/*****************************************************************************
-** FILE IDENTIFICATION
+** File IDENTIFICATION
**
** Name: filter.cpp
** Purpose: Routines for signal-procesing filters
** Date Started: Aug 1984
**
** This is part of the CTSim program
-** Copyright (C) 1983-2000 Kevin Rosenberg
+** Copyright (c) 1983-2000 Kevin Rosenberg
**
-** $Id: filter.cpp,v 1.4 2000/06/25 17:32:24 kevin Exp $
+** $Id: filter.cpp,v 1.36 2001/02/11 04:56:37 kevin Exp $
**
** This program is free software; you can redistribute it and/or modify
** it under the terms of the GNU General Public License (version 2) as
#include "ct.h"
+int SignalFilter::N_INTEGRAL=500; //static member
+
+const int SignalFilter::FILTER_INVALID = -1 ;
+const int SignalFilter::FILTER_ABS_BANDLIMIT = 0; // filter times |x|
+const int SignalFilter::FILTER_ABS_G_HAMMING = 1;
+const int SignalFilter::FILTER_ABS_COSINE = 2;
+const int SignalFilter::FILTER_ABS_SINC = 3;
+const int SignalFilter::FILTER_SHEPP = 4;
+const int SignalFilter::FILTER_BANDLIMIT = 5;
+const int SignalFilter::FILTER_SINC = 6;
+const int SignalFilter::FILTER_G_HAMMING = 7;
+const int SignalFilter::FILTER_COSINE = 8;
+const int SignalFilter::FILTER_TRIANGLE = 9;
+
+const int SignalFilter::s_iReconstructFilterCount = 5;
+
+const char* SignalFilter::s_aszFilterName[] = {
+ {"abs_bandlimit"},
+ {"abs_hamming"},
+ {"abs_cosine"},
+ {"abs_sinc"},
+ {"shepp"},
+ {"bandlimit"},
+ {"sinc"},
+ {"hamming"},
+ {"cosine"},
+ {"triangle"},
+};
+
+const char* SignalFilter::s_aszFilterTitle[] = {
+ {"Abs(w) * Bandlimit"},
+ {"Abs(w) * Hamming"},
+ {"Abs(w) * Cosine"},
+ {"Abs(w) * Sinc"},
+ {"Shepp"},
+ {"Bandlimit"},
+ {"Sinc"},
+ {"Hamming"},
+ {"Cosine"},
+ {"Triangle"},
+};
+
+const int SignalFilter::s_iFilterCount = sizeof(s_aszFilterName) / sizeof(const char*);
+
+
+const int SignalFilter::DOMAIN_INVALID = -1;
+const int SignalFilter::DOMAIN_FREQUENCY = 0;
+const int SignalFilter::DOMAIN_SPATIAL = 1;
+
+const char* SignalFilter::s_aszDomainName[] = {
+ {"frequency"},
+ {"spatial"},
+};
+
+const char* SignalFilter::s_aszDomainTitle[] = {
+ {"Frequency"},
+ {"Spatial"},
+};
+
+const int SignalFilter::s_iDomainCount = sizeof(s_aszDomainName) / sizeof(const char*);
+
/* NAME
* SignalFilter::SignalFilter Construct a signal
*
* SYNOPSIS
- * f = SignalFilter (filt_type, bw, xmin, xmax, n, param, domain, analytic)
+ * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic)
* double f Generated filter vector
* int filt_type Type of filter wanted
* double bw Bandwidth of filter
- * double xmin, xmax Filter limits
- * int n Number of points in filter
+ * double filterMin, filterMax Filter limits
+ * int nFilterPoints Number of points in signal
* double param General input parameter to filters
- * int domain FREQ or SPATIAL domain wanted
- * int numint Number if intervals for calculating discrete inverse fourier xform
- * for spatial domain filters. For ANALYTIC solutions, use numint = 0
+ * int domain FREQUENCY or SPATIAL domain wanted
*/
-SignalFilter::SignalFilter (const char* filterName, double bw, double xmin, double xmax, int n, double param, const char* domainName, int numIntegral = 0)
+SignalFilter::SignalFilter (const char* szFilterName, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const char* szDomainName)
+ : m_adFilter(NULL), m_fail(false)
{
- m_vecFilter = NULL;
- m_idFilter = convertFilterNameToID (filterName);
+ m_idFilter = convertFilterNameToID (szFilterName);
if (m_idFilter == FILTER_INVALID) {
m_fail = true;
m_failMessage = "Invalid Filter name ";
- m_failMessage += filterName;
+ m_failMessage += szFilterName;
return;
}
- m_idDomain = convertDomainNameToID (domainName);
+ m_idDomain = convertDomainNameToID (szDomainName);
if (m_idDomain == DOMAIN_INVALID) {
m_fail = true;
m_failMessage = "Invalid domain name ";
- m_failMessage += domainName;
+ m_failMessage += szDomainName;
return;
}
- init (m_idFilter, bw, xmin, xmax, n, param, m_idDomain, numIntegral);
+ init (m_idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, m_idDomain);
}
-SignalFilter::SignalFilter (const FilterID filterID, double bw, double xmin, double xmax, int n, double param, const DomainID domainID, int numIntegral = 0)
+SignalFilter::SignalFilter (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
+ : m_adFilter(NULL), m_fail(false)
{
- init (filterID, bw, xmin, xmax, n, param, domainID, numIntegral);
+ init (idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, idDomain);
}
-SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param, int numIntegral = 0)
+SignalFilter::SignalFilter (const char* szFilterName, const char* szDomainName, double dBandwidth, double dFilterParam)
+ : m_adFilter(NULL), m_fail(false)
{
- m_bw = bw;
- m_nPoints = 0;
- m_vecFilter = NULL;
- m_filterParam = param;
- m_numIntegral = numIntegral;
- m_idFilter = convertFilterNameToID (filterName);
+ m_nFilterPoints = 0;
+ m_dBandwidth = dBandwidth;
+ m_dFilterParam = dFilterParam;
+ m_idFilter = convertFilterNameToID (szFilterName);
if (m_idFilter == FILTER_INVALID) {
m_fail = true;
m_failMessage = "Invalid Filter name ";
- m_failMessage += filterName;
+ m_failMessage += szFilterName;
return;
}
- m_idDomain = convertDomainNameToID (domainName);
+ m_idDomain = convertDomainNameToID (szDomainName);
if (m_idDomain == DOMAIN_INVALID) {
m_fail = true;
m_failMessage = "Invalid domain name ";
- m_failMessage += domainName;
+ m_failMessage += szDomainName;
return;
}
}
void
-SignalFilter::init (const FilterID filterID, double bw, double xmin, double xmax, int n, double param, const DomainID domainID, int numint)
+SignalFilter::init (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
{
- m_bw = bw;
- m_idFilter = filterID;
- m_idDomain = domainID;
+ m_idFilter = idFilter;
+ m_idDomain = idDomain;
if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID) {
m_fail = true;
return;
}
+ if (nFilterPoints < 2) {
+ m_fail = true;
+ m_failMessage = "Number of filter points ";
+ m_failMessage += nFilterPoints;
+ m_failMessage = " less than 2";
+ return;
+ }
+
m_nameFilter = convertFilterIDToName (m_idFilter);
m_nameDomain = convertDomainIDToName (m_idDomain);
- m_fail = false;
- m_nPoints = n;
- m_xmin = xmin;
- m_xmax = xmax;
- m_numIntegral = numint;
- m_filterParam = param;
- m_vecFilter = new double[n];
+ m_nFilterPoints = nFilterPoints;
+ m_dFilterParam = dFilterParam;
+ m_dBandwidth = dBandwidth;
+ m_dFilterMin = dFilterMinimum;
+ m_dFilterMax = dFilterMaximum;
+
+ m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
+ m_adFilter = new double [m_nFilterPoints];
+
+ if (m_idDomain == DOMAIN_FREQUENCY)
+ createFrequencyFilter (m_adFilter);
+ else if (m_idDomain == DOMAIN_SPATIAL)
+ createSpatialFilter (m_adFilter);
+}
- double xinc = (m_xmax - m_xmin) / (m_nPoints - 1);
+SignalFilter::~SignalFilter (void)
+{
+ delete [] m_adFilter;
+}
+
+void
+SignalFilter::createFrequencyFilter (double* adFilter) const
+{
+ double x;
+ int i;
+ for (x = m_dFilterMin, i = 0; i < m_nFilterPoints; x += m_dFilterInc, i++)
+ adFilter[i] = frequencyResponse (x);
+}
+
+
+void
+SignalFilter::createSpatialFilter (double* adFilter) const
+{
if (m_idFilter == FILTER_SHEPP) {
- double a = 2 * m_bw;
+ double a = 2 * m_dBandwidth;
double c = - 4. / (a * a);
- int center = (m_nPoints - 1) / 2;
+ int center = (m_nFilterPoints - 1) / 2;
int sidelen = center;
- m_vecFilter[center] = 4. / (a * a);
-
+ m_adFilter[center] = 4. / (a * a);
+
for (int i = 1; i <= sidelen; i++ )
- m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1);
- } else if (m_idDomain == DOMAIN_FREQ) {
- double x;
- int i;
- for (x = m_xmin, i = 0; i < m_nPoints; x += xinc, i++)
- m_vecFilter[i] = frequencyResponse (x, param);
- } else if (m_idDomain == DOMAIN_SPATIAL) {
- double x;
- int i;
- for (x = m_xmin, i = 0; i < m_nPoints; x += xinc, i++)
- if (numint == 0)
- m_vecFilter[i] = spatialResponseAnalytic (x, param);
- else
- m_vecFilter[i] = spatialResponseCalc (x, param, numint);
+ m_adFilter [center + i] = m_adFilter [center - i] = c / (4 * (i * i) - 1);
} else {
- m_failMessage = "Illegal domain name ";
- m_failMessage += m_idDomain;
- m_fail = true;
+ double x = m_dFilterMin;
+ for (int i = 0; i < m_nFilterPoints; i++, x += m_dFilterInc) {
+ if (haveAnalyticSpatial(m_idFilter))
+ m_adFilter[i] = spatialResponseAnalytic (x);
+ else
+ m_adFilter[i] = spatialResponseCalc (x);
+ }
}
}
-SignalFilter::~SignalFilter (void)
-{
- delete m_vecFilter;
-}
-
-
-SignalFilter::FilterID
+int
SignalFilter::convertFilterNameToID (const char *filterName)
{
- FilterID filterID = FILTER_INVALID;
-
- if (strcasecmp (filterName, FILTER_BANDLIMIT_STR) == 0)
- filterID = FILTER_BANDLIMIT;
- else if (strcasecmp (filterName, FILTER_HAMMING_STR) == 0)
- filterID = FILTER_G_HAMMING;
- else if (strcasecmp (filterName, FILTER_SINC_STR) == 0)
- filterID = FILTER_SINC;
- else if (strcasecmp (filterName, FILTER_COS_STR) == 0)
- filterID = FILTER_COSINE;
- else if (strcasecmp (filterName, FILTER_TRIANGLE_STR) == 0)
- filterID = FILTER_TRIANGLE;
- else if (strcasecmp (filterName, FILTER_ABS_BANDLIMIT_STR) == 0)
- filterID = FILTER_ABS_BANDLIMIT;
- else if (strcasecmp (filterName, FILTER_ABS_HAMMING_STR) == 0)
- filterID = FILTER_ABS_G_HAMMING;
- else if (strcasecmp (filterName, FILTER_ABS_SINC_STR) == 0)
- filterID = FILTER_ABS_SINC;
- else if (strcasecmp (filterName, FILTER_ABS_COS_STR) == 0)
- filterID = FILTER_ABS_COSINE;
- else if (strcasecmp (filterName, FILTER_SHEPP_STR) == 0)
- filterID = FILTER_SHEPP;
+ int filterID = FILTER_INVALID;
+
+ for (int i = 0; i < s_iFilterCount; i++)
+ if (strcasecmp (filterName, s_aszFilterName[i]) == 0) {
+ filterID = i;
+ break;
+ }
return (filterID);
}
const char *
-SignalFilter::convertFilterIDToName (const FilterID filterID)
+SignalFilter::convertFilterIDToName (const int filterID)
{
- const char *name = "";
-
- if (filterID == FILTER_SHEPP)
- name = FILTER_SHEPP_STR;
- else if (filterID == FILTER_ABS_COSINE)
- name = FILTER_ABS_COS_STR;
- else if (filterID == FILTER_ABS_SINC)
- name = FILTER_ABS_SINC_STR;
- else if (filterID == FILTER_ABS_G_HAMMING)
- name = FILTER_ABS_HAMMING_STR;
- else if (filterID == FILTER_ABS_BANDLIMIT)
- name = FILTER_ABS_BANDLIMIT_STR;
- else if (filterID == FILTER_COSINE)
- name = FILTER_COS_STR;
- else if (filterID == FILTER_SINC)
- name = FILTER_SINC_STR;
- else if (filterID == FILTER_G_HAMMING)
- name = FILTER_HAMMING_STR;
- else if (filterID == FILTER_BANDLIMIT)
- name = FILTER_BANDLIMIT_STR;
- else if (filterID == FILTER_TRIANGLE)
- name = FILTER_TRIANGLE_STR;
-
+ static const char *name = "";
+
+ if (filterID >= 0 && filterID < s_iFilterCount)
+ return (s_aszFilterName [filterID]);
+
return (name);
}
+
+const char *
+SignalFilter::convertFilterIDToTitle (const int filterID)
+{
+ static const char *title = "";
+
+ if (filterID >= 0 && filterID < s_iFilterCount)
+ return (s_aszFilterTitle [filterID]);
+
+ return (title);
+}
-const SignalFilter::DomainID
+int
SignalFilter::convertDomainNameToID (const char* const domainName)
{
- DomainID dID = DOMAIN_INVALID;
+ int dID = DOMAIN_INVALID;
- if (strcasecmp (domainName, DOMAIN_SPATIAL_STR) == 0)
- dID = DOMAIN_SPATIAL;
- else if (strcasecmp (domainName, DOMAIN_FREQ_STR) == 0)
- dID = DOMAIN_FREQ;
+ for (int i = 0; i < s_iDomainCount; i++)
+ if (strcasecmp (domainName, s_aszDomainName[i]) == 0) {
+ dID = i;
+ break;
+ }
return (dID);
}
const char *
-SignalFilter::convertDomainIDToName (const DomainID domain)
+SignalFilter::convertDomainIDToName (const int domainID)
{
- const char *name = "";
+ static const char *name = "";
- if (domain == DOMAIN_SPATIAL)
- return (DOMAIN_SPATIAL_STR);
- else if (domain == DOMAIN_FREQ)
- return (DOMAIN_FREQ_STR);
+ if (domainID >= 0 && domainID < s_iDomainCount)
+ return (s_aszDomainName [domainID]);
return (name);
}
+const char *
+SignalFilter::convertDomainIDToTitle (const int domainID)
+{
+ static const char *title = "";
+
+ if (domainID >= 0 && domainID < s_iDomainCount)
+ return (s_aszDomainTitle [domainID]);
+
+ return (title);
+}
+
double
SignalFilter::response (double x)
double response = 0;
if (m_idDomain == DOMAIN_SPATIAL)
- response = spatialResponse (m_idFilter, m_bw, x, m_filterParam, m_numIntegral);
- else if (m_idDomain == DOMAIN_FREQ)
- response = frequencyResponse (m_idFilter, m_bw, x, m_filterParam);
+ response = spatialResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
+ else if (m_idDomain == DOMAIN_FREQUENCY)
+ response = frequencyResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
return (response);
}
double
-SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param, int nIntegral = 0)
+SignalFilter::spatialResponse (int filterID, double bw, double x, double param)
{
- if (nIntegral == 0)
+ if (haveAnalyticSpatial(filterID))
return spatialResponseAnalytic (filterID, bw, x, param);
else
- return spatialResponseCalc (filterID, bw, x, param, nIntegral);
+ return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL);
+}
+
+void
+SignalFilter::copyFilterData (double* pdFilter, const int iStart, const int nPoints) const
+{
+ int iFirst = clamp (iStart, 0, m_nFilterPoints - 1);
+ int iLast = clamp (iFirst + nPoints - 1, 0, m_nFilterPoints - 1);
+
+ for (int i = iFirst; i <= iLast; i++)
+ pdFilter[i - iFirst] = m_adFilter[i];
}
/* NAME
*/
double
-SignalFilter::spatialResponseCalc (double x, double param, int nIntegral) const
+SignalFilter::spatialResponseCalc (double x) const
{
- return (spatialResponseCalc (m_idFilter, m_bw, x, param, nIntegral));
+ return (spatialResponseCalc (m_idFilter, m_dBandwidth, x, m_dFilterParam, N_INTEGRAL));
}
double
-SignalFilter::spatialResponseCalc (FilterID filterID, double bw, double x, double param, int n)
+SignalFilter::spatialResponseCalc (int filterID, double bw, double x, double param, int n)
{
double zmin, zmax;
double zinc = (zmax - zmin) / (n - 1);
double z = zmin;
- double q [n];
+ double* q = new double [n];
for (int i = 0; i < n; i++, z += zinc)
q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
double y = 2 * integrateSimpson (zmin, zmax, q, n);
-
+ delete q;
+
return (y);
}
*/
double
-SignalFilter::frequencyResponse (double u, double param) const
+SignalFilter::frequencyResponse (double u) const
{
- return frequencyResponse (m_idFilter, m_bw, u, param);
+ return frequencyResponse (m_idFilter, m_dBandwidth, u, m_dFilterParam);
}
double
-SignalFilter::frequencyResponse (FilterID filterID, double bw, double u, double param)
+SignalFilter::frequencyResponse (int filterID, double bw, double u, double param)
{
double q;
double au = fabs (u);
switch (filterID) {
case FILTER_BANDLIMIT:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0.;
else
q = 1;
break;
case FILTER_ABS_BANDLIMIT:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0.;
else
q = au;
break;
case FILTER_TRIANGLE:
- if (au >= bw)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0;
else
q = 1 - au / bw;
break;
case FILTER_COSINE:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0;
else
q = cos(PI * u / bw);
break;
case FILTER_ABS_COSINE:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0;
else
q = au * cos(PI * u / bw);
q = au * bw * sinc (PI * bw * u, 1.);
break;
case FILTER_G_HAMMING:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0;
else
q = param + (1 - param) * cos (TWOPI * u / bw);
break;
case FILTER_ABS_G_HAMMING:
- if (au >= bw / 2)
+ if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
q = 0;
else
q = au * (param + (1 - param) * cos(TWOPI * u / bw));
*/
double
-SignalFilter::spatialResponseAnalytic (double x, double param) const
+SignalFilter::spatialResponseAnalytic (double x) const
{
- return spatialResponseAnalytic (m_idFilter, m_bw, x, param);
+ return spatialResponseAnalytic (m_idFilter, m_dBandwidth, x, m_dFilterParam);
+}
+
+const bool
+SignalFilter::haveAnalyticSpatial (int filterID)
+{
+ bool haveAnalytic = false;
+
+ switch (filterID) {
+ case FILTER_BANDLIMIT:
+ case FILTER_TRIANGLE:
+ case FILTER_COSINE:
+ case FILTER_G_HAMMING:
+ case FILTER_ABS_BANDLIMIT:
+ case FILTER_ABS_COSINE:
+ case FILTER_ABS_G_HAMMING:
+ case FILTER_SHEPP:
+ case FILTER_SINC:
+ haveAnalytic = true;
+ break;
+ default:
+ break;
+ }
+
+ return (haveAnalytic);
}
double
-SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, double param)
+SignalFilter::spatialResponseAnalytic (int filterID, double bw, double x, double param)
{
double q, temp;
double u = TWOPI * x;
}
-/* NAME
- * sinc Return sin(x)/x function
- *
- * SYNOPSIS
- * v = sinc (x, mult)
- * double v sinc value
- * double x, mult
- *
- * DESCRIPTION
- * v = sin(x * mult) / x;
- */
-
-
-/* NAME
- * integral_abscos Returns integral of u*cos(u)
- *
- * SYNOPSIS
- * q = integral_abscos (u, w)
- * double q Integral value
- * double u Integration variable
- * double w Upper integration boundary
- *
- * DESCRIPTION
- * Returns the value of integral of u*cos(u)*dV for V = 0 to w
- */
-double
-SignalFilter::integral_abscos (double u, double w)
-{
- if (fabs (u) > F_EPSILON)
- return (cos(u * w) - 1) / (u * u) + w / u * sin (u * w);
- else
- return (w * w / 2);
-}
+// Functions that are inline in filter.h
-/* NAME
- * convolve Discrete convolution of two functions
- *
- * SYNOPSIS
- * r = convolve (f1, f2, dx, n, np, func_type)
- * double r Convolved result
- * double f1[], f2[] Functions to be convolved
- * double dx Difference between successive x values
- * int n Array index to center convolution about
- * int np Number of points in f1 array
- * int func_type EVEN or ODD or EVEN_AND_ODD function f2
- *
- * NOTES
- * f1 is the projection data, its indices range from 0 to np - 1.
- * The index for f2, the filter, ranges from -(np-1) to (np-1).
- * There are 3 ways to handle the negative vertices of f2:
- * 1. If we know f2 is an EVEN function, then f2[-n] = f2[n].
- * All filters used in reconstruction are even.
- * 2. If we know f2 is an ODD function, then f2[-n] = -f2[n]
- * 3. If f2 is both ODD AND EVEN, then we must store the value of f2
- * for negative indices. Since f2 must range from -(np-1) to (np-1),
- * if we add (np - 1) to f2's array index, then f2's index will
- * range from 0 to 2 * (np - 1), and the origin, x = 0, will be
- * stored at f2[np-1].
- */
+// sinc Return sin(x)/x function
+// v = sinc (x, mult)
+// Calculates sin(x * mult) / x;
-double
-SignalFilter::convolve (const double func[], const double dx, const int n, const int np) const
-{
- double sum = 0.0;
-
-#if UNOPTIMIZED_CONVOLUTION
- for (int i = 0; i < np; i++)
- sum += func[i] * m_vecFilter[n - i + (np - 1)];
-#else
- double* f2 = m_vecFilter + n + (np - 1);
- for (int i = 0; i < np; i++)
- sum += *func++ * *f2--;
-#endif
-
- return (sum * dx);
-}
+// integral_abscos Returns integral of u*cos(u)
+//
+// q = integral_abscos (u, w)
+// double q Integral value
+// double u Integration variable
+// double w Upper integration boundary
+// Returns the value of integral of u*cos(u)*dV for V = 0 to w
-double
-SignalFilter::convolve (const float func[], const double dx, const int n, const int np) const
-{
- double sum = 0.0;
-
-#if UNOPTIMIZED_CONVOLUTION
-for (int i = 0; i < np; i++)
- sum += func[i] * m_vecFilter[n - i + (np - 1)];
-#else
-double* f2 = m_vecFilter + n + (np - 1);
-for (int i = 0; i < np; i++)
- sum += *func++ * *f2--;
-#endif
-
- return (sum * dx);
-}
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