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e6exam1secBsolnsF06

# e6exam1secBsolnsF06 - Engineering 6 Fall 2006 Midterm...

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Note that the residues are still all different. If there were three repeated roots, then you would have a term with a 3 2 ) ( r x - denominator, and so on. Third key part (3 points): In Matlab, the residue function calculates the residues and roots for us, i.e., [c r] = residue(a,b) where a and b are the coefficient polynomials of A(x) and B(x) and c is a vector with the residues and r is a vector with the roots. Fourth key part (3 points): If the order of A is greater than or equal to the order of B (an “improper rational function”), then we can’t use the partial fraction expansion directly. Instead we have to write the ratio as a quotient plus a remainder term, and then rewrite the remainder term (which is guaranteed to be a proper rational function) as a partial fraction expansion. That is: ) ( ) ( ) ( ) ( ) ( x B x R x Q x B x A + = , where the second term is the remainder term
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e6exam1secBsolnsF06 - Engineering 6 Fall 2006 Midterm...

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