and odd since this is the only ecse 2410 signals

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Unformatted text preview: he only ECSE-2410 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 )) ( )) ( ( )) ( ) ( ( ( )) ( )) () () ( ). ECSE-2410 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 discrete-time 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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