IIRFilter.h

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/*
*  Copyright (C) 2007 Jolien Creighton, Teviet Creighton
*
*  This program is free software; you can redistribute it and/or modify
*  it under the terms of the GNU General Public License as published by
*  the Free Software Foundation; either version 2 of the License, or
*  (at your option) any later version.
*
*  This program is distributed in the hope that it will be useful,
*  but WITHOUT ANY WARRANTY; without even the implied warranty of
*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
*  GNU General Public License for more details.
*
*  You should have received a copy of the GNU General Public License
*  along with with program; see the file COPYING. If not, write to the
*  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
*  MA  02110-1301  USA
*/
 
#ifndef _IIRFILTER_H
#define _IIRFILTER_H
 
#include <lal/LALStdlib.h>
#include <lal/ZPGFilter.h>
 
#if defined(__cplusplus)
extern "C" {
#elif 0
} /* so that editors will match preceding brace */
#endif
 
/**
 * \defgroup IIRFilter_h Header IIRFilter.h
 * \ingroup lal_tdfilter
 * \author Creighton, T. D.
 *
 * \brief Provides routines to make and apply IIR filters.
 *
 * ### Synopsis ###
 *
 * \code
 * #include <lal/IIRFilter.h>
 * \endcode
 *
 * The \ref IIRFilter_h provides routines for creating actual
 * time-domain filters from the ZPG representation, and applying these
 * filters to data.
 *
 * This header covers routines that create, destroy, and apply
 * generic time-domain filters, given by objects of type
 * <tt><datatype>IIRFilter</tt>, where <tt><datatype></tt> is either
 * \c REAL4 or \c REAL8.
 *
 * An IIR (Infinite Impulse Response) filter is a generalized linear
 * causal time-domain filter, in which the filter output \f$y_n=y(t_n)\f$ at
 * any sampled time \f$t_n=t_0+n\Delta t\f$ is a linear combination of the
 * input \f$x\f$ \e and output \f$y\f$ at previous sampled times:
 * \f[
 * y_n = \sum_{k=0}^M c_k x_{n-k} + \sum_{l=1}^N d_l y_{n-l} \; .
 * \f]
 * The coefficients \f$c_k\f$ are called the direct filter coefficients, and
 * the coefficients \f$d_l\f$ are the recursive filter coefficients.  The
 * filter order is the larger of \f$M\f$ or \f$N\f$, and determines how far back
 * in time the filter must look to determine its next output.  However,
 * the recursive nature of the filter means that the output can depend on
 * input arbitrarily far in the past; hence the name "infinite impulse
 * response".  Nonetheless, for a well-designed, stable filter, the
 * actual filter response to an impulse should diminish rapidly beyond
 * some characteristic timescale.
 *
 * Note that nonrecursive FIR (Finite Impulse Response) filters are
 * considered a subset of IIR filters, having \f$N=0\f$.
 *
 * For practical implementation, it is convenient to express the bilinear
 * equation above as two linear equations involving an auxiliary sequence
 * \f$w\f$:
 * \f[
 * w_n = x_n + \sum_{l=1}^N d_l w_{n-l} \; ,
 * \f]
 * \f[
 * y_n = \sum_{k=0}^M c_k w_{n-k} \; .
 * \f]
 * The equivalence of this to the first expression is not obvious, but
 * can be proven by mathematical induction.  The advantage of the
 * auxiliary variable representation is twofold.  First, when one is
 * feeding data point by point to the filter, the filter needs only
 * "remember" the previous \f$M\f$ or \f$N\f$ (whichever is larger) values of
 * \f$w\f$, rather than remembering the previous \f$M\f$ values of \f$x\f$ \e and
 * the previous \f$N\f$ values of \f$y\f$.  Second, when filtering a large stored
 * data vector, the filter response can be computed in place: one first
 * runs forward through the vector replacing \f$x\f$ with \f$w\f$, and then
 * backward replacing \f$w\f$ with \f$y\f$.
 *
 * Although the IIR filters in these routines are explicitly real, one
 * can consider formally their complex response.  A sinusoidal input can
 * thus be written as \f$x_n=X\exp(2\pi ifn\Delta t)=Xz^n\f$, where \f$X\f$ is a
 * complex amplitude and \f$z=\exp(2\pi if\Delta t)\f$ is a complex
 * parametrization of the frequency.  By linearity, the output must also
 * be sinusoidal: \f$y_m=Y\exp(2\pi ifm\Delta t)=Yz^m\f$.  Putting these into
 * the bilinear equation, one can easily compute the filter's complex
 * transfer function:
 * \f[
 * T(z) = \frac{Y}{X} = \frac{\sum_{k=0}^M c_k z^{-k}}
 * {1 - \sum_{l=1}^N d_l z^{-l}}
 * \f]
 * This can be readily converted to and from the "zeros, poles, gain"
 * representation of a filter, which expresses \f$T(z)\f$ as a factored
 * rational function of \f$z\f$.
 *
 * It should also be noted that, in the routines covered by this header,
 * I have adopted the convention of including a redundant recursive
 * coefficient \f$d_0\f$, in order to make the indexing more intuitive.  For
 * formal correctness \f$d_0\f$ should be set to \f$-1\f$, although the filtering
 * routines never actually use this coefficient.
 *
 */
/** @{ */
 
/**
 * @{
 * \defgroup CreateIIRFilter_c  Module CreateIIRFilter.c
 * \defgroup DestroyIIRFilter_c         Module DestroyIIRFilter.c
 * \defgroup IIRFilter_c                Module IIRFilter.c
 * \defgroup IIRFilterVector_c  Module IIRFilterVector.c
 * \defgroup IIRFilterVectorR_c         Module IIRFilterVectorR.c
 * @}
 */
 
/** \name Error Codes */
/** @{ */
#define IIRFILTERH_ENUL  1      /**< Unexpected null pointer in arguments */
#define IIRFILTERH_EOUT  2      /**< Output handle points to a non-null pointer */
#define IIRFILTERH_EMEM  3      /**< Memory allocation error */
#define IIRFILTERH_EPAIR 4      /**< Input has unpaired nonreal poles or zeros */
/** @} */
 
/** \cond DONT_DOXYGEN */
#define IIRFILTERH_MSGENUL  "Unexpected null pointer in arguments"
#define IIRFILTERH_MSGEOUT  "Output handle points to a non-null pointer"
#define IIRFILTERH_MSGEMEM  "Memory allocation error"
#define IIRFILTERH_MSGEPAIR "Input has unpaired nonreal poles or zeros"
/** \endcond */
 
/**
 * This structure stores the direct and recursive REAL4 filter coefficients, as
 * well as the history of the auxiliary sequence \f$w\f$.
 * The length of the history vector gives the order of the filter
 */
#ifdef SWIG /* SWIG interface directives */
SWIGLAL(IMMUTABLE_MEMBERS(tagREAL4IIRFilter, name));
#endif /* SWIG */
typedef struct tagREAL4IIRFilter{
  const CHAR *name;        /**< User assigned name. */
  REAL8 deltaT;            /**< Sampling time interval of the filter; If \f$\leq0\f$, it will be ignored (ie it will be taken from the data stream) */
  REAL4Vector *directCoef; /**< The direct filter coefficients. */
  REAL4Vector *recursCoef; /**< The recursive filter coefficients. */
  REAL4Vector *history;    /**< The previous values of w. */
} REAL4IIRFilter;
 
/**
 * This structure stores the direct and recursive REAL8 filter coefficients, as
 * well as the history of the auxiliary sequence \f$w\f$.
 * The length of the history vector gives the order of the filter
 */
#ifdef SWIG /* SWIG interface directives */
SWIGLAL(IMMUTABLE_MEMBERS(tagREAL8IIRFilter, name));
#endif /* SWIG */
typedef struct tagREAL8IIRFilter{
  const CHAR *name;        /**< User assigned name. */
  REAL8 deltaT;            /**< Sampling time interval of the filter; If \f$\leq0\f$, it will be ignored (ie it will be taken from the data stream). */
  REAL8Vector *directCoef; /**< The direct filter coefficients. */
  REAL8Vector *recursCoef; /**< The recursive filter coefficients. */
  REAL8Vector *history;    /**< The previous values of w. */
} REAL8IIRFilter;
 
/**
 * This structure stores the direct and recursive REAL8 filter coefficients, as
 * well as the complex-valued history of the auxiliary sequence \f$w\f$.
 * The length of the history vector gives the order of the filter
 */
#ifdef SWIG /* SWIG interface directives */
SWIGLAL(IMMUTABLE_MEMBERS(tagCOMPLEX16IIRFilter, name));
#endif /* SWIG */
typedef struct tagCOMPLEX16IIRFilter{
  const CHAR *name;        /**< User assigned name. */
  REAL8 deltaT;            /**< Sampling time interval of the filter; If \f$\leq0\f$, it will be ignored (ie it will be taken from the data stream). */
  REAL8Vector *directCoef; /**< The direct filter coefficients. */
  REAL8Vector *recursCoef; /**< The recursive filter coefficients. */
  COMPLEX16Vector *history;    /**< The previous values of w. */
} COMPLEX16IIRFilter;
 
/** @} */
 
/* Function prototypes. */
REAL4IIRFilter *XLALCreateREAL4IIRFilter( COMPLEX8ZPGFilter *input );
REAL8IIRFilter *XLALCreateREAL8IIRFilter( COMPLEX16ZPGFilter *input );
COMPLEX16IIRFilter *XLALCreateCOMPLEX16IIRFilter( COMPLEX16ZPGFilter *input );
void XLALDestroyREAL4IIRFilter( REAL4IIRFilter *filter );
void XLALDestroyREAL8IIRFilter( REAL8IIRFilter *filter );
void XLALDestroyCOMPLEX16IIRFilter( COMPLEX16IIRFilter *filter );
 
int XLALIIRFilterREAL4Vector( REAL4Vector *vector, REAL8IIRFilter *filter );
int XLALIIRFilterREAL8Vector( REAL8Vector *vector, REAL8IIRFilter *filter );
int XLALIIRFilterCOMPLEX8Vector( COMPLEX8Vector *vector, COMPLEX16IIRFilter *filter );
int XLALIIRFilterCOMPLEX16Vector( COMPLEX16Vector *vector, COMPLEX16IIRFilter *filter );
int XLALIIRFilterReverseREAL4Vector( REAL4Vector *vector, REAL8IIRFilter *filter );
int XLALIIRFilterReverseREAL8Vector( REAL8Vector *vector, REAL8IIRFilter *filter );
int XLALIIRFilterReverseCOMPLEX8Vector( COMPLEX8Vector *vector, COMPLEX16IIRFilter *filter );
int XLALIIRFilterReverseCOMPLEX16Vector( COMPLEX16Vector *vector, COMPLEX16IIRFilter *filter );
 
REAL4 XLALIIRFilterREAL4( REAL4 x, REAL8IIRFilter *filter );
REAL8 XLALIIRFilterREAL8( REAL8 x, REAL8IIRFilter *filter );
/* WARNING: THIS FUNCTION IS OBSOLETE */
REAL4 LALSIIRFilter( REAL4 x, REAL4IIRFilter *filter );
/* REAL8 LALDIIRFilter( REAL8 x, REAL8IIRFilter *filter ); */
#define LALDIIRFilter(x,f) XLALIIRFilterREAL8(x,f)
 
 
 
/* ----- CreateIIRFilter.c ---------- */
void
LALCreateREAL4IIRFilter( LALStatus         *status,
                         REAL4IIRFilter    **output,
                         COMPLEX8ZPGFilter *input );
 
void
LALCreateREAL8IIRFilter( LALStatus          *status,
                         REAL8IIRFilter     **output,
                         COMPLEX16ZPGFilter *input );
 
/* ----- DestroyIIRFilter.c ---------- */
void
LALDestroyREAL4IIRFilter( LALStatus      *status,
                          REAL4IIRFilter **input );
 
void
LALDestroyREAL8IIRFilter( LALStatus      *status,
                          REAL8IIRFilter **input );
 
/* ----- IIRFilter.c ---------- */
void
LALIIRFilterREAL4( LALStatus      *status,
                   REAL4          *output,
                   REAL4          input,
                   REAL4IIRFilter *filter );
 
void
LALIIRFilterREAL8( LALStatus      *status,
                   REAL8          *output,
                   REAL8          input,
                   REAL8IIRFilter *filter );
 
/* ----- IIRFilterVector.c ---------- */
void
LALIIRFilterREAL4Vector( LALStatus      *status,
                         REAL4Vector    *vector,
                         REAL4IIRFilter *filter );
 
void
LALIIRFilterREAL8Vector( LALStatus      *status,
                         REAL8Vector    *vector,
                         REAL8IIRFilter *filter );
 
void
LALDIIRFilterREAL4Vector( LALStatus      *status,
                          REAL4Vector    *vector,
                          REAL8IIRFilter *filter );
 
/* ----- IIRFilterVectorR.c ---------- */
void
LALIIRFilterREAL4VectorR( LALStatus      *status,
                          REAL4Vector    *vector,
                          REAL4IIRFilter *filter );
 
void
LALIIRFilterREAL8VectorR( LALStatus      *status,
                          REAL8Vector    *vector,
                          REAL8IIRFilter *filter );
 
void
LALDIIRFilterREAL4VectorR( LALStatus      *status,
                           REAL4Vector    *vector,
                           REAL8IIRFilter *filter );
 
 
#if 0
{ /* so that editors will match succeeding brace */
#elif defined(__cplusplus)
}
#endif
 
#endif /* _IIRFILTER_H */