# 4 - h 2 n guaranteed to be zero 3 ±ind the discrete-time...

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Cauley September 20, 2009 ECE301 Homework #4 Due: September 29, 2009 1. (a) x 1 ( t ) is defined to be non-zero for only t = 0. h 1 ( t ) is defined to be non-zero for only 0 < t - 2 < 2. Over what range of values of t is x 1 ( t ) * h 1 ( t ) guaranteed to be zero? (b) x 2 ( t ) is defined to be non-zero for only 0 < 2 t - 3 < 5. h 2 ( t ) is defined to be non-zero for only 0 < t < 2. Over what range of values of t is x 2 ( t ) * h 2 ( t ) guaranteed to be zero? 2. (a) x 1 [ n ] is defined to be non-zero for only n = 2. h 1 [ n ] is defined to be non-zero for only - 7 n - 2 3. Over what range of values of n is x 1 [ n ] * h 1 [ n ] guaranteed to be zero? (b) x 2 [ n ] is defined to be non-zero for only - 2 n - 2 5. h 2 [ n ] is defined to be non-zero for only - 5 n + 2 < - 2. Over what range of values of
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Unformatted text preview: ] * h 2 [ n ] guaranteed to be zero? 3. ±ind the discrete-time convolution y [ n ] = x [ n ] * h [ n ], where: x [ n ] = u [ n + 2]-u [ n-4] + δ [ n-6] , h [ n ] = u [ n + 1] + 3 u [ n-2]-5 u [ n-4] + u [ n-6] . 4. ±ind the continuous-time convolution y ( t ) = x ( t ) * h ( t ) where: x ( t ) = 3 2 t + 6 ,-4 < t ≤ -2 , 3 ,-2 < t ≤ 2 ,-3 2 t + 6 , 2 < t ≤ 4 , , otherwise. h ( t ) = 1 ,-1 < t ≤ 1 ,-1 , 1 < t ≤ 3 , , otherwise. 5. Problems 3.1, 3.3, and 3.4 From the class text....
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