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 1.13 2000/07/06 08:30:30 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 zeropad = 0, int numIntegral = 0)
50 m_vecFourierCosTable = NULL;
51 m_vecFourierSinTable = NULL;
53 m_idFilter = convertFilterNameToID (filterName);
54 if (m_idFilter == FILTER_INVALID) {
56 m_failMessage = "Invalid Filter name ";
57 m_failMessage += filterName;
60 m_idFilterMethod = convertFilterMethodNameToID (filterMethodName);
61 if (m_idFilterMethod == FILTER_METHOD_INVALID) {
63 m_failMessage = "Invalid filter method name ";
64 m_failMessage += filterMethodName;
67 m_idDomain = convertDomainNameToID (domainName);
68 if (m_idDomain == DOMAIN_INVALID) {
70 m_failMessage = "Invalid domain name ";
71 m_failMessage += domainName;
74 init (m_idFilter, m_idFilterMethod, bw, signalIncrement, nSignalPoints, param, m_idDomain, zeropad, numIntegral);
77 SignalFilter::SignalFilter (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const DomainID domainID, int zeropad = 0, int numIntegral = 0)
79 init (filterID, filterMethodID, bw, signalIncrement, nSignalPoints, param, domainID, zeropad, numIntegral);
82 SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param, int numIntegral = 0)
88 m_vecFourierCosTable = NULL;
89 m_vecFourierSinTable = NULL;
91 m_filterParam = param;
92 m_numIntegral = numIntegral;
93 m_idFilter = convertFilterNameToID (filterName);
94 if (m_idFilter == FILTER_INVALID) {
96 m_failMessage = "Invalid Filter name ";
97 m_failMessage += filterName;
100 m_idDomain = convertDomainNameToID (domainName);
101 if (m_idDomain == DOMAIN_INVALID) {
103 m_failMessage = "Invalid domain name ";
104 m_failMessage += domainName;
110 SignalFilter::init (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const DomainID domainID, int zeropad, int numint)
113 m_idFilter = filterID;
114 m_idDomain = domainID;
115 m_idFilterMethod = filterMethodID;
116 if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID || m_idFilterMethod == FILTER_METHOD_INVALID) {
120 m_traceLevel = TRACE_NONE;
121 m_nameFilter = convertFilterIDToName (m_idFilter);
122 m_nameDomain = convertDomainIDToName (m_idDomain);
123 m_nameFilterMethod = convertFilterMethodIDToName (m_idFilterMethod);
125 m_nSignalPoints = nSignalPoints;
126 m_signalInc = signalIncrement;
127 m_filterParam = param;
130 m_vecFourierCosTable = NULL;
131 m_vecFourierSinTable = NULL;
133 m_vecFftInput = NULL;
135 if (m_idFilterMethod == FILTER_METHOD_FFT)
136 m_idFilterMethod = FILTER_METHOD_FFTW;
138 if (m_idFilterMethod == FILTER_METHOD_FOURIER || m_idFilterMethod == FILTER_METHOD_FFT || m_idFilterMethod == FILTER_METHOD_FFTW) {
139 m_nFilterPoints = m_nSignalPoints;
141 double logBase2 = log(m_nSignalPoints) / log(2);
142 int nextPowerOf2 = static_cast<int>(floor(logBase2));
143 if (logBase2 != floor(logBase2))
145 nextPowerOf2 += m_zeropad;
146 m_nFilterPoints = 1 << nextPowerOf2;
147 cout << "nFilterPoints = " << m_nFilterPoints << endl;
149 m_filterMin = -1. / (2 * m_signalInc);
150 m_filterMax = 1. / (2 * m_signalInc);
151 m_filterInc = (m_filterMax - m_filterMin) / m_nFilterPoints;
152 m_vecFilter = new double [m_nFilterPoints];
153 int halfFilter = m_nFilterPoints / 2;
154 for (int i = 0; i <= halfFilter; i++)
155 m_vecFilter[i] = static_cast<double>(i) / halfFilter/ (2. * m_signalInc);
156 for (int i = 1; i <= halfFilter; i++)
157 m_vecFilter[m_nFilterPoints - i] = static_cast<double>(i) / halfFilter / (2. * m_signalInc);
160 // precalculate sin and cosine tables for fourier transform
161 if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
162 int nFourier = m_nFilterPoints * m_nFilterPoints + 1;
163 double angleIncrement = (2. * PI) / m_nFilterPoints;
164 m_vecFourierCosTable = new double[ nFourier ];
165 m_vecFourierSinTable = new double[ nFourier ];
167 for (int i = 0; i < nFourier; i++) {
168 m_vecFourierCosTable[i] = cos (angle);
169 m_vecFourierSinTable[i] = sin (angle);
170 angle += angleIncrement;
175 if (m_idFilterMethod == FILTER_METHOD_FFTW) {
176 for (int i = 0; i < m_nFilterPoints; i++) //fftw uses unnormalized fft
177 m_vecFilter[i] /= m_nFilterPoints;
179 m_planForward = fftw_create_plan (m_nFilterPoints, FFTW_FORWARD, FFTW_ESTIMATE);
180 m_planBackward = fftw_create_plan (m_nFilterPoints, FFTW_BACKWARD, FFTW_ESTIMATE);
181 m_vecFftInput = new fftw_complex [ m_nFilterPoints ];
182 for (int i = 0; i < m_nFilterPoints; i++)
183 m_vecFftInput[i].re = m_vecFftInput[i].im = 0;
187 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
188 m_nFilterPoints = 2 * m_nSignalPoints - 1;
189 m_filterMin = -m_signalInc * (m_nSignalPoints - 1);
190 m_filterMax = m_signalInc * (m_nSignalPoints - 1);
191 m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1);
192 m_numIntegral = numint;
193 m_vecFilter = new double[ m_nFilterPoints ];
195 if (m_idFilter == FILTER_SHEPP) {
197 double c = - 4. / (a * a);
198 int center = (m_nFilterPoints - 1) / 2;
199 int sidelen = center;
200 m_vecFilter[center] = 4. / (a * a);
202 for (int i = 1; i <= sidelen; i++ )
203 m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1);
204 } else if (m_idDomain == DOMAIN_FREQUENCY) {
207 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
208 m_vecFilter[i] = frequencyResponse (x, param);
209 } else if (m_idDomain == DOMAIN_SPATIAL) {
212 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
214 m_vecFilter[i] = spatialResponseAnalytic (x, param);
216 m_vecFilter[i] = spatialResponseCalc (x, param, numint);
218 m_failMessage = "Illegal domain name ";
219 m_failMessage += m_idDomain;
225 SignalFilter::~SignalFilter (void)
227 delete [] m_vecFilter;
228 delete [] m_vecFourierSinTable;
229 delete [] m_vecFourierCosTable;
230 delete [] m_vecFftInput;
232 if (m_idFilterMethod == FILTER_METHOD_FFTW) {
233 fftw_destroy_plan(m_planForward);
234 fftw_destroy_plan(m_planBackward);
240 const SignalFilter::FilterID
241 SignalFilter::convertFilterNameToID (const char *filterName)
243 FilterID filterID = FILTER_INVALID;
245 if (strcasecmp (filterName, FILTER_BANDLIMIT_STR) == 0)
246 filterID = FILTER_BANDLIMIT;
247 else if (strcasecmp (filterName, FILTER_HAMMING_STR) == 0)
248 filterID = FILTER_G_HAMMING;
249 else if (strcasecmp (filterName, FILTER_SINC_STR) == 0)
250 filterID = FILTER_SINC;
251 else if (strcasecmp (filterName, FILTER_COS_STR) == 0)
252 filterID = FILTER_COSINE;
253 else if (strcasecmp (filterName, FILTER_TRIANGLE_STR) == 0)
254 filterID = FILTER_TRIANGLE;
255 else if (strcasecmp (filterName, FILTER_ABS_BANDLIMIT_STR) == 0)
256 filterID = FILTER_ABS_BANDLIMIT;
257 else if (strcasecmp (filterName, FILTER_ABS_HAMMING_STR) == 0)
258 filterID = FILTER_ABS_G_HAMMING;
259 else if (strcasecmp (filterName, FILTER_ABS_SINC_STR) == 0)
260 filterID = FILTER_ABS_SINC;
261 else if (strcasecmp (filterName, FILTER_ABS_COS_STR) == 0)
262 filterID = FILTER_ABS_COSINE;
263 else if (strcasecmp (filterName, FILTER_SHEPP_STR) == 0)
264 filterID = FILTER_SHEPP;
270 SignalFilter::convertFilterIDToName (const FilterID filterID)
272 const char *name = "";
274 if (filterID == FILTER_SHEPP)
275 name = FILTER_SHEPP_STR;
276 else if (filterID == FILTER_ABS_COSINE)
277 name = FILTER_ABS_COS_STR;
278 else if (filterID == FILTER_ABS_SINC)
279 name = FILTER_ABS_SINC_STR;
280 else if (filterID == FILTER_ABS_G_HAMMING)
281 name = FILTER_ABS_HAMMING_STR;
282 else if (filterID == FILTER_ABS_BANDLIMIT)
283 name = FILTER_ABS_BANDLIMIT_STR;
284 else if (filterID == FILTER_COSINE)
285 name = FILTER_COS_STR;
286 else if (filterID == FILTER_SINC)
287 name = FILTER_SINC_STR;
288 else if (filterID == FILTER_G_HAMMING)
289 name = FILTER_HAMMING_STR;
290 else if (filterID == FILTER_BANDLIMIT)
291 name = FILTER_BANDLIMIT_STR;
292 else if (filterID == FILTER_TRIANGLE)
293 name = FILTER_TRIANGLE_STR;
298 const SignalFilter::FilterMethodID
299 SignalFilter::convertFilterMethodNameToID (const char* const filterMethodName)
301 FilterMethodID fmID = FILTER_METHOD_INVALID;
303 if (strcasecmp (filterMethodName, FILTER_METHOD_CONVOLUTION_STR) == 0)
304 fmID = FILTER_METHOD_CONVOLUTION;
305 else if (strcasecmp (filterMethodName, FILTER_METHOD_FOURIER_STR) == 0)
306 fmID = FILTER_METHOD_FOURIER;
307 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_STR) == 0)
308 fmID = FILTER_METHOD_FFT;
309 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFTW_STR) == 0)
310 fmID = FILTER_METHOD_FFTW;
316 SignalFilter::convertFilterMethodIDToName (const FilterMethodID fmID)
318 const char *name = "";
320 if (fmID == FILTER_METHOD_CONVOLUTION)
321 return (FILTER_METHOD_CONVOLUTION_STR);
322 else if (fmID == FILTER_METHOD_FOURIER)
323 return (FILTER_METHOD_FOURIER_STR);
324 else if (fmID == FILTER_METHOD_FFT)
325 return (FILTER_METHOD_FFT_STR);
326 else if (fmID == FILTER_METHOD_FFTW)
327 return (FILTER_METHOD_FFTW_STR);
332 const SignalFilter::DomainID
333 SignalFilter::convertDomainNameToID (const char* const domainName)
335 DomainID dID = DOMAIN_INVALID;
337 if (strcasecmp (domainName, DOMAIN_SPATIAL_STR) == 0)
338 dID = DOMAIN_SPATIAL;
339 else if (strcasecmp (domainName, DOMAIN_FREQUENCY_STR) == 0)
340 dID = DOMAIN_FREQUENCY;
346 SignalFilter::convertDomainIDToName (const DomainID domain)
348 const char *name = "";
350 if (domain == DOMAIN_SPATIAL)
351 return (DOMAIN_SPATIAL_STR);
352 else if (domain == DOMAIN_FREQUENCY)
353 return (DOMAIN_FREQUENCY_STR);
360 SignalFilter::filterSignal (const float input[], double output[]) const
362 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
363 for (int i = 0; i < m_nSignalPoints; i++)
364 output[i] = convolve (input, m_signalInc, i, m_nSignalPoints);
365 } else if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
366 complex<double> fftSignal[m_nFilterPoints];
367 complex<double> complexOutput[m_nFilterPoints];
368 complex<double> filteredSignal[m_nFilterPoints];
369 double inputSignal[m_nFilterPoints];
370 for (int i = 0; i < m_nSignalPoints; i++)
371 inputSignal[i] = input[i];
372 for (int i = m_nSignalPoints; i < m_nFilterPoints; i++)
373 inputSignal[i] = 0; // zeropad
374 finiteFourierTransform (inputSignal, fftSignal, m_nFilterPoints, -1);
375 dotProduct (m_vecFilter, fftSignal, filteredSignal, m_nFilterPoints);
376 finiteFourierTransform (filteredSignal, complexOutput, m_nFilterPoints, 1);
377 for (int i = 0; i < m_nSignalPoints; i++)
378 output[i] = complexOutput[i].real();
381 else if (m_idFilterMethod == FILTER_METHOD_FFTW) {
382 for (int i = 0; i < m_nSignalPoints; i++)
383 m_vecFftInput[i].re = input[i];
385 fftw_complex out[m_nFilterPoints];
386 fftw_one(m_planForward, m_vecFftInput, out);
387 for (int i = 0; i < m_nFilterPoints; i++) {
388 out[i].re = m_vecFilter[i] * out[i].re;
389 out[i].im = m_vecFilter[i] * out[i].im;
391 fftw_complex outFiltered[m_nFilterPoints];
392 fftw_one(m_planBackward, out, outFiltered);
393 for (int i = 0; i < m_nSignalPoints; i++)
394 output[i] = outFiltered[i].re;
400 SignalFilter::response (double x)
404 if (m_idDomain == DOMAIN_SPATIAL)
405 response = spatialResponse (m_idFilter, m_bw, x, m_filterParam, m_numIntegral);
406 else if (m_idDomain == DOMAIN_FREQUENCY)
407 response = frequencyResponse (m_idFilter, m_bw, x, m_filterParam);
414 SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param, int nIntegral = 0)
417 return spatialResponseAnalytic (filterID, bw, x, param);
419 return spatialResponseCalc (filterID, bw, x, param, nIntegral);
423 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
424 * transform of filters's frequency
428 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
429 * double y Filter's response in spatial domain
430 * int filt_type Type of filter (definitions in ct.h)
431 * double x Spatial position to evaluate filter
432 * double m_bw Bandwidth of window
433 * double param General parameter for various filters
434 * int n Number of points to calculate integrations
438 SignalFilter::spatialResponseCalc (double x, double param, int nIntegral) const
440 return (spatialResponseCalc (m_idFilter, m_bw, x, param, nIntegral));
444 SignalFilter::spatialResponseCalc (FilterID filterID, double bw, double x, double param, int n)
448 if (filterID == FILTER_TRIANGLE) {
455 double zinc = (zmax - zmin) / (n - 1);
459 for (int i = 0; i < n; i++, z += zinc)
460 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
462 double y = 2 * integrateSimpson (zmin, zmax, q, n);
469 * filter_frequency_response Return filter frequency response
472 * h = filter_frequency_response (filt_type, u, m_bw, param)
473 * double h Filters frequency response at u
474 * int filt_type Type of filter
475 * double u Frequency to evaluate filter at
476 * double m_bw Bandwidth of filter
477 * double param General input parameter for various filters
481 SignalFilter::frequencyResponse (double u, double param) const
483 return frequencyResponse (m_idFilter, m_bw, u, param);
488 SignalFilter::frequencyResponse (FilterID filterID, double bw, double u, double param)
491 double au = fabs (u);
494 case FILTER_BANDLIMIT:
500 case FILTER_ABS_BANDLIMIT:
506 case FILTER_TRIANGLE:
516 q = cos(PI * u / bw);
518 case FILTER_ABS_COSINE:
522 q = au * cos(PI * u / bw);
525 q = bw * sinc (PI * bw * u, 1.);
527 case FILTER_ABS_SINC:
528 q = au * bw * sinc (PI * bw * u, 1.);
530 case FILTER_G_HAMMING:
534 q = param + (1 - param) * cos (TWOPI * u / bw);
536 case FILTER_ABS_G_HAMMING:
540 q = au * (param + (1 - param) * cos(TWOPI * u / bw));
544 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
553 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
554 * transform of filters's frequency
558 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
559 * double y Filter's response in spatial domain
560 * int filt_type Type of filter (definitions in ct.h)
561 * double x Spatial position to evaluate filter
562 * double m_bw Bandwidth of window
563 * double param General parameter for various filters
567 SignalFilter::spatialResponseAnalytic (double x, double param) const
569 return spatialResponseAnalytic (m_idFilter, m_bw, x, param);
573 SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, double param)
576 double u = TWOPI * x;
579 double b2 = TWOPI / bw;
582 case FILTER_BANDLIMIT:
583 q = bw * sinc(u * w, 1.0);
585 case FILTER_TRIANGLE:
586 temp = sinc (u * w, 1.0);
587 q = bw * temp * temp;
590 q = sinc(b-u,w) + sinc(b+u,w);
592 case FILTER_G_HAMMING:
593 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
595 case FILTER_ABS_BANDLIMIT:
596 q = 2 * integral_abscos (u, w);
598 case FILTER_ABS_COSINE:
599 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
601 case FILTER_ABS_G_HAMMING:
602 q = 2 * param * integral_abscos(u,w) +
603 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
607 q = 4. / (PI * bw * bw);
609 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
612 if (fabs (x) < bw / 2)
617 case FILTER_ABS_SINC:
619 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
629 * sinc Return sin(x)/x function
633 * double v sinc value
637 * v = sin(x * mult) / x;
642 * integral_abscos Returns integral of u*cos(u)
645 * q = integral_abscos (u, w)
646 * double q Integral value
647 * double u Integration variable
648 * double w Upper integration boundary
651 * Returns the value of integral of u*cos(u)*dV for V = 0 to w
655 SignalFilter::integral_abscos (double u, double w)
657 return (fabs (u) > F_EPSILON
658 ? (cos(u * w) - 1) / (u * u) + w / u * sin (u * w)
664 * convolve Discrete convolution of two functions
667 * r = convolve (f1, f2, dx, n, np, func_type)
668 * double r Convolved result
669 * double f1[], f2[] Functions to be convolved
670 * double dx Difference between successive x values
671 * int n Array index to center convolution about
672 * int np Number of points in f1 array
673 * int func_type EVEN or ODD or EVEN_AND_ODD function f2
676 * f1 is the projection data, its indices range from 0 to np - 1.
677 * The index for f2, the filter, ranges from -(np-1) to (np-1).
678 * There are 3 ways to handle the negative vertices of f2:
679 * 1. If we know f2 is an EVEN function, then f2[-n] = f2[n].
680 * All filters used in reconstruction are even.
681 * 2. If we know f2 is an ODD function, then f2[-n] = -f2[n]
682 * 3. If f2 is both ODD AND EVEN, then we must store the value of f2
683 * for negative indices. Since f2 must range from -(np-1) to (np-1),
684 * if we add (np - 1) to f2's array index, then f2's index will
685 * range from 0 to 2 * (np - 1), and the origin, x = 0, will be
686 * stored at f2[np-1].
690 SignalFilter::convolve (const double func[], const double dx, const int n, const int np) const
694 #if UNOPTIMIZED_CONVOLUTION
695 for (int i = 0; i < np; i++)
696 sum += func[i] * m_vecFilter[n - i + (np - 1)];
698 double* f2 = m_vecFilter + n + (np - 1);
699 for (int i = 0; i < np; i++)
700 sum += *func++ * *f2--;
708 SignalFilter::convolve (const float func[], const double dx, const int n, const int np) const
712 #if UNOPTIMIZED_CONVOLUTION
713 for (int i = 0; i < np; i++)
714 sum += func[i] * m_vecFilter[n - i + (np - 1)];
716 double* f2 = m_vecFilter + n + (np - 1);
717 for (int i = 0; i < np; i++)
718 sum += *func++ * *f2--;
726 SignalFilter::finiteFourierTransform (const double input[], complex<double> output[], const int n, int direction)
733 double angleIncrement = direction * 2 * PI / n;
734 for (int i = 0; i < n; i++) {
737 for (int j = 0; j < n; j++) {
738 double angle = i * j * angleIncrement;
739 sumReal += input[j] * cos(angle);
740 sumImag += input[j] * sin(angle);
746 output[i] = complex<double> (sumReal, sumImag);
752 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], const int n, int direction)
759 double angleIncrement = 2 * PI / n;
760 for (int i = 0; i < n; i++) {
761 complex<double> sum (0,0);
762 for (int j = 0; j < n; j++) {
763 double angle = i * j * angleIncrement * direction;
764 complex<double> exponentTerm (cos(angle), sin(angle));
765 sum += input[j] * exponentTerm;
775 SignalFilter::finiteFourierTransform (const double input[], complex<double> output[], int direction) const
782 for (int i = 0; i < m_nFilterPoints; i++) {
783 double sumReal = 0, sumImag = 0;
784 for (int j = 0; j < m_nFilterPoints; j++) {
785 int tableIndex = i * j;
787 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
788 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
790 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
791 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
795 sumReal /= m_nFilterPoints;
796 sumImag /= m_nFilterPoints;
798 output[i] = complex<double> (sumReal, sumImag);
802 // (a+bi) * (c + di) = (ac - db) + (bc + da)i
805 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], int direction) const
812 for (int i = 0; i < m_nSignalPoints; i++) {
813 double sumReal = 0, sumImag = 0;
814 for (int j = 0; j < m_nSignalPoints; j++) {
815 int tableIndex = i * j;
817 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
818 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
820 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
821 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
825 sumReal /= m_nSignalPoints;
826 sumImag /= m_nSignalPoints;
828 output[i] = complex<double> (sumReal, sumImag);
834 SignalFilter::dotProduct (const double v1[], const complex<double> v2[], complex<double> output[], const int n)
836 for (int i = 0; i < n; i++)
837 output[i] = v1[i] * v2[i];