If you are given a Laplace transform F(s) where the degree of the numerator is equal to the degree of the denominator, what is the first step in finding the inverse transform?
Explanation
For a Laplace transform F(s) = N(s)/D(s), the technique of partial fraction expansion is only directly applicable if F(s) is a proper rational function, meaning degree(N) < degree(D). If degree(N) >= degree(D), the first step is to perform polynomial long division. This separates F(s) into a polynomial part (whose inverse transform includes impulses and their derivatives) and a proper rational function remainder, which can then be handled with partial fractions.
Other questions
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