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# hw1 - ∑ ∞ k =0 ± 1 2 ² k e-j 5 k Hint ∑ ∞ n =0 r...

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ECE 301 HW1: Math Review Due: 6/15/11 Problem 1 Compute the following integrals: R 3 π π cos ± t + 2 ² dt R π - π sin 2 (3 s ) ds R 1 0 R 2 1 cos ± π ( x + y ) 12 ² dxdy Problem 2 Compute the following integrals: R -∞ e -| x | dx R π - π ωsin ( ω ) R 1 - 1 (1 - y 2 ) e jπy dy Problem 3 Suppose f ( t ) = tcos ( πt ). Let g ( t ) = f (1 - 2 t ). Part a: Find g ( t ). Part b: Compute Z 3 0 g (1 + s ) ds 1

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Problem 4 Suppose f ( t ) = | t - 1 | . Let g ( t ) = Z t +2 t - 3 f ( s ) ds Part a: Compute g (3). Part b: Compute R 5 2 g ( s ) ds Part c: Compute R 4 - 2 g ( s ) f (1 - s ) ds Problem 5 Compute
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Unformatted text preview: ∑ ∞ k =0 ± 1 2 ² k e-j 5 k . Hint: ∑ ∞ n =0 r k = 1 1-r if | r | < 1. Problem 6 Suppose f [ n ] = | n | . Let g [ n ] = f [ n-1]-f [ n + 1]. Part a: Compute g [3]. Part b: Compute ∑ 5 n =0 g [ n ]. Problem 7 Compute the partial fraction decomposition of 2-x 1-x-20 x 2 2...
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hw1 - ∑ ∞ k =0 ± 1 2 ² k e-j 5 k Hint ∑ ∞ n =0 r...

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