Homework5 - Homework 5 ECE 220 Due Tuesday 1 Express each...

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= 0 ) ( ) 2 ( 1 . 0 t e t h Homework 5 ECE 220 Due: Tuesday, April 19, 2005 1. Express each of the following in a simpler form: (a) ( ) ) 20 cos( ) ( 2 ) 2 ( ) 5 ( π δ δ t t u e t t t + + + note: convolution is denoted by the symbol (b) ( ) ) 2 ( ) 2 ( 2 t u e dt d t (c) 5 ) 1 ( t d τ τ δ (d) ) ( ) 2 ( ) 1 ( t t t δ δ δ CD: Simplify expressions with impulses 2. Use linearity and time-invariance to convolve the following two rectangular pulses x(t) = 2u(t) – 2u(t-2) h(t) = 3u(t-5) – 3u(t-1) (a) Expand the convolution into four terms and exploit the result from Example 9-9 in the textbook to get ) ( ) ( ) ( t x t h t y = . (b) Write y(t) as separate cases over five different regions of the time axis. (c) Make a plot of y(t) versus t. 3. The impulse response of a LIT system is 2 t < 12 otherwise (a) Is the system stable? Justify your answer. (b) Is the system causal? Justify your answer. (c) Find y(t) when the input is x(t) = δ (t-2).
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