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Unformatted text preview: he only ECSE2410 Signals & Systems Fall 2012 Graded by Jie Chen HW#2 Solutions
f. y(t) = f(cos(t)), where f(u) = u3 + u
Periodic with fundamental period
( ) ( since ( )) Also, this is an even function since ( (
) (
( 2. (20 points: 4 points each part)
a. Sketch ( ) () ( Recall from class that ( ) ). ( ), so we have 1
1/2
1 b. Sketch [ Recall from class that [ [ 0 1 [
. [ ], so we have
3 1
1 0 1 ))
( )) ( ( ))
( ) (
( ( ))
( )) ()
() ( ). ECSE2410 Signals & Systems Fall 2012 Graded by Jie Chen HW#2 Solutions
c. Evaluate et (t 2) (t 10)dt . For parts (c) and (d), we apply the rule for delta functions that
∫ () ( ) { ∫ () ( So for (c), we have
[( ∫ d. Evaluate ∫ [( 4 4 ) ( )] ) ( ∫ ) e t (t 2) (t 10)dt . (Note the limits on the integral!) ) ( )] ∫ ( ) ∫ ( ) f. Consider a discretetime function with x[2] = 5, x[1] = 2, x[3] = 3, and x[n] = 0 for all other n.
Write an expression for x[n] in terms of delta functions.
[ [ [...
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 Fall '07
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