1 /*****************************************************************************
5 ** Purpose: Routines for signal-procesing filters
6 ** Progammer: Kevin Rosenberg
7 ** Date Started: Aug 1984
9 ** This is part of the CTSim program
10 ** Copyright (C) 1983-2000 Kevin Rosenberg
12 ** $Id: filter.cpp,v 1.33 2001/01/02 16:02:13 kevin Exp $
14 ** This program is free software; you can redistribute it and/or modify
15 ** it under the terms of the GNU General Public License (version 2) as
16 ** published by the Free Software Foundation.
18 ** This program is distributed in the hope that it will be useful,
19 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
20 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 ** GNU General Public License for more details.
23 ** You should have received a copy of the GNU General Public License
24 ** along with this program; if not, write to the Free Software
25 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 ******************************************************************************/
30 int SignalFilter::N_INTEGRAL=500; //static member
32 const int SignalFilter::FILTER_INVALID = -1 ;
33 const int SignalFilter::FILTER_ABS_BANDLIMIT = 0; // filter times |x = |
34 const int SignalFilter::FILTER_ABS_G_HAMMING = 1;
35 const int SignalFilter::FILTER_ABS_COSINE = 2;
36 const int SignalFilter::FILTER_ABS_SINC = 3;
37 const int SignalFilter::FILTER_SHEPP = 4;
38 const int SignalFilter::FILTER_BANDLIMIT = 5;
39 const int SignalFilter::FILTER_SINC = 6;
40 const int SignalFilter::FILTER_G_HAMMING = 7;
41 const int SignalFilter::FILTER_COSINE = 8;
42 const int SignalFilter::FILTER_TRIANGLE = 9;
44 const char* SignalFilter::s_aszFilterName[] = {
57 const char* SignalFilter::s_aszFilterTitle[] = {
58 {"Abs(w) * Bandlimit"},
70 const int SignalFilter::s_iFilterCount = sizeof(s_aszFilterName) / sizeof(const char*);
73 const int SignalFilter::DOMAIN_INVALID = -1;
74 const int SignalFilter::DOMAIN_FREQUENCY = 0;
75 const int SignalFilter::DOMAIN_SPATIAL = 1;
77 const char* SignalFilter::s_aszDomainName[] = {
82 const char* SignalFilter::s_aszDomainTitle[] = {
87 const int SignalFilter::s_iDomainCount = sizeof(s_aszDomainName) / sizeof(const char*);
91 * SignalFilter::SignalFilter Construct a signal
94 * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic)
95 * double f Generated filter vector
96 * int filt_type Type of filter wanted
97 * double bw Bandwidth of filter
98 * double filterMin, filterMax Filter limits
99 * int nFilterPoints Number of points in signal
100 * double param General input parameter to filters
101 * int domain FREQUENCY or SPATIAL domain wanted
104 SignalFilter::SignalFilter (const char* szFilterName, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const char* szDomainName)
105 : m_adFilter(NULL), m_fail(false)
107 m_idFilter = convertFilterNameToID (szFilterName);
108 if (m_idFilter == FILTER_INVALID) {
110 m_failMessage = "Invalid Filter name ";
111 m_failMessage += szFilterName;
114 m_idDomain = convertDomainNameToID (szDomainName);
115 if (m_idDomain == DOMAIN_INVALID) {
117 m_failMessage = "Invalid domain name ";
118 m_failMessage += szDomainName;
121 init (m_idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, m_idDomain);
124 SignalFilter::SignalFilter (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
125 : m_adFilter(NULL), m_fail(false)
127 init (idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, idDomain);
130 SignalFilter::SignalFilter (const char* szFilterName, const char* szDomainName, double dBandwidth, double dFilterParam)
131 : m_adFilter(NULL), m_fail(false)
134 m_dBandwidth = dBandwidth;
135 m_dFilterParam = dFilterParam;
136 m_idFilter = convertFilterNameToID (szFilterName);
137 if (m_idFilter == FILTER_INVALID) {
139 m_failMessage = "Invalid Filter name ";
140 m_failMessage += szFilterName;
143 m_idDomain = convertDomainNameToID (szDomainName);
144 if (m_idDomain == DOMAIN_INVALID) {
146 m_failMessage = "Invalid domain name ";
147 m_failMessage += szDomainName;
153 SignalFilter::init (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
155 m_idFilter = idFilter;
156 m_idDomain = idDomain;
157 if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID) {
161 if (nFilterPoints < 2) {
163 m_failMessage = "Number of filter points ";
164 m_failMessage += nFilterPoints;
165 m_failMessage = " less than 2";
169 m_nameFilter = convertFilterIDToName (m_idFilter);
170 m_nameDomain = convertDomainIDToName (m_idDomain);
171 m_nFilterPoints = nFilterPoints;
172 m_dFilterParam = dFilterParam;
173 m_dBandwidth = dBandwidth;
174 m_dFilterMin = dFilterMinimum;
175 m_dFilterMax = dFilterMaximum;
177 m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
178 m_adFilter = new double [m_nFilterPoints];
180 if (m_idDomain == DOMAIN_FREQUENCY)
181 createFrequencyFilter (m_adFilter);
182 else if (m_idDomain == DOMAIN_SPATIAL)
183 createSpatialFilter (m_adFilter);
187 SignalFilter::~SignalFilter (void)
189 delete [] m_adFilter;
193 SignalFilter::createFrequencyFilter (double* adFilter) const
197 for (x = m_dFilterMin, i = 0; i < m_nFilterPoints; x += m_dFilterInc, i++)
198 adFilter[i] = frequencyResponse (x);
203 SignalFilter::createSpatialFilter (double* adFilter) const
205 if (m_idFilter == FILTER_SHEPP) {
206 double a = 2 * m_dBandwidth;
207 double c = - 4. / (a * a);
208 int center = (m_nFilterPoints - 1) / 2;
209 int sidelen = center;
210 m_adFilter[center] = 4. / (a * a);
212 for (int i = 1; i <= sidelen; i++ )
213 m_adFilter [center + i] = m_adFilter [center - i] = c / (4 * (i * i) - 1);
215 double x = m_dFilterMin;
216 for (int i = 0; i < m_nFilterPoints; i++, x += m_dFilterInc) {
217 if (haveAnalyticSpatial(m_idFilter))
218 m_adFilter[i] = spatialResponseAnalytic (x);
220 m_adFilter[i] = spatialResponseCalc (x);
226 SignalFilter::convertFilterNameToID (const char *filterName)
228 int filterID = FILTER_INVALID;
230 for (int i = 0; i < s_iFilterCount; i++)
231 if (strcasecmp (filterName, s_aszFilterName[i]) == 0) {
240 SignalFilter::convertFilterIDToName (const int filterID)
242 static const char *name = "";
244 if (filterID >= 0 && filterID < s_iFilterCount)
245 return (s_aszFilterName [filterID]);
251 SignalFilter::convertFilterIDToTitle (const int filterID)
253 static const char *title = "";
255 if (filterID >= 0 && filterID < s_iFilterCount)
256 return (s_aszFilterTitle [filterID]);
262 SignalFilter::convertDomainNameToID (const char* const domainName)
264 int dID = DOMAIN_INVALID;
266 for (int i = 0; i < s_iDomainCount; i++)
267 if (strcasecmp (domainName, s_aszDomainName[i]) == 0) {
276 SignalFilter::convertDomainIDToName (const int domainID)
278 static const char *name = "";
280 if (domainID >= 0 && domainID < s_iDomainCount)
281 return (s_aszDomainName [domainID]);
287 SignalFilter::convertDomainIDToTitle (const int domainID)
289 static const char *title = "";
291 if (domainID >= 0 && domainID < s_iDomainCount)
292 return (s_aszDomainTitle [domainID]);
299 SignalFilter::response (double x)
303 if (m_idDomain == DOMAIN_SPATIAL)
304 response = spatialResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
305 else if (m_idDomain == DOMAIN_FREQUENCY)
306 response = frequencyResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
313 SignalFilter::spatialResponse (int filterID, double bw, double x, double param)
315 if (haveAnalyticSpatial(filterID))
316 return spatialResponseAnalytic (filterID, bw, x, param);
318 return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL);
322 SignalFilter::copyFilterData (double* pdFilter, const int iStart, const int nPoints) const
324 int iFirst = clamp (iStart, 0, m_nFilterPoints - 1);
325 int iLast = clamp (iFirst + nPoints - 1, 0, m_nFilterPoints - 1);
327 for (int i = iFirst; i <= iLast; i++)
328 pdFilter[i - iFirst] = m_adFilter[i];
332 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
333 * transform of filters's frequency
337 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
338 * double y Filter's response in spatial domain
339 * int filt_type Type of filter (definitions in ct.h)
340 * double x Spatial position to evaluate filter
341 * double m_bw Bandwidth of window
342 * double param General parameter for various filters
343 * int n Number of points to calculate integrations
347 SignalFilter::spatialResponseCalc (double x) const
349 return (spatialResponseCalc (m_idFilter, m_dBandwidth, x, m_dFilterParam, N_INTEGRAL));
353 SignalFilter::spatialResponseCalc (int filterID, double bw, double x, double param, int n)
357 if (filterID == FILTER_TRIANGLE) {
364 double zinc = (zmax - zmin) / (n - 1);
367 double* q = new double [n];
368 for (int i = 0; i < n; i++, z += zinc)
369 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
371 double y = 2 * integrateSimpson (zmin, zmax, q, n);
379 * filter_frequency_response Return filter frequency response
382 * h = filter_frequency_response (filt_type, u, m_bw, param)
383 * double h Filters frequency response at u
384 * int filt_type Type of filter
385 * double u Frequency to evaluate filter at
386 * double m_bw Bandwidth of filter
387 * double param General input parameter for various filters
391 SignalFilter::frequencyResponse (double u) const
393 return frequencyResponse (m_idFilter, m_dBandwidth, u, m_dFilterParam);
398 SignalFilter::frequencyResponse (int filterID, double bw, double u, double param)
401 double au = fabs (u);
404 case FILTER_BANDLIMIT:
405 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
410 case FILTER_ABS_BANDLIMIT:
411 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
416 case FILTER_TRIANGLE:
417 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
423 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
426 q = cos(PI * u / bw);
428 case FILTER_ABS_COSINE:
429 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
432 q = au * cos(PI * u / bw);
435 q = bw * sinc (PI * bw * u, 1.);
437 case FILTER_ABS_SINC:
438 q = au * bw * sinc (PI * bw * u, 1.);
440 case FILTER_G_HAMMING:
441 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
444 q = param + (1 - param) * cos (TWOPI * u / bw);
446 case FILTER_ABS_G_HAMMING:
447 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
450 q = au * (param + (1 - param) * cos(TWOPI * u / bw));
454 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
463 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
464 * transform of filters's frequency
468 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
469 * double y Filter's response in spatial domain
470 * int filt_type Type of filter (definitions in ct.h)
471 * double x Spatial position to evaluate filter
472 * double m_bw Bandwidth of window
473 * double param General parameter for various filters
477 SignalFilter::spatialResponseAnalytic (double x) const
479 return spatialResponseAnalytic (m_idFilter, m_dBandwidth, x, m_dFilterParam);
483 SignalFilter::haveAnalyticSpatial (int filterID)
485 bool haveAnalytic = false;
488 case FILTER_BANDLIMIT:
489 case FILTER_TRIANGLE:
491 case FILTER_G_HAMMING:
492 case FILTER_ABS_BANDLIMIT:
493 case FILTER_ABS_COSINE:
494 case FILTER_ABS_G_HAMMING:
503 return (haveAnalytic);
507 SignalFilter::spatialResponseAnalytic (int filterID, double bw, double x, double param)
510 double u = TWOPI * x;
513 double b2 = TWOPI / bw;
516 case FILTER_BANDLIMIT:
517 q = bw * sinc(u * w, 1.0);
519 case FILTER_TRIANGLE:
520 temp = sinc (u * w, 1.0);
521 q = bw * temp * temp;
524 q = sinc(b-u,w) + sinc(b+u,w);
526 case FILTER_G_HAMMING:
527 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
529 case FILTER_ABS_BANDLIMIT:
530 q = 2 * integral_abscos (u, w);
532 case FILTER_ABS_COSINE:
533 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
535 case FILTER_ABS_G_HAMMING:
536 q = 2 * param * integral_abscos(u,w) +
537 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
541 q = 4. / (PI * bw * bw);
543 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
546 if (fabs (x) < bw / 2)
551 case FILTER_ABS_SINC:
553 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
563 * sinc Return sin(x)/x function
567 * double v sinc value
571 * v = sin(x * mult) / x;
576 * integral_abscos Returns integral of u*cos(u)
579 * q = integral_abscos (u, w)
580 * double q Integral value
581 * double u Integration variable
582 * double w Upper integration boundary
585 * Returns the value of integral of u*cos(u)*dV for V = 0 to w