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) 1983-2009 Kevin Rosenberg
12 ** This program is free software; you can redistribute it and/or modify
13 ** it under the terms of the GNU General Public License (version 2) as
14 ** published by the Free Software Foundation.
16 ** This program is distributed in the hope that it will be useful,
17 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
18 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 ** GNU General Public License for more details.
21 ** You should have received a copy of the GNU General Public License
22 ** along with this program; if not, write to the Free Software
23 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 ******************************************************************************/
28 int SignalFilter::N_INTEGRAL=500; //static member
30 const int SignalFilter::FILTER_INVALID = -1 ;
31 const int SignalFilter::FILTER_ABS_BANDLIMIT = 0; // filter times |x|
32 const int SignalFilter::FILTER_ABS_G_HAMMING = 1;
33 const int SignalFilter::FILTER_ABS_HANNING = 2;
34 const int SignalFilter::FILTER_ABS_COSINE = 3;
35 const int SignalFilter::FILTER_ABS_SINC = 4;
36 const int SignalFilter::FILTER_SHEPP = 5;
37 const int SignalFilter::FILTER_BANDLIMIT = 6;
38 const int SignalFilter::FILTER_SINC = 7;
39 const int SignalFilter::FILTER_G_HAMMING = 8;
40 const int SignalFilter::FILTER_HANNING = 9;
41 const int SignalFilter::FILTER_COSINE = 10;
42 const int SignalFilter::FILTER_TRIANGLE = 11;
44 const int SignalFilter::s_iReconstructFilterCount = 4;
46 const char* const SignalFilter::s_aszFilterName[] = {
61 const char* const SignalFilter::s_aszFilterTitle[] = {
76 const int SignalFilter::s_iFilterCount = sizeof(s_aszFilterName) / sizeof(const char*);
79 const int SignalFilter::DOMAIN_INVALID = -1;
80 const int SignalFilter::DOMAIN_FREQUENCY = 0;
81 const int SignalFilter::DOMAIN_SPATIAL = 1;
83 const char* const SignalFilter::s_aszDomainName[] = {
88 const char* const SignalFilter::s_aszDomainTitle[] = {
93 const int SignalFilter::s_iDomainCount = sizeof(s_aszDomainName) / sizeof(const char*);
97 * SignalFilter::SignalFilter Construct a signal
100 * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic)
101 * double f Generated filter vector
102 * int filt_type Type of filter wanted
103 * double bw Bandwidth of filter
104 * double filterMin, filterMax Filter limits
105 * int nFilterPoints Number of points in signal
106 * double param General input parameter to filters
107 * int domain FREQUENCY or SPATIAL domain wanted
110 SignalFilter::SignalFilter (const char* szFilterName, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const char* szDomainName)
111 : m_adFilter(NULL), m_fail(false)
113 m_idFilter = convertFilterNameToID (szFilterName);
114 if (m_idFilter == FILTER_INVALID) {
116 m_failMessage = "Invalid Filter name ";
117 m_failMessage += szFilterName;
120 m_idDomain = convertDomainNameToID (szDomainName);
121 if (m_idDomain == DOMAIN_INVALID) {
123 m_failMessage = "Invalid domain name ";
124 m_failMessage += szDomainName;
127 init (m_idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, m_idDomain);
130 SignalFilter::SignalFilter (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
131 : m_adFilter(NULL), m_fail(false)
133 init (idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, idDomain);
136 SignalFilter::SignalFilter (const char* szFilterName, const char* szDomainName, double dBandwidth, double dFilterParam)
137 : m_adFilter(NULL), m_fail(false)
140 m_dBandwidth = dBandwidth;
141 m_dFilterParam = dFilterParam;
142 m_idFilter = convertFilterNameToID (szFilterName);
143 if (m_idFilter == FILTER_INVALID) {
145 m_failMessage = "Invalid Filter name ";
146 m_failMessage += szFilterName;
149 m_idDomain = convertDomainNameToID (szDomainName);
150 if (m_idDomain == DOMAIN_INVALID) {
152 m_failMessage = "Invalid domain name ";
153 m_failMessage += szDomainName;
159 SignalFilter::init (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
161 m_idFilter = idFilter;
162 m_idDomain = idDomain;
163 if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID) {
167 if (nFilterPoints < 2) {
169 m_failMessage = "Number of filter points ";
170 m_failMessage += nFilterPoints;
171 m_failMessage = " less than 2";
175 m_nameFilter = convertFilterIDToName (m_idFilter);
176 m_nameDomain = convertDomainIDToName (m_idDomain);
177 m_nFilterPoints = nFilterPoints;
178 m_dFilterParam = dFilterParam;
179 m_dBandwidth = dBandwidth;
180 m_dFilterMin = dFilterMinimum;
181 m_dFilterMax = dFilterMaximum;
183 m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
184 m_adFilter = new double [m_nFilterPoints];
186 if (m_idDomain == DOMAIN_FREQUENCY)
187 createFrequencyFilter (m_adFilter);
188 else if (m_idDomain == DOMAIN_SPATIAL)
189 createSpatialFilter (m_adFilter);
193 SignalFilter::~SignalFilter (void)
195 delete [] m_adFilter;
199 SignalFilter::createFrequencyFilter (double* adFilter) const
201 double xstart = m_dFilterMin;
203 #pragma omp parallel for
205 for (int i = 0; i < m_nFilterPoints; i++) {
206 double x = xstart + (i * m_dFilterInc);
207 adFilter[i] = frequencyResponse (x);
213 SignalFilter::createSpatialFilter (double* adFilter) const
215 if (m_idFilter == FILTER_SHEPP) {
216 double a = 2 * m_dBandwidth;
217 double c = - 4. / (a * a);
218 int center = (m_nFilterPoints - 1) / 2;
219 int sidelen = center;
220 m_adFilter[center] = 4. / (a * a);
222 for (int i = 1; i <= sidelen; i++ )
223 m_adFilter [center + i] = m_adFilter [center - i] = c / (4 * (i * i) - 1);
225 double xstart = m_dFilterMin;
227 #pragma omp parallel for
229 for (int i = 0; i < m_nFilterPoints; i++) {
230 double x = xstart + (i * m_dFilterInc);
231 if (haveAnalyticSpatial(m_idFilter))
232 m_adFilter[i] = spatialResponseAnalytic (x);
234 m_adFilter[i] = spatialResponseCalc (x);
240 SignalFilter::convertFilterNameToID (const char *filterName)
242 int filterID = FILTER_INVALID;
244 for (int i = 0; i < s_iFilterCount; i++) {
245 if (strcasecmp (filterName, s_aszFilterName[i]) == 0) {
255 SignalFilter::convertFilterIDToName (const int filterID)
257 static const char *name = "";
259 if (filterID >= 0 && filterID < s_iFilterCount)
260 return (s_aszFilterName [filterID]);
266 SignalFilter::convertFilterIDToTitle (const int filterID)
268 static const char *title = "";
270 if (filterID >= 0 && filterID < s_iFilterCount) {
271 return (s_aszFilterTitle [filterID]);
277 SignalFilter::convertDomainNameToID (const char* const domainName)
279 int dID = DOMAIN_INVALID;
281 for (int i = 0; i < s_iDomainCount; i++) {
282 if (strcasecmp (domainName, s_aszDomainName[i]) == 0) {
291 SignalFilter::convertDomainIDToName (const int domainID)
293 static const char *name = "";
295 if (domainID >= 0 && domainID < s_iDomainCount)
296 return (s_aszDomainName [domainID]);
302 SignalFilter::convertDomainIDToTitle (const int domainID)
304 static const char *title = "";
306 if (domainID >= 0 && domainID < s_iDomainCount)
307 return (s_aszDomainTitle [domainID]);
314 SignalFilter::response (double x)
318 if (m_idDomain == DOMAIN_SPATIAL)
319 response = spatialResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
320 else if (m_idDomain == DOMAIN_FREQUENCY)
321 response = frequencyResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
328 SignalFilter::spatialResponse (int filterID, double bw, double x, double param)
330 if (haveAnalyticSpatial(filterID))
331 return spatialResponseAnalytic (filterID, bw, x, param);
333 return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL);
337 SignalFilter::copyFilterData (double* pdFilter, const int iStart, const int nPoints) const
339 int iFirst = clamp (iStart, 0, m_nFilterPoints - 1);
340 int iLast = clamp (iFirst + nPoints - 1, 0, m_nFilterPoints - 1);
342 for (int i = iFirst; i <= iLast; i++)
343 pdFilter[i - iFirst] = m_adFilter[i];
347 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
348 * transform of filters's frequency
352 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
353 * double y Filter's response in spatial domain
354 * int filt_type Type of filter (definitions in ct.h)
355 * double x Spatial position to evaluate filter
356 * double m_bw Bandwidth of window
357 * double param General parameter for various filters
358 * int n Number of points to calculate integrations
362 SignalFilter::spatialResponseCalc (double x) const
364 return (spatialResponseCalc (m_idFilter, m_dBandwidth, x, m_dFilterParam, N_INTEGRAL));
368 SignalFilter::spatialResponseCalc (int filterID, double bw, double x, double param, int n)
372 if (filterID == FILTER_TRIANGLE) {
379 double zinc = (zmax - zmin) / (n - 1);
382 double* q = new double [n];
383 for (int i = 0; i < n; i++, z += zinc)
384 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
386 double y = 2 * integrateSimpson (zmin, zmax, q, n);
394 * filter_frequency_response Return filter frequency response
397 * h = filter_frequency_response (filt_type, u, m_bw, param)
398 * double h Filters frequency response at u
399 * int filt_type Type of filter
400 * double u Frequency to evaluate filter at
401 * double m_bw Bandwidth of filter
402 * double param General input parameter for various filters
406 SignalFilter::frequencyResponse (double u) const
408 return frequencyResponse (m_idFilter, m_dBandwidth, u, m_dFilterParam);
413 SignalFilter::frequencyResponse (int filterID, double bw, double u, double param)
416 double au = fabs (u);
417 double abw = fabs (bw);
420 case FILTER_BANDLIMIT:
421 if (au >= (abw / 2) + F_EPSILON)
426 case FILTER_ABS_BANDLIMIT:
427 if (au >= (abw / 2) + F_EPSILON)
432 case FILTER_TRIANGLE:
433 if (au >= (abw / 2) + F_EPSILON)
439 if (au >= (abw / 2) + F_EPSILON)
442 q = cos(PI * au / abw);
444 case FILTER_ABS_COSINE:
445 if (au >= (abw / 2) + F_EPSILON)
448 q = au * cos(PI * au / abw);
451 q = abw * sinc (PI * abw * au, 1.);
453 case FILTER_ABS_SINC:
454 if (au >= (abw / 2) + F_EPSILON)
457 q = au * abw * sinc (PI * abw * au, 1.);
461 // follow through to G_HAMMING
462 case FILTER_G_HAMMING:
463 if (au >= (abw / 2) + F_EPSILON)
466 q = param + (1 - param) * cos (TWOPI * au / abw);
468 case FILTER_ABS_HANNING:
470 // follow through to ABS_G_HAMMING
471 case FILTER_ABS_G_HAMMING:
472 if (au >= (abw / 2) + F_EPSILON)
475 q = au * (param + (1 - param) * cos(TWOPI * au / abw));
479 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
489 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
490 * transform of filters's frequency
494 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
495 * double y Filter's response in spatial domain
496 * int filt_type Type of filter (definitions in ct.h)
497 * double x Spatial position to evaluate filter
498 * double m_bw Bandwidth of window
499 * double param General parameter for various filters
503 SignalFilter::spatialResponseAnalytic (double x) const
505 return spatialResponseAnalytic (m_idFilter, m_dBandwidth, x, m_dFilterParam);
509 SignalFilter::haveAnalyticSpatial (int filterID)
511 bool haveAnalytic = false;
514 case FILTER_BANDLIMIT:
515 case FILTER_TRIANGLE:
517 case FILTER_G_HAMMING:
519 case FILTER_ABS_BANDLIMIT:
520 case FILTER_ABS_COSINE:
521 case FILTER_ABS_G_HAMMING:
522 case FILTER_ABS_HANNING:
531 return (haveAnalytic);
535 SignalFilter::spatialResponseAnalytic (int filterID, double bw, double x, double param)
538 double u = TWOPI * x;
541 double b2 = TWOPI / bw;
544 case FILTER_BANDLIMIT:
545 q = bw * sinc(u * w, 1.0);
547 case FILTER_TRIANGLE:
548 temp = sinc (u * w, 1.0);
549 q = bw * temp * temp;
552 q = sinc(b-u,w) + sinc(b+u,w);
556 // follow through to G_HAMMING
557 case FILTER_G_HAMMING:
558 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
560 case FILTER_ABS_BANDLIMIT:
561 q = 2 * integral_abscos (u, w);
563 case FILTER_ABS_COSINE:
564 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
566 case FILTER_ABS_HANNING:
568 // follow through to ABS_G_HAMMING
569 case FILTER_ABS_G_HAMMING:
570 q = 2 * param * integral_abscos(u,w) +
571 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
575 q = 4. / (PI * bw * bw);
577 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
580 if (fabs (x) < bw / 2)
585 case FILTER_ABS_SINC:
587 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
597 // Functions that are inline in filter.h
600 // sinc Return sin(x)/x function
601 // v = sinc (x, mult)
602 // Calculates sin(x * mult) / x;
604 // integral_abscos Returns integral of u*cos(u)
606 // q = integral_abscos (u, w)
607 // double q Integral value
608 // double u Integration variable
609 // double w Upper integration boundary
610 // Returns the value of integral of u*cos(u)*dV for V = 0 to w