30 lines
954 B
Plaintext
30 lines
954 B
Plaintext
/* libiir/src/docs/iir_structure.dox
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*
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* Copyright: ©2010, Laurence Withers.
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* Author: Laurence Withers <l@lwithers.me.uk>
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* License: GPLv3
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*/
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/*! \page iir_structure Structure of IIR filter
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For the purposes of this library, the following notation is used:
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\li <code>x(t)</code>: value of input function at time \a t (\a t = 0, 1, 2, …)
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\li <code>y(t)</code>: value of output at time \a t
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\li <code>c[n]</code>: array of \c x(t) coefficients
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\li <code>d[n]</code>: array of \c y(t) coefficients
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This leads to a general IIR filter equation:
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<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>
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For initial conditions, the library sets <code>y(t)</code> for t < 0 to 0,
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and <code>x(t)</code> for t < 0 to <code>x(0)</code>.
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*/
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/* options for text editors
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kate: replace-trailing-space-save true; space-indent true; tab-width 4;
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vim: expandtab:ts=4:sw=4:syntax=doxygen
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*/
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