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 1.10 2000/07/05 01:34:46 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 ******************************************************************************/
32 * SignalFilter::SignalFilter Construct a signal
35 * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic)
36 * double f Generated filter vector
37 * int filt_type Type of filter wanted
38 * double bw Bandwidth of filter
39 * double filterMin, filterMax Filter limits
40 * int nSignalPoints Number of points in signal
41 * double param General input parameter to filters
42 * int domain FREQUENCY or SPATIAL domain wanted
43 * int numint Number if intervals for calculating discrete inverse fourier xform
44 * for spatial domain filters. For ANALYTIC solutions, use numint = 0
47 SignalFilter::SignalFilter (const char* filterName, const char* filterMethodName, double bw, double signalIncrement, int nSignalPoints, double param, const char* domainName, int numIntegral = 0)
50 m_vecFourierCosTable = NULL;
51 m_vecFourierSinTable = NULL;
52 m_idFilter = convertFilterNameToID (filterName);
53 if (m_idFilter == FILTER_INVALID) {
55 m_failMessage = "Invalid Filter name ";
56 m_failMessage += filterName;
59 m_idFilterMethod = convertFilterMethodNameToID (filterMethodName);
60 if (m_idFilterMethod == FILTER_METHOD_INVALID) {
62 m_failMessage = "Invalid filter method name ";
63 m_failMessage += filterMethodName;
66 m_idDomain = convertDomainNameToID (domainName);
67 if (m_idDomain == DOMAIN_INVALID) {
69 m_failMessage = "Invalid domain name ";
70 m_failMessage += domainName;
73 init (m_idFilter, m_idFilterMethod, bw, signalIncrement, nSignalPoints, param, m_idDomain, numIntegral);
76 SignalFilter::SignalFilter (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const DomainID domainID, int numIntegral = 0)
78 init (filterID, filterMethodID, bw, signalIncrement, nSignalPoints, param, domainID, numIntegral);
81 SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param, int numIntegral = 0)
87 m_vecFourierCosTable = NULL;
88 m_vecFourierSinTable = NULL;
89 m_filterParam = param;
90 m_numIntegral = numIntegral;
91 m_idFilter = convertFilterNameToID (filterName);
92 if (m_idFilter == FILTER_INVALID) {
94 m_failMessage = "Invalid Filter name ";
95 m_failMessage += filterName;
98 m_idDomain = convertDomainNameToID (domainName);
99 if (m_idDomain == DOMAIN_INVALID) {
101 m_failMessage = "Invalid domain name ";
102 m_failMessage += domainName;
108 SignalFilter::init (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const DomainID domainID, int numint)
111 m_idFilter = filterID;
112 m_idDomain = domainID;
113 m_idFilterMethod = filterMethodID;
114 if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID || m_idFilterMethod == FILTER_METHOD_INVALID) {
118 m_traceLevel = TRACE_NONE;
119 m_nameFilter = convertFilterIDToName (m_idFilter);
120 m_nameDomain = convertDomainIDToName (m_idDomain);
121 m_nameFilterMethod = convertFilterMethodIDToName (m_idFilterMethod);
123 m_nSignalPoints = nSignalPoints;
124 m_signalInc = signalIncrement;
125 m_filterParam = param;
127 if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
128 int nFourier = m_nSignalPoints * m_nSignalPoints + 1;
129 double angleIncrement = (2. * PI) / m_nSignalPoints;
130 m_vecFourierCosTable = new double[ nFourier ];
131 m_vecFourierSinTable = new double[ nFourier ];
132 for (int i = 0; i < nFourier; i++) {
133 m_vecFourierCosTable[i] = cos (angleIncrement * i);
134 m_vecFourierSinTable[i] = sin (angleIncrement * i);
136 m_nFilterPoints = m_nSignalPoints;
137 m_filterMin = -1. / (2 * m_signalInc);
138 m_filterMax = 1. / (2 * m_signalInc);
139 m_filterInc = (m_filterMax - m_filterMin) / m_nFilterPoints;
140 m_vecFilter = new double [m_nFilterPoints];
141 int halfFilter = m_nFilterPoints / 2;
142 for (int i = 0; i < halfFilter; i++)
143 m_vecFilter[i] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
144 for (int i = 0; i < halfFilter; i++)
145 m_vecFilter[m_nFilterPoints - i - 1] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
146 if (halfFilter % 2) // odd
147 m_vecFilter[halfFilter] = 1 / (2 * m_signalInc);
148 } else if (m_idFilterMethod == FILTER_METHOD_FFT || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_2 || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4) {
149 m_nFilterPoints = m_nSignalPoints;
150 if (m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_2 || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4) {
151 double logBase2 = log(m_nSignalPoints) / log(2);
152 int nextPowerOf2 = static_cast<int>(floor(logBase2)) + 1;
153 if (m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4)
155 if (logBase2 != floor(logBase2))
157 m_nFilterPoints = 1 << nextPowerOf2;
158 cout << "nFilterPoints = " << m_nFilterPoints << endl;
160 m_filterMin = -1. / (2 * m_signalInc);
161 m_filterMax = 1. / (2 * m_signalInc);
162 m_filterInc = (m_filterMax - m_filterMin) / m_nFilterPoints;
163 m_vecFilter = new double [m_nFilterPoints];
164 int halfFilter = m_nFilterPoints / 2;
165 for (int i = 0; i < halfFilter; i++)
166 m_vecFilter[i] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
167 for (int i = 0; i < halfFilter; i++)
168 m_vecFilter[m_nFilterPoints - i - 1] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
169 if (halfFilter % 2) // odd
170 m_vecFilter[halfFilter] = 1 / (2 * m_signalInc);
173 m_planForward = fftw_create_plan (m_nFilterPoints, FFTW_FORWARD, FFTW_ESTIMATE);
174 m_planBackward = fftw_create_plan (m_nFilterPoints, FFTW_BACKWARD, FFTW_ESTIMATE);
178 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
179 m_nFilterPoints = 2 * m_nSignalPoints - 1;
180 m_filterMin = -m_signalInc * (m_nSignalPoints - 1);
181 m_filterMax = m_signalInc * (m_nSignalPoints - 1);
182 m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1);
183 m_numIntegral = numint;
184 m_vecFilter = new double[ m_nFilterPoints ];
186 if (m_idFilter == FILTER_SHEPP) {
188 double c = - 4. / (a * a);
189 int center = (m_nFilterPoints - 1) / 2;
190 int sidelen = center;
191 m_vecFilter[center] = 4. / (a * a);
193 for (int i = 1; i <= sidelen; i++ )
194 m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1);
195 } else if (m_idDomain == DOMAIN_FREQUENCY) {
198 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
199 m_vecFilter[i] = frequencyResponse (x, param);
200 } else if (m_idDomain == DOMAIN_SPATIAL) {
203 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
205 m_vecFilter[i] = spatialResponseAnalytic (x, param);
207 m_vecFilter[i] = spatialResponseCalc (x, param, numint);
209 m_failMessage = "Illegal domain name ";
210 m_failMessage += m_idDomain;
216 SignalFilter::~SignalFilter (void)
219 delete m_vecFourierSinTable;
220 delete m_vecFourierCosTable;
222 if (m_idFilterMethod == FILTER_METHOD_FFT) {
223 fftw_destroy_plan(m_planForward);
224 fftw_destroy_plan(m_planBackward);
230 const SignalFilter::FilterID
231 SignalFilter::convertFilterNameToID (const char *filterName)
233 FilterID filterID = FILTER_INVALID;
235 if (strcasecmp (filterName, FILTER_BANDLIMIT_STR) == 0)
236 filterID = FILTER_BANDLIMIT;
237 else if (strcasecmp (filterName, FILTER_HAMMING_STR) == 0)
238 filterID = FILTER_G_HAMMING;
239 else if (strcasecmp (filterName, FILTER_SINC_STR) == 0)
240 filterID = FILTER_SINC;
241 else if (strcasecmp (filterName, FILTER_COS_STR) == 0)
242 filterID = FILTER_COSINE;
243 else if (strcasecmp (filterName, FILTER_TRIANGLE_STR) == 0)
244 filterID = FILTER_TRIANGLE;
245 else if (strcasecmp (filterName, FILTER_ABS_BANDLIMIT_STR) == 0)
246 filterID = FILTER_ABS_BANDLIMIT;
247 else if (strcasecmp (filterName, FILTER_ABS_HAMMING_STR) == 0)
248 filterID = FILTER_ABS_G_HAMMING;
249 else if (strcasecmp (filterName, FILTER_ABS_SINC_STR) == 0)
250 filterID = FILTER_ABS_SINC;
251 else if (strcasecmp (filterName, FILTER_ABS_COS_STR) == 0)
252 filterID = FILTER_ABS_COSINE;
253 else if (strcasecmp (filterName, FILTER_SHEPP_STR) == 0)
254 filterID = FILTER_SHEPP;
260 SignalFilter::convertFilterIDToName (const FilterID filterID)
262 const char *name = "";
264 if (filterID == FILTER_SHEPP)
265 name = FILTER_SHEPP_STR;
266 else if (filterID == FILTER_ABS_COSINE)
267 name = FILTER_ABS_COS_STR;
268 else if (filterID == FILTER_ABS_SINC)
269 name = FILTER_ABS_SINC_STR;
270 else if (filterID == FILTER_ABS_G_HAMMING)
271 name = FILTER_ABS_HAMMING_STR;
272 else if (filterID == FILTER_ABS_BANDLIMIT)
273 name = FILTER_ABS_BANDLIMIT_STR;
274 else if (filterID == FILTER_COSINE)
275 name = FILTER_COS_STR;
276 else if (filterID == FILTER_SINC)
277 name = FILTER_SINC_STR;
278 else if (filterID == FILTER_G_HAMMING)
279 name = FILTER_HAMMING_STR;
280 else if (filterID == FILTER_BANDLIMIT)
281 name = FILTER_BANDLIMIT_STR;
282 else if (filterID == FILTER_TRIANGLE)
283 name = FILTER_TRIANGLE_STR;
288 const SignalFilter::FilterMethodID
289 SignalFilter::convertFilterMethodNameToID (const char* const filterMethodName)
291 FilterMethodID fmID = FILTER_METHOD_INVALID;
293 if (strcasecmp (filterMethodName, FILTER_METHOD_CONVOLUTION_STR) == 0)
294 fmID = FILTER_METHOD_CONVOLUTION;
295 else if (strcasecmp (filterMethodName, FILTER_METHOD_FOURIER_STR) == 0)
296 fmID = FILTER_METHOD_FOURIER;
297 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_STR) == 0)
298 fmID = FILTER_METHOD_FFT;
299 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_2_STR) == 0)
300 fmID = FILTER_METHOD_FFT_ZEROPAD_2;
301 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_4_STR) == 0)
302 fmID = FILTER_METHOD_FFT_ZEROPAD_4;
303 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_6_STR) == 0)
304 fmID = FILTER_METHOD_FFT_ZEROPAD_6;
310 SignalFilter::convertFilterMethodIDToName (const FilterMethodID fmID)
312 const char *name = "";
314 if (fmID == FILTER_METHOD_CONVOLUTION)
315 return (FILTER_METHOD_CONVOLUTION_STR);
316 else if (fmID == FILTER_METHOD_FOURIER)
317 return (FILTER_METHOD_FOURIER_STR);
318 else if (fmID == FILTER_METHOD_FFT)
319 return (FILTER_METHOD_FFT_STR);
320 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_2)
321 return (FILTER_METHOD_FFT_ZEROPAD_2_STR);
322 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_4)
323 return (FILTER_METHOD_FFT_ZEROPAD_4_STR);
324 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_6)
325 return (FILTER_METHOD_FFT_ZEROPAD_6_STR);
330 const SignalFilter::DomainID
331 SignalFilter::convertDomainNameToID (const char* const domainName)
333 DomainID dID = DOMAIN_INVALID;
335 if (strcasecmp (domainName, DOMAIN_SPATIAL_STR) == 0)
336 dID = DOMAIN_SPATIAL;
337 else if (strcasecmp (domainName, DOMAIN_FREQUENCY_STR) == 0)
338 dID = DOMAIN_FREQUENCY;
344 SignalFilter::convertDomainIDToName (const DomainID domain)
346 const char *name = "";
348 if (domain == DOMAIN_SPATIAL)
349 return (DOMAIN_SPATIAL_STR);
350 else if (domain == DOMAIN_FREQUENCY)
351 return (DOMAIN_FREQUENCY_STR);
358 SignalFilter::filterSignal (const float input[], double output[]) const
360 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
361 for (int i = 0; i < m_nSignalPoints; i++)
362 output[i] = convolve (input, m_signalInc, i, m_nSignalPoints);
363 } else if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
364 complex<double> fftSignal[m_nSignalPoints];
365 complex<double> complexOutput[m_nSignalPoints];
366 complex<double> filteredSignal[m_nSignalPoints];
367 finiteFourierTransform (input, fftSignal, m_nSignalPoints, -1);
368 if (m_traceLevel >= TRACE_PLOT) {
369 double test[m_nSignalPoints];
370 for (int i = 0; i < m_nSignalPoints; i++)
371 test[i] = abs(fftSignal[i]);
372 ezplot_1d(test, m_nSignalPoints);
375 dotProduct (m_vecFilter, fftSignal, filteredSignal, m_nSignalPoints);
376 if (m_traceLevel >= TRACE_PLOT) {
377 double test[m_nSignalPoints];
378 for (int i = 0; i < m_nSignalPoints; i++)
379 test[i] = abs(filteredSignal[i]);
380 ezplot_1d(test, m_nSignalPoints);
383 finiteFourierTransform (filteredSignal, complexOutput, m_nSignalPoints, 1);
384 for (int i = 0; i < m_nSignalPoints; i++)
385 output[i] = abs( complexOutput[i] );
386 } else if (m_idFilterMethod == FILTER_METHOD_FFT || FILTER_METHOD_FFT_ZEROPAD_2 || FILTER_METHOD_FFT_ZEROPAD_4) {
387 fftw_complex in[m_nFilterPoints], out[m_nFilterPoints];
388 for (int i = 0; i < m_nSignalPoints; i++) {
392 for (int i = m_nSignalPoints; i < m_nFilterPoints; i++) {
393 in[i].re = in[i].im = 0; // ZeroPad
395 fftw_one(m_planForward, in, out);
396 if (m_traceLevel >= TRACE_PLOT) {
397 double test[m_nFilterPoints];
398 for (int i = 0; i < m_nFilterPoints; i++)
399 test[i] = sqrt(out[i].re * out[i].re + out[i].im * out[i].im);
400 ezplot_1d(test, m_nFilterPoints);
403 for (int i = 0; i < m_nFilterPoints; i++) {
404 out[i].re = m_vecFilter[i] * out[i].re / m_nSignalPoints;
405 out[i].im = m_vecFilter[i] * out[i].im / m_nSignalPoints;
407 if (m_traceLevel >= TRACE_PLOT) {
408 double test[m_nFilterPoints];
409 for (int i = 0; i < m_nFilterPoints; i++)
410 test[i] = sqrt(out[i].re * out[i].re + out[i].im * out[i].im);
411 ezplot_1d(test, m_nFilterPoints);
414 fftw_one(m_planBackward, out, in);
415 if (m_traceLevel >= TRACE_PLOT) {
416 double test[m_nFilterPoints];
417 for (int i = 0; i < m_nFilterPoints; i++)
418 test[i] = sqrt(in[i].re * in[i].re + in[i].im * in[i].im);
419 ezplot_1d(test, m_nFilterPoints);
422 for (int i = 0; i < m_nSignalPoints; i++)
423 output[i] = sqrt (in[i].re * in[i].re + in[i].im * in[i].im);
428 SignalFilter::response (double x)
432 if (m_idDomain == DOMAIN_SPATIAL)
433 response = spatialResponse (m_idFilter, m_bw, x, m_filterParam, m_numIntegral);
434 else if (m_idDomain == DOMAIN_FREQUENCY)
435 response = frequencyResponse (m_idFilter, m_bw, x, m_filterParam);
442 SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param, int nIntegral = 0)
445 return spatialResponseAnalytic (filterID, bw, x, param);
447 return spatialResponseCalc (filterID, bw, x, param, nIntegral);
451 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
452 * transform of filters's frequency
456 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
457 * double y Filter's response in spatial domain
458 * int filt_type Type of filter (definitions in ct.h)
459 * double x Spatial position to evaluate filter
460 * double m_bw Bandwidth of window
461 * double param General parameter for various filters
462 * int n Number of points to calculate integrations
466 SignalFilter::spatialResponseCalc (double x, double param, int nIntegral) const
468 return (spatialResponseCalc (m_idFilter, m_bw, x, param, nIntegral));
472 SignalFilter::spatialResponseCalc (FilterID filterID, double bw, double x, double param, int n)
476 if (filterID == FILTER_TRIANGLE) {
483 double zinc = (zmax - zmin) / (n - 1);
487 for (int i = 0; i < n; i++, z += zinc)
488 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
490 double y = 2 * integrateSimpson (zmin, zmax, q, n);
497 * filter_frequency_response Return filter frequency response
500 * h = filter_frequency_response (filt_type, u, m_bw, param)
501 * double h Filters frequency response at u
502 * int filt_type Type of filter
503 * double u Frequency to evaluate filter at
504 * double m_bw Bandwidth of filter
505 * double param General input parameter for various filters
509 SignalFilter::frequencyResponse (double u, double param) const
511 return frequencyResponse (m_idFilter, m_bw, u, param);
516 SignalFilter::frequencyResponse (FilterID filterID, double bw, double u, double param)
519 double au = fabs (u);
522 case FILTER_BANDLIMIT:
528 case FILTER_ABS_BANDLIMIT:
534 case FILTER_TRIANGLE:
544 q = cos(PI * u / bw);
546 case FILTER_ABS_COSINE:
550 q = au * cos(PI * u / bw);
553 q = bw * sinc (PI * bw * u, 1.);
555 case FILTER_ABS_SINC:
556 q = au * bw * sinc (PI * bw * u, 1.);
558 case FILTER_G_HAMMING:
562 q = param + (1 - param) * cos (TWOPI * u / bw);
564 case FILTER_ABS_G_HAMMING:
568 q = au * (param + (1 - param) * cos(TWOPI * u / bw));
572 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
581 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
582 * transform of filters's frequency
586 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
587 * double y Filter's response in spatial domain
588 * int filt_type Type of filter (definitions in ct.h)
589 * double x Spatial position to evaluate filter
590 * double m_bw Bandwidth of window
591 * double param General parameter for various filters
595 SignalFilter::spatialResponseAnalytic (double x, double param) const
597 return spatialResponseAnalytic (m_idFilter, m_bw, x, param);
601 SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, double param)
604 double u = TWOPI * x;
607 double b2 = TWOPI / bw;
610 case FILTER_BANDLIMIT:
611 q = bw * sinc(u * w, 1.0);
613 case FILTER_TRIANGLE:
614 temp = sinc (u * w, 1.0);
615 q = bw * temp * temp;
618 q = sinc(b-u,w) + sinc(b+u,w);
620 case FILTER_G_HAMMING:
621 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
623 case FILTER_ABS_BANDLIMIT:
624 q = 2 * integral_abscos (u, w);
626 case FILTER_ABS_COSINE:
627 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
629 case FILTER_ABS_G_HAMMING:
630 q = 2 * param * integral_abscos(u,w) +
631 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
635 q = 4. / (PI * bw * bw);
637 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
640 if (fabs (x) < bw / 2)
645 case FILTER_ABS_SINC:
647 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
657 * sinc Return sin(x)/x function
661 * double v sinc value
665 * v = sin(x * mult) / x;
670 * integral_abscos Returns integral of u*cos(u)
673 * q = integral_abscos (u, w)
674 * double q Integral value
675 * double u Integration variable
676 * double w Upper integration boundary
679 * Returns the value of integral of u*cos(u)*dV for V = 0 to w
683 SignalFilter::integral_abscos (double u, double w)
685 return (fabs (u) > F_EPSILON
686 ? (cos(u * w) - 1) / (u * u) + w / u * sin (u * w)
692 * convolve Discrete convolution of two functions
695 * r = convolve (f1, f2, dx, n, np, func_type)
696 * double r Convolved result
697 * double f1[], f2[] Functions to be convolved
698 * double dx Difference between successive x values
699 * int n Array index to center convolution about
700 * int np Number of points in f1 array
701 * int func_type EVEN or ODD or EVEN_AND_ODD function f2
704 * f1 is the projection data, its indices range from 0 to np - 1.
705 * The index for f2, the filter, ranges from -(np-1) to (np-1).
706 * There are 3 ways to handle the negative vertices of f2:
707 * 1. If we know f2 is an EVEN function, then f2[-n] = f2[n].
708 * All filters used in reconstruction are even.
709 * 2. If we know f2 is an ODD function, then f2[-n] = -f2[n]
710 * 3. If f2 is both ODD AND EVEN, then we must store the value of f2
711 * for negative indices. Since f2 must range from -(np-1) to (np-1),
712 * if we add (np - 1) to f2's array index, then f2's index will
713 * range from 0 to 2 * (np - 1), and the origin, x = 0, will be
714 * stored at f2[np-1].
718 SignalFilter::convolve (const double func[], const double dx, const int n, const int np) const
722 #if UNOPTIMIZED_CONVOLUTION
723 for (int i = 0; i < np; i++)
724 sum += func[i] * m_vecFilter[n - i + (np - 1)];
726 double* f2 = m_vecFilter + n + (np - 1);
727 for (int i = 0; i < np; i++)
728 sum += *func++ * *f2--;
736 SignalFilter::convolve (const float func[], const double dx, const int n, const int np) const
740 #if UNOPTIMIZED_CONVOLUTION
741 for (int i = 0; i < np; i++)
742 sum += func[i] * m_vecFilter[n - i + (np - 1)];
744 double* f2 = m_vecFilter + n + (np - 1);
745 for (int i = 0; i < np; i++)
746 sum += *func++ * *f2--;
754 SignalFilter::finiteFourierTransform (const float input[], complex<double> output[], const int n, int direction)
761 double angleIncrement = 2 * PI / n;
762 for (int i = 0; i < n; i++) {
765 for (int j = 0; j < n; j++) {
766 double angle = i * j * angleIncrement * direction;
767 sumReal += input[j] * cos(angle);
768 sumImag += input[j] * sin(angle);
774 output[i] = complex<double> (sumReal, sumImag);
780 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], const int n, int direction)
787 double angleIncrement = 2 * PI / n;
788 for (int i = 0; i < n; i++) {
789 complex<double> sum (0,0);
790 for (int j = 0; j < n; j++) {
791 double angle = i * j * angleIncrement * direction;
792 complex<double> exponentTerm (cos(angle), sin(angle));
793 sum += input[j] * exponentTerm;
803 SignalFilter::finiteFourierTransform (const float input[], complex<double> output[], int direction) const
810 for (int i = 0; i < m_nSignalPoints; i++) {
811 double sumReal = 0, sumImag = 0;
812 for (int j = 0; j < m_nSignalPoints; j++) {
813 int tableIndex = i * j;
815 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
816 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
818 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
819 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
823 sumReal /= m_nSignalPoints;
824 sumImag /= m_nSignalPoints;
826 output[i] = complex<double> (sumReal, sumImag);
830 // (a+bi) * (c + di) = (ac - db) + (bc + da)i
833 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], int direction) const
840 for (int i = 0; i < m_nSignalPoints; i++) {
841 double sumReal = 0, sumImag = 0;
842 for (int j = 0; j < m_nSignalPoints; j++) {
843 int tableIndex = i * j;
845 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
846 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
848 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
849 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
853 sumReal /= m_nSignalPoints;
854 sumImag /= m_nSignalPoints;
856 output[i] = complex<double> (sumReal, sumImag);
862 SignalFilter::dotProduct (const double v1[], const complex<double> v2[], complex<double> output[], const int n)
864 for (int i = 0; i < n; i++)
865 output[i] = v1[i] * v2[i];