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# hw2 - -2 ≤ n ≤ 3 Part a x n = U n 2-2 U n U n-1 Part b...

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ECE 301 HW2 Due: 6/21/11 Problem 1 Consider the two functions f ( t ) and g ( t ) described below. f ( t ) = U ( t + 1) - U ( t - 1) g ( t ) = cos ( πt ) U (3 - t ) Now, define a new function, h ( t ) = R -∞ f ( s ) g ( t - s ) ds . Plot h ( t ) as a function of t. Problem 2 Part a: Compute the energies of the three functions from Problem 1. State whether they are finite or infinite. Part b: Compute the powers of the three functions from Problem 2. State whether they are finite or infinite. Problem 3 Define the three signals below. x 1 ( t ) = e - 1 - 2 jt x 2 ( t ) = cos t + π 4 x 3 ( t ) = e -| t - 1 | Find the energy and average power for x 1 ( t ), x 2 ( t ), and x 3 ( t ). Problem 4 Page 59, Problem 1.21 (e),(f) 1

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Problem 5 Page 59, Problem 1.22 (f), (h) Problem 6 Page 61, Problem 1.25 (e), (f) Problem 7 Sketch each signal for
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Unformatted text preview: -2 ≤ n ≤ 3. Part a: x [ n ] = U [ n + 2]-2 U [ n ] + U [ n-1] Part b: x [ n ] = ( n + 1) U [ n + 1]-2 U [ n ]-( n-1) U [ n-3] Part c: x [ n ] = δ [ n ]-δ [ n-1] + U [ n-2]-U [ n + 1] Problem 8 Part a: Any discrete-time signal can be expressed as x [ n ] = ∞ X k =-∞ α k δ [ n-k ] Find the coeﬃcients, α k . (Hint: we did this in class) Part b: x [ n ] can also be expressed as a sum of unit-step functions x [ n ] = ∞ X k =-∞ β k U [ n-k ] Find the coeﬃcints, β k . (Hint: δ [ n ] and U [ n ] are related). Problem 9 Problem 1.27 (a), (b), (c) 2...
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hw2 - -2 ≤ n ≤ 3 Part a x n = U n 2-2 U n U n-1 Part b...

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