 / 10

102_1_102-MT-SOLS - UCLA DEPARTMENT OF ELECTRICAL...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online