libiir/src/docs/iir_structure.dox

/* libiir/src/docs/iir_structure.dox
 * 
 *  Copyright: ©2010, Laurence Withers.
 *  Author: Laurence Withers <l@lwithers.me.uk>
 *  License: GPLv3
*/

/*! \page iir_structure Structure of IIR filter

For the purposes of this library, the following notation is used:

\li <code>x(t)</code>: value of input function at time \a t (\a t = 0, 1, 2, …)
\li <code>y(t)</code>: value of output at time \a t
\li <code>c[n]</code>: array of \c x(t) coefficients
\li <code>d[n]</code>: array of \c y(t) coefficients

This leads to a general IIR filter equation:

<code>y(t) = x(t).c[0] + x(t-1).c[1] + … + x(t-N).c[N] - y(t-1).d[0] - y(t-2).d[1] - … - y(t-1-M).d[M]</code>

For initial conditions, the library sets <code>y(t)</code> for t &lt; 0 to
<code>x(0).G</code> (where <code>G</code> is the DC gain of the filter, or 0 if
it looks like the filter is unstable at DC), and <code>x(t)</code> for t &lt; 0
to <code>x(0)</code>.

*/

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