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 1.37 2001/02/16 00:28:41 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_HANNING = 2;
36 const int SignalFilter::FILTER_ABS_COSINE = 3;
37 const int SignalFilter::FILTER_ABS_SINC = 4;
38 const int SignalFilter::FILTER_SHEPP = 5;
39 const int SignalFilter::FILTER_BANDLIMIT = 6;
40 const int SignalFilter::FILTER_SINC = 7;
41 const int SignalFilter::FILTER_G_HAMMING = 8;
42 const int SignalFilter::FILTER_HANNING = 9;
43 const int SignalFilter::FILTER_COSINE = 10;
44 const int SignalFilter::FILTER_TRIANGLE = 11;
46 const int SignalFilter::s_iReconstructFilterCount = 4;
48 const char* SignalFilter::s_aszFilterName[] = {
63 const char* SignalFilter::s_aszFilterTitle[] = {
64 {"Abs(w) * Bandlimit"},
78 const int SignalFilter::s_iFilterCount = sizeof(s_aszFilterName) / sizeof(const char*);
81 const int SignalFilter::DOMAIN_INVALID = -1;
82 const int SignalFilter::DOMAIN_FREQUENCY = 0;
83 const int SignalFilter::DOMAIN_SPATIAL = 1;
85 const char* SignalFilter::s_aszDomainName[] = {
90 const char* SignalFilter::s_aszDomainTitle[] = {
95 const int SignalFilter::s_iDomainCount = sizeof(s_aszDomainName) / sizeof(const char*);
99 * SignalFilter::SignalFilter Construct a signal
102 * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic)
103 * double f Generated filter vector
104 * int filt_type Type of filter wanted
105 * double bw Bandwidth of filter
106 * double filterMin, filterMax Filter limits
107 * int nFilterPoints Number of points in signal
108 * double param General input parameter to filters
109 * int domain FREQUENCY or SPATIAL domain wanted
112 SignalFilter::SignalFilter (const char* szFilterName, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const char* szDomainName)
113 : m_adFilter(NULL), m_fail(false)
115 m_idFilter = convertFilterNameToID (szFilterName);
116 if (m_idFilter == FILTER_INVALID) {
118 m_failMessage = "Invalid Filter name ";
119 m_failMessage += szFilterName;
122 m_idDomain = convertDomainNameToID (szDomainName);
123 if (m_idDomain == DOMAIN_INVALID) {
125 m_failMessage = "Invalid domain name ";
126 m_failMessage += szDomainName;
129 init (m_idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, m_idDomain);
132 SignalFilter::SignalFilter (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
133 : m_adFilter(NULL), m_fail(false)
135 init (idFilter, dFilterMinimum, dFilterMaximum, nFilterPoints, dBandwidth, dFilterParam, idDomain);
138 SignalFilter::SignalFilter (const char* szFilterName, const char* szDomainName, double dBandwidth, double dFilterParam)
139 : m_adFilter(NULL), m_fail(false)
142 m_dBandwidth = dBandwidth;
143 m_dFilterParam = dFilterParam;
144 m_idFilter = convertFilterNameToID (szFilterName);
145 if (m_idFilter == FILTER_INVALID) {
147 m_failMessage = "Invalid Filter name ";
148 m_failMessage += szFilterName;
151 m_idDomain = convertDomainNameToID (szDomainName);
152 if (m_idDomain == DOMAIN_INVALID) {
154 m_failMessage = "Invalid domain name ";
155 m_failMessage += szDomainName;
161 SignalFilter::init (const int idFilter, double dFilterMinimum, double dFilterMaximum, int nFilterPoints, double dBandwidth, double dFilterParam, const int idDomain)
163 m_idFilter = idFilter;
164 m_idDomain = idDomain;
165 if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID) {
169 if (nFilterPoints < 2) {
171 m_failMessage = "Number of filter points ";
172 m_failMessage += nFilterPoints;
173 m_failMessage = " less than 2";
177 m_nameFilter = convertFilterIDToName (m_idFilter);
178 m_nameDomain = convertDomainIDToName (m_idDomain);
179 m_nFilterPoints = nFilterPoints;
180 m_dFilterParam = dFilterParam;
181 m_dBandwidth = dBandwidth;
182 m_dFilterMin = dFilterMinimum;
183 m_dFilterMax = dFilterMaximum;
185 m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
186 m_adFilter = new double [m_nFilterPoints];
188 if (m_idDomain == DOMAIN_FREQUENCY)
189 createFrequencyFilter (m_adFilter);
190 else if (m_idDomain == DOMAIN_SPATIAL)
191 createSpatialFilter (m_adFilter);
195 SignalFilter::~SignalFilter (void)
197 delete [] m_adFilter;
201 SignalFilter::createFrequencyFilter (double* adFilter) const
205 for (x = m_dFilterMin, i = 0; i < m_nFilterPoints; x += m_dFilterInc, i++)
206 adFilter[i] = frequencyResponse (x);
211 SignalFilter::createSpatialFilter (double* adFilter) const
213 if (m_idFilter == FILTER_SHEPP) {
214 double a = 2 * m_dBandwidth;
215 double c = - 4. / (a * a);
216 int center = (m_nFilterPoints - 1) / 2;
217 int sidelen = center;
218 m_adFilter[center] = 4. / (a * a);
220 for (int i = 1; i <= sidelen; i++ )
221 m_adFilter [center + i] = m_adFilter [center - i] = c / (4 * (i * i) - 1);
223 double x = m_dFilterMin;
224 for (int i = 0; i < m_nFilterPoints; i++, x += m_dFilterInc) {
225 if (haveAnalyticSpatial(m_idFilter))
226 m_adFilter[i] = spatialResponseAnalytic (x);
228 m_adFilter[i] = spatialResponseCalc (x);
234 SignalFilter::convertFilterNameToID (const char *filterName)
236 int filterID = FILTER_INVALID;
238 for (int i = 0; i < s_iFilterCount; i++)
239 if (strcasecmp (filterName, s_aszFilterName[i]) == 0) {
248 SignalFilter::convertFilterIDToName (const int filterID)
250 static const char *name = "";
252 if (filterID >= 0 && filterID < s_iFilterCount)
253 return (s_aszFilterName [filterID]);
259 SignalFilter::convertFilterIDToTitle (const int filterID)
261 static const char *title = "";
263 if (filterID >= 0 && filterID < s_iFilterCount)
264 return (s_aszFilterTitle [filterID]);
270 SignalFilter::convertDomainNameToID (const char* const domainName)
272 int dID = DOMAIN_INVALID;
274 for (int i = 0; i < s_iDomainCount; i++)
275 if (strcasecmp (domainName, s_aszDomainName[i]) == 0) {
284 SignalFilter::convertDomainIDToName (const int domainID)
286 static const char *name = "";
288 if (domainID >= 0 && domainID < s_iDomainCount)
289 return (s_aszDomainName [domainID]);
295 SignalFilter::convertDomainIDToTitle (const int domainID)
297 static const char *title = "";
299 if (domainID >= 0 && domainID < s_iDomainCount)
300 return (s_aszDomainTitle [domainID]);
307 SignalFilter::response (double x)
311 if (m_idDomain == DOMAIN_SPATIAL)
312 response = spatialResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
313 else if (m_idDomain == DOMAIN_FREQUENCY)
314 response = frequencyResponse (m_idFilter, m_dBandwidth, x, m_dFilterParam);
321 SignalFilter::spatialResponse (int filterID, double bw, double x, double param)
323 if (haveAnalyticSpatial(filterID))
324 return spatialResponseAnalytic (filterID, bw, x, param);
326 return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL);
330 SignalFilter::copyFilterData (double* pdFilter, const int iStart, const int nPoints) const
332 int iFirst = clamp (iStart, 0, m_nFilterPoints - 1);
333 int iLast = clamp (iFirst + nPoints - 1, 0, m_nFilterPoints - 1);
335 for (int i = iFirst; i <= iLast; i++)
336 pdFilter[i - iFirst] = m_adFilter[i];
340 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
341 * transform of filters's frequency
345 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
346 * double y Filter's response in spatial domain
347 * int filt_type Type of filter (definitions in ct.h)
348 * double x Spatial position to evaluate filter
349 * double m_bw Bandwidth of window
350 * double param General parameter for various filters
351 * int n Number of points to calculate integrations
355 SignalFilter::spatialResponseCalc (double x) const
357 return (spatialResponseCalc (m_idFilter, m_dBandwidth, x, m_dFilterParam, N_INTEGRAL));
361 SignalFilter::spatialResponseCalc (int filterID, double bw, double x, double param, int n)
365 if (filterID == FILTER_TRIANGLE) {
372 double zinc = (zmax - zmin) / (n - 1);
375 double* q = new double [n];
376 for (int i = 0; i < n; i++, z += zinc)
377 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
379 double y = 2 * integrateSimpson (zmin, zmax, q, n);
387 * filter_frequency_response Return filter frequency response
390 * h = filter_frequency_response (filt_type, u, m_bw, param)
391 * double h Filters frequency response at u
392 * int filt_type Type of filter
393 * double u Frequency to evaluate filter at
394 * double m_bw Bandwidth of filter
395 * double param General input parameter for various filters
399 SignalFilter::frequencyResponse (double u) const
401 return frequencyResponse (m_idFilter, m_dBandwidth, u, m_dFilterParam);
406 SignalFilter::frequencyResponse (int filterID, double bw, double u, double param)
409 double au = fabs (u);
412 case FILTER_BANDLIMIT:
413 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
418 case FILTER_ABS_BANDLIMIT:
419 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
424 case FILTER_TRIANGLE:
425 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
431 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
434 q = cos(PI * u / bw);
436 case FILTER_ABS_COSINE:
437 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
440 q = au * cos(PI * u / bw);
443 q = bw * sinc (PI * bw * u, 1.);
445 case FILTER_ABS_SINC:
446 q = au * bw * sinc (PI * bw * u, 1.);
450 // follow through to G_HAMMING
451 case FILTER_G_HAMMING:
452 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
455 q = param + (1 - param) * cos (TWOPI * u / bw);
457 case FILTER_ABS_HANNING:
459 // follow through to ABS_G_HAMMING
460 case FILTER_ABS_G_HAMMING:
461 if (fabs(au) >= fabs(bw / 2) + F_EPSILON)
464 q = au * (param + (1 - param) * cos(TWOPI * u / bw));
468 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
477 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
478 * transform of filters's frequency
482 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
483 * double y Filter's response in spatial domain
484 * int filt_type Type of filter (definitions in ct.h)
485 * double x Spatial position to evaluate filter
486 * double m_bw Bandwidth of window
487 * double param General parameter for various filters
491 SignalFilter::spatialResponseAnalytic (double x) const
493 return spatialResponseAnalytic (m_idFilter, m_dBandwidth, x, m_dFilterParam);
497 SignalFilter::haveAnalyticSpatial (int filterID)
499 bool haveAnalytic = false;
502 case FILTER_BANDLIMIT:
503 case FILTER_TRIANGLE:
505 case FILTER_G_HAMMING:
507 case FILTER_ABS_BANDLIMIT:
508 case FILTER_ABS_COSINE:
509 case FILTER_ABS_G_HAMMING:
510 case FILTER_ABS_HANNING:
519 return (haveAnalytic);
523 SignalFilter::spatialResponseAnalytic (int filterID, double bw, double x, double param)
526 double u = TWOPI * x;
529 double b2 = TWOPI / bw;
532 case FILTER_BANDLIMIT:
533 q = bw * sinc(u * w, 1.0);
535 case FILTER_TRIANGLE:
536 temp = sinc (u * w, 1.0);
537 q = bw * temp * temp;
540 q = sinc(b-u,w) + sinc(b+u,w);
544 // follow through to G_HAMMING
545 case FILTER_G_HAMMING:
546 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
548 case FILTER_ABS_BANDLIMIT:
549 q = 2 * integral_abscos (u, w);
551 case FILTER_ABS_COSINE:
552 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
554 case FILTER_ABS_HANNING:
556 // follow through to ABS_G_HAMMING
557 case FILTER_ABS_G_HAMMING:
558 q = 2 * param * integral_abscos(u,w) +
559 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
563 q = 4. / (PI * bw * bw);
565 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
568 if (fabs (x) < bw / 2)
573 case FILTER_ABS_SINC:
575 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
585 // Functions that are inline in filter.h
588 // sinc Return sin(x)/x function
589 // v = sinc (x, mult)
590 // Calculates sin(x * mult) / x;
592 // integral_abscos Returns integral of u*cos(u)
594 // q = integral_abscos (u, w)
595 // double q Integral value
596 // double u Integration variable
597 // double w Upper integration boundary
598 // Returns the value of integral of u*cos(u)*dV for V = 0 to w