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Finite Differences: Some basics

Suppose we begin with the simplest possible differential equation, that relating current and voltage in an inductor:

\begin{eqnarray*}
v(t)=L\frac{di}{dt}
\end{eqnarray*}

We assume that one of the quantities, say $ i$ is provided by some source. We need to discretize this continuous time equation. First sample $ i$ at regular intervals $ nT$ (in the simplest case), to obtain a sequence $ i_{n}$ , and assume that we will be obtaining a voltage sequence $ v_{n}$ from it. There are many ways of approximating the differentiation operator;



Subsections
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``Discrete-Time Lumped Models'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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