20082ee102_1_102_hw1

20082ee102_1_102_hw1 - Spring Put First Letter of LAST Name...

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Unformatted text preview: Spring Put First Letter of LAST Name in the corner→→→__ Spring 2008 Name (Print)(LAST, Middle, First):_______________________ Name (Print) ID: _______________________ Student ID EE102: SYSTEMS & SIGNALS HW: HW: # 1 LATE A LATE HW IS NOT A HW! Due in class: April 10. class: Attach This Sheet To Your HW Each problem has 10 points. The maximum scores is 60 points. 1. Given z=1+i and w=3-4i. (i) Compute the real part and the imaginary part of : z , and zw w (ii) Re{is } = ? and Im{is } = ? , where s is a complex number and s is the ( z − w)2 , Complex conjugate of s. 2. Consider the differential equation: dy (t ) dx(t ) + y (t ) = − 2 x(t ), t ≥ 0, dt dt y (0) = 0, x(0) = 0. (i) Solve for y(t) in terms of x(t). (ii) Find y(t) given that x(t ) = (t − 1)e − t for t>0. 3. A system S is described by the following IPOP description: y (t ) = T [ x(t )], y (t ) = ∫ e − t eτ x(τ )dτ , t > −∞ −∞ t where x(.) is input and y(.) is output. Is this system L or NL, TI or TV? 4. A system has the IPOP description: y (.) = T [ x(.)], y (t ) = x(t ) − 2 ∫ et e−σ x(σ )dσ , t > −∞ t ∞ (i) Rewrite y(t) as y (t ) = ∫ [?]dσ , −∞ ∞ where [?] is to be determined. (ii) State all properties of the system (L, NL, TI, TV, C, NC). 1 (iii) Find y(.) given that x(t ) = tU (t ) 5. Sketch the following functions: (i) f (t ) = U (t − 2)U (σ − t ) (ii) g (t ) = U (−t )U (t + 1) . 6. Compute ∫ ∞ −∞ δ (t − σ ) − 2e − (t −σ )U (t − σ ) × δ (τ − σ ) − e − (τ −σ )U (τ − σ ) dσ for −∞ < t ,τ < ∞ . 2 ...
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20082ee102_1_102_hw1 - Spring Put First Letter of LAST Name...

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