ECE 220 Signals and Systems I
Fall 2007
Laboratory Assignment #5
Report due: November 17
Part 1: Partial Fractions by
residue
The MATLAB function
residue
computes partial fractions for Laplace transforms given
in rational form. The inputs are the numerator and denominator polynomial coefficients,
the outputs are

the poles

the partial fraction weights (the “residues”)

the constant term (in case Deg(Num)=Deg(Den)).
Residue
uses the Heaviside approach. This implies that pairs of complex poles are
handled separately, leading to complex weights. It also handles multiple poles. The
inverse Laplace transform then needs to be done “by hand”, including the conversion of
pairs of terms with complex exponentials and complex weights to real cosine and sine
functions.
To do:
a.
Familiarize yourself with the
residue
function (type
help residue
)
b.
Consider the Laplace transform
10s
2
+ 59s +75
H
1
(s) = 
s
3
+ 8s
2
+ 15s
Obtain its inverse h
1
(t) using the
residue
function. Plot h
1
(t). Compare this
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 Fall '08
 JANOS
 Fourier Series, Laplace, Leonhard Euler, function residue computes

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