Partial Fraction Expansion in MATLAB

Question

I am to use MATLAB to find the partial fraction expansion of the following function. Can this be done in that format or do I have to manipulate the function?

Note: This must be done using pure MATLAB only. No add-ons or anything like that. Not even Math Toolbox.

Answer 1

The matlab function residue does the job. For multiplication of the polynomial roots to convert to standard form use conv:

b = 1e4*conv( [1 5], [1 70] );
a = conv( [1 0], conv([1 45], conv([1 55], conv([1 7 110],[1 6 95]) ) ) );

[r, p, k] = residue(b,a);

with r, p and k containing the partial fraction decomposition:

$\frac{b(s)}{a(s)} = k + \sum_i \frac{r_i}{s - p_i}$

check also documentation of the residue function. It is part of the base package and does not need toolboxes.