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lab 2 - ECE 101 Linear Systems Winter 2009 Lab 2...

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ECE 101 - Linear Systems, Winter 2009 Lab # 2 Solutions (send comments/questions to [email protected]) Problem 1 The plot for this problem is: 0 2 4 6 8 10 12 14 16 -1 0 1 n y a conv(x 1 ,h 1 ) 0 2 4 6 8 10 12 14 16 -5 0 5 n b conv(x 1 ,h 2 ) The effect of a shifted impulse response δ [ n - n 0 ] is to shift the original input x [ n ] by an amount n = n 0 . Problem 2 The plot for this problem is: 0 5 10 -2 0 2 n (a) x1 0 5 10 -2 0 2 n (b) 0 5 10 15 -4 -2 0 2 4 n (c) x2 0 5 10 15 -5 0 5 n (d) In problem 1 we established that if h [ n ] = δ [ n - n 0 ], it will shift the 1
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original input x [ n ] by an amount n = n 0 . It follows that if the input x [ n ] is an alternation of 1 and - 1 (figure a), and h [ n ] = δ [ n ] + delta [ n - 1], then by superposition the shifted solutions will cancel, except at the edges of the data (figure b). Figures (c) and (d) are an additional variation on this theme. Two copies of the input (c) are superimposed, the second copy also being reversed in sign, generating figure (d). Problem 3
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