** This is part of the CTSim program
** Copyright (C) 1983-2000 Kevin Rosenberg
**
-** $Id: filter.cpp,v 1.1 2000/06/19 02:59:34 kevin Exp $
+** $Id: filter.cpp,v 1.2 2000/06/20 17:54:51 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
* ANALYTIC solutions, use numint = 0
*/
-double *
-filter_generate (const FilterType filt_type, double bw, double xmin, double xmax, int n, double param, const DomainType domain, int numint)
+SignalFilter::SignalFilter (const FilterType filt_type, double bw, double xmin, double xmax, int n, double param, const DomainType domain, int numint)
{
- double *f = new double [n];
+ m_vecFilter = new double [n];
+ m_filterType = filt_type;
+ m_bw = bw;
+
double xinc = (xmax - xmin) / (n - 1);
- if (filt_type == FILTER_SHEPP) {
- double a = 2 * bw;
+ if (m_filterType == FILTER_SHEPP) {
+ double a = 2 * m_bw;
double c = - 4. / (a * a);
int center = (n - 1) / 2;
int sidelen = center;
- f[center] = 4. / (a * a);
+ m_vecFilter[center] = 4. / (a * a);
for (int i = 1; i <= sidelen; i++ )
- f [center + i] = f [center - i] = c / (4 * (i * i) - 1);
+ m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1);
} else if (domain == D_FREQ) {
double x;
int i;
for (x = xmin, i = 0; i < n; x += xinc, i++)
- f[i] = filter_frequency_response (filt_type, x, bw, param);
+ m_vecFilter[i] = frequencyResponse (x, param);
} else if (domain == D_SPATIAL) {
double x;
int i;
for (x = xmin, i = 0; i < n; x += xinc, i++)
if (numint == 0)
- f[i] = filter_spatial_response_analytic (filt_type, x, bw, param);
+ m_vecFilter[i] = spatialResponseAnalytic (x, param);
else
- f[i] = filter_spatial_response_calc (filt_type, x, bw, param, numint);
+ m_vecFilter[i] = spatialResponseCalc (x, param, numint);
} else {
sys_error (ERR_WARNING, "Illegal domain %d [filt_generate]", domain);
- return (NULL);
}
-
- return (f);
+}
+
+SignalFilter::~SignalFilter (void)
+{
+ delete m_vecFilter;
}
* response
*
* SYNOPSIS
- * y = filter_spatial_response_calc (filt_type, x, bw, param, n)
+ * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
* double y Filter's response in spatial domain
* int filt_type Type of filter (definitions in ct.h)
* double x Spatial position to evaluate filter
- * double bw Bandwidth of window
+ * double m_bw Bandwidth of window
* double param General parameter for various filters
* int n Number of points to calculate integrations
*/
double
-filter_spatial_response_calc (int filt_type, double x, double bw, double param, int n)
+SignalFilter::spatialResponseCalc (double x, double param, int n) const
+{
+ return (spatialResponseCalc (m_filterType, m_bw, x, param, n));
+}
+
+double
+SignalFilter::spatialResponseCalc (FilterType fType, double bw, double x, double param, int n)
{
double zmin, zmax;
- if (filt_type == FILTER_TRIANGLE) {
+ if (fType == FILTER_TRIANGLE) {
zmin = 0;
zmax = bw;
} else {
double z = zmin;
double q [n];
for (int i = 0; i < n; i++, z += zinc)
- q[i] = filter_frequency_response (filt_type, z, bw, param) * cos (TWOPI * z * x);
+ q[i] = frequencyResponse (fType, bw, z, param) * cos (TWOPI * z * x);
double y = 2 * integrateSimpson (zmin, zmax, q, n);
* filter_frequency_response Return filter frequency response
*
* SYNOPSIS
- * h = filter_frequency_response (filt_type, u, bw, param)
+ * h = filter_frequency_response (filt_type, u, m_bw, param)
* double h Filters frequency response at u
* int filt_type Type of filter
* double u Frequency to evaluate filter at
- * double bw Bandwidth of filter
+ * double m_bw Bandwidth of filter
* double param General input parameter for various filters
*/
double
-filter_frequency_response (int filt_type, double u, double bw, double param)
+SignalFilter::frequencyResponse (double u, double param) const
+{
+ return frequencyResponse (m_filterType, m_bw, u, param);
+}
+
+
+double
+SignalFilter::frequencyResponse (FilterType fType, double bw, double u, double param)
{
double q;
double au = fabs (u);
- switch (filt_type) {
+ switch (fType) {
case FILTER_BANDLIMIT:
if (au >= bw / 2)
q = 0.;
break;
default:
q = 0;
- sys_error (ERR_WARNING,
- "Frequency response for filter %d not implemented [filter_frequency_response]",
- filt_type);
+ sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", fType);
break;
}
return (q);
* response
*
* SYNOPSIS
- * y = filter_spatial_response_analytic (filt_type, x, bw, param)
+ * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
* double y Filter's response in spatial domain
* int filt_type Type of filter (definitions in ct.h)
* double x Spatial position to evaluate filter
- * double bw Bandwidth of window
+ * double m_bw Bandwidth of window
* double param General parameter for various filters
*/
double
-filter_spatial_response_analytic (int filt_type, double x, double bw, double param)
+SignalFilter::spatialResponseAnalytic (double x, double param) const
+{
+ return spatialResponseAnalytic (m_filterType, m_bw, x, param);
+}
+
+double
+SignalFilter::spatialResponseAnalytic (FilterType fType, double bw, double x, double param)
{
double q, temp;
double u = TWOPI * x;
double b = PI / bw;
double b2 = TWOPI / bw;
- switch (filt_type) {
+ switch (fType) {
case FILTER_BANDLIMIT:
q = bw * sinc(u * w, 1.0);
break;
q = sinc(b-u,w) + sinc(b+u,w);
break;
case FILTER_G_HAMMING:
- q = 2 * param * sin(u*w)/u + (1-param) *
- (sinc(b2-u, w) + sinc(b2+u, w));
+ q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
break;
case FILTER_ABS_BANDLIMIT:
q = 2 * integral_abscos (u, w);
break;
case FILTER_ABS_SINC:
default:
- sys_error (ERR_WARNING,
- "Analytic filter type %d not implemented [filter_spatial_response_analytic]",
- filt_type);
+ sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", fType);
q = 0;
break;
}
* v = sin(x * mult) / x;
*/
-double
-sinc (double x, double mult)
-{
- return (fabs(x) > F_EPSILON ? (sin (x * mult) / x) : 1.0);
-}
-
/* NAME
* integral_abscos Returns integral of u*cos(u)
*/
double
-integral_abscos (double u, double w)
+SignalFilter::integral_abscos (double u, double w)
{
if (fabs (u) > F_EPSILON)
return (cos(u * w) - 1) / (u * u) + w / u * sin (u * w);
}
+/* 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].
+ */
+
+double
+SignalFilter::convolve (const double func[], const double dx, const int n, const int np, const FunctionSymmetry func_type) const
+{
+ double sum = 0.0;
+
+ if (func_type == FUNC_BOTH) {
+#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
+ } else if (func_type == FUNC_EVEN) {
+ for (int i = 0; i < np; i++) {
+ int k = abs (n - i);
+ sum += func[i] * m_vecFilter[k];
+ }
+ } else if (func_type == FUNC_ODD) {
+ for (int i = 0; i < np; i++) {
+ int k = n - i;
+ if (k < 0)
+ sum -= func[i] * m_vecFilter[k];
+ else
+ sum += func[i] * m_vecFilter[k];
+ }
+ } else
+ sys_error (ERR_WARNING, "Illegal function type %d [convolve]", func_type);
+
+ return (sum * dx);
+}
+
+
+double
+SignalFilter::convolve (const float func[], const double dx, const int n, const int np, const FunctionSymmetry func_type) const
+{
+ double sum = 0.0;
+
+ if (func_type == FUNC_BOTH) {
+#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
+ } else if (func_type == FUNC_EVEN) {
+ for (int i = 0; i < np; i++) {
+ int k = abs (n - i);
+ sum += func[i] * m_vecFilter[k];
+ }
+ } else if (func_type == FUNC_ODD) {
+ for (int i = 0; i < np; i++) {
+ int k = n - i;
+ if (k < 0)
+ sum -= func[i] * m_vecFilter[k];
+ else
+ sum += func[i] * m_vecFilter[k];
+ }
+ } else
+ sys_error (ERR_WARNING, "Illegal function type %d [convolve]", func_type);
+
+ return (sum * dx);
+}
+
projects / ctsim.git / blobdiff