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 1.8 2000/07/04 18:33:35 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_nameFilter = convertFilterIDToName (m_idFilter);
119 m_nameDomain = convertDomainIDToName (m_idDomain);
120 m_nameFilterMethod = convertFilterMethodIDToName (m_idFilterMethod);
122 m_nSignalPoints = nSignalPoints;
123 m_signalInc = signalIncrement;
124 m_filterParam = param;
126 if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
127 int nFourier = m_nSignalPoints * m_nSignalPoints + 1;
128 double angleIncrement = (2. * PI) / m_nSignalPoints;
129 m_vecFourierCosTable = new double[ nFourier ];
130 m_vecFourierSinTable = new double[ nFourier ];
131 for (int i = 0; i < nFourier; i++) {
132 m_vecFourierCosTable[i] = cos (angleIncrement * i);
133 m_vecFourierSinTable[i] = sin (angleIncrement * i);
135 m_nFilterPoints = m_nSignalPoints;
137 m_filterMax = m_nSignalPoints * m_signalInc;
138 m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1);
139 m_vecFilter = new double [m_nFilterPoints];
140 int halfFilter = m_nFilterPoints / 2;
141 for (int i = 0; i < halfFilter; i++)
142 m_vecFilter[i] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
143 for (int i = 0; i < halfFilter; i++)
144 m_vecFilter[m_nFilterPoints - i - 1] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
145 if (halfFilter % 2) // odd
146 m_vecFilter[halfFilter] = 1;
147 } else if (m_idFilterMethod == FILTER_METHOD_FFT || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_2 || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4) {
148 m_nFilterPoints = m_nSignalPoints;
149 if (m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_2 || m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4) {
150 double logBase2 = log(m_nSignalPoints) / log(2);
151 int nextPowerOf2 = static_cast<int>(floor(logBase2)) + 1;
152 if (m_idFilterMethod == FILTER_METHOD_FFT_ZEROPAD_4)
154 if (logBase2 != floor(logBase2))
156 m_nFilterPoints = 1 << nextPowerOf2;
157 cout << "nFilterPoints = " << m_nFilterPoints << endl;
160 m_filterMax = m_nSignalPoints * m_signalInc;
161 m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1);
162 m_vecFilter = new double [m_nFilterPoints];
163 int halfFilter = m_nFilterPoints / 2;
164 for (int i = 0; i < halfFilter; i++)
165 m_vecFilter[i] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
166 for (int i = 0; i < halfFilter; i++)
167 m_vecFilter[m_nFilterPoints - i - 1] = static_cast<double>(i) / (halfFilter - 1) / (2 * m_signalInc);
168 if (halfFilter % 2) // odd
169 m_vecFilter[halfFilter] = 1;
172 m_planForward = fftw_create_plan (m_nFilterPoints, FFTW_FORWARD, FFTW_ESTIMATE);
173 m_planBackward = fftw_create_plan (m_nFilterPoints, FFTW_BACKWARD, FFTW_ESTIMATE);
177 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
178 m_nFilterPoints = 2 * m_nSignalPoints - 1;
179 m_filterMin = -m_signalInc * (m_nSignalPoints - 1);
180 m_filterMax = m_signalInc * (m_nSignalPoints - 1);
181 m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1);
182 m_numIntegral = numint;
183 m_vecFilter = new double[ m_nFilterPoints ];
185 if (m_idFilter == FILTER_SHEPP) {
187 double c = - 4. / (a * a);
188 int center = (m_nFilterPoints - 1) / 2;
189 int sidelen = center;
190 m_vecFilter[center] = 4. / (a * a);
192 for (int i = 1; i <= sidelen; i++ )
193 m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1);
194 } else if (m_idDomain == DOMAIN_FREQUENCY) {
197 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
198 m_vecFilter[i] = frequencyResponse (x, param);
199 } else if (m_idDomain == DOMAIN_SPATIAL) {
202 for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++)
204 m_vecFilter[i] = spatialResponseAnalytic (x, param);
206 m_vecFilter[i] = spatialResponseCalc (x, param, numint);
208 m_failMessage = "Illegal domain name ";
209 m_failMessage += m_idDomain;
215 SignalFilter::~SignalFilter (void)
218 delete m_vecFourierSinTable;
219 delete m_vecFourierCosTable;
221 if (m_idFilterMethod == FILTER_METHOD_FFT) {
222 fftw_destroy_plan(m_planForward);
223 fftw_destroy_plan(m_planBackward);
229 const SignalFilter::FilterID
230 SignalFilter::convertFilterNameToID (const char *filterName)
232 FilterID filterID = FILTER_INVALID;
234 if (strcasecmp (filterName, FILTER_BANDLIMIT_STR) == 0)
235 filterID = FILTER_BANDLIMIT;
236 else if (strcasecmp (filterName, FILTER_HAMMING_STR) == 0)
237 filterID = FILTER_G_HAMMING;
238 else if (strcasecmp (filterName, FILTER_SINC_STR) == 0)
239 filterID = FILTER_SINC;
240 else if (strcasecmp (filterName, FILTER_COS_STR) == 0)
241 filterID = FILTER_COSINE;
242 else if (strcasecmp (filterName, FILTER_TRIANGLE_STR) == 0)
243 filterID = FILTER_TRIANGLE;
244 else if (strcasecmp (filterName, FILTER_ABS_BANDLIMIT_STR) == 0)
245 filterID = FILTER_ABS_BANDLIMIT;
246 else if (strcasecmp (filterName, FILTER_ABS_HAMMING_STR) == 0)
247 filterID = FILTER_ABS_G_HAMMING;
248 else if (strcasecmp (filterName, FILTER_ABS_SINC_STR) == 0)
249 filterID = FILTER_ABS_SINC;
250 else if (strcasecmp (filterName, FILTER_ABS_COS_STR) == 0)
251 filterID = FILTER_ABS_COSINE;
252 else if (strcasecmp (filterName, FILTER_SHEPP_STR) == 0)
253 filterID = FILTER_SHEPP;
259 SignalFilter::convertFilterIDToName (const FilterID filterID)
261 const char *name = "";
263 if (filterID == FILTER_SHEPP)
264 name = FILTER_SHEPP_STR;
265 else if (filterID == FILTER_ABS_COSINE)
266 name = FILTER_ABS_COS_STR;
267 else if (filterID == FILTER_ABS_SINC)
268 name = FILTER_ABS_SINC_STR;
269 else if (filterID == FILTER_ABS_G_HAMMING)
270 name = FILTER_ABS_HAMMING_STR;
271 else if (filterID == FILTER_ABS_BANDLIMIT)
272 name = FILTER_ABS_BANDLIMIT_STR;
273 else if (filterID == FILTER_COSINE)
274 name = FILTER_COS_STR;
275 else if (filterID == FILTER_SINC)
276 name = FILTER_SINC_STR;
277 else if (filterID == FILTER_G_HAMMING)
278 name = FILTER_HAMMING_STR;
279 else if (filterID == FILTER_BANDLIMIT)
280 name = FILTER_BANDLIMIT_STR;
281 else if (filterID == FILTER_TRIANGLE)
282 name = FILTER_TRIANGLE_STR;
287 const SignalFilter::FilterMethodID
288 SignalFilter::convertFilterMethodNameToID (const char* const filterMethodName)
290 FilterMethodID fmID = FILTER_METHOD_INVALID;
292 if (strcasecmp (filterMethodName, FILTER_METHOD_CONVOLUTION_STR) == 0)
293 fmID = FILTER_METHOD_CONVOLUTION;
294 else if (strcasecmp (filterMethodName, FILTER_METHOD_FOURIER_STR) == 0)
295 fmID = FILTER_METHOD_FOURIER;
296 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_STR) == 0)
297 fmID = FILTER_METHOD_FFT;
298 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_2_STR) == 0)
299 fmID = FILTER_METHOD_FFT_ZEROPAD_2;
300 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_4_STR) == 0)
301 fmID = FILTER_METHOD_FFT_ZEROPAD_4;
302 else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_ZEROPAD_6_STR) == 0)
303 fmID = FILTER_METHOD_FFT_ZEROPAD_6;
309 SignalFilter::convertFilterMethodIDToName (const FilterMethodID fmID)
311 const char *name = "";
313 if (fmID == FILTER_METHOD_CONVOLUTION)
314 return (FILTER_METHOD_CONVOLUTION_STR);
315 else if (fmID == FILTER_METHOD_FOURIER)
316 return (FILTER_METHOD_FOURIER_STR);
317 else if (fmID == FILTER_METHOD_FFT)
318 return (FILTER_METHOD_FFT_STR);
319 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_2)
320 return (FILTER_METHOD_FFT_ZEROPAD_2_STR);
321 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_4)
322 return (FILTER_METHOD_FFT_ZEROPAD_4_STR);
323 else if (fmID == FILTER_METHOD_FFT_ZEROPAD_6)
324 return (FILTER_METHOD_FFT_ZEROPAD_6_STR);
329 const SignalFilter::DomainID
330 SignalFilter::convertDomainNameToID (const char* const domainName)
332 DomainID dID = DOMAIN_INVALID;
334 if (strcasecmp (domainName, DOMAIN_SPATIAL_STR) == 0)
335 dID = DOMAIN_SPATIAL;
336 else if (strcasecmp (domainName, DOMAIN_FREQUENCY_STR) == 0)
337 dID = DOMAIN_FREQUENCY;
343 SignalFilter::convertDomainIDToName (const DomainID domain)
345 const char *name = "";
347 if (domain == DOMAIN_SPATIAL)
348 return (DOMAIN_SPATIAL_STR);
349 else if (domain == DOMAIN_FREQUENCY)
350 return (DOMAIN_FREQUENCY_STR);
357 SignalFilter::filterSignal (const float input[], double output[]) const
359 if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) {
360 for (int i = 0; i < m_nSignalPoints; i++)
361 output[i] = convolve (input, m_signalInc, i, m_nSignalPoints);
362 } else if (m_idFilterMethod == FILTER_METHOD_FOURIER) {
363 complex<double> fftSignal[m_nSignalPoints];
364 complex<double> complexOutput[m_nSignalPoints];
365 complex<double> filteredSignal[m_nSignalPoints];
366 finiteFourierTransform (input, fftSignal, m_nSignalPoints, -1);
367 dotProduct (m_vecFilter, fftSignal, filteredSignal, m_nSignalPoints);
368 finiteFourierTransform (filteredSignal, complexOutput, m_nSignalPoints, 1);
369 for (int i = 0; i < m_nSignalPoints; i++) {
370 output[i] = abs( complexOutput[i] );
372 } else if (m_idFilterMethod == FILTER_METHOD_FFT || FILTER_METHOD_FFT_ZEROPAD_2 || FILTER_METHOD_FFT_ZEROPAD_4) {
373 fftw_complex in[m_nFilterPoints], out[m_nFilterPoints];
374 for (int i = 0; i < m_nSignalPoints; i++) {
378 for (int i = m_nSignalPoints; i < m_nFilterPoints; i++) {
379 in[i].re = in[i].im = 0; // ZeroPad
381 fftw_one(m_planForward, in, out);
382 for (int i = 0; i < m_nFilterPoints; i++) {
383 out[i].re = m_vecFilter[i] * out[i].re / m_nSignalPoints;
384 out[i].im = m_vecFilter[i] * out[i].im / m_nSignalPoints;
386 fftw_one(m_planBackward, out, in);
387 for (int i = 0; i < m_nSignalPoints; i++)
388 output[i] = sqrt (in[i].re * in[i].re + in[i].im * in[i].im);
393 SignalFilter::response (double x)
397 if (m_idDomain == DOMAIN_SPATIAL)
398 response = spatialResponse (m_idFilter, m_bw, x, m_filterParam, m_numIntegral);
399 else if (m_idDomain == DOMAIN_FREQUENCY)
400 response = frequencyResponse (m_idFilter, m_bw, x, m_filterParam);
407 SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param, int nIntegral = 0)
410 return spatialResponseAnalytic (filterID, bw, x, param);
412 return spatialResponseCalc (filterID, bw, x, param, nIntegral);
416 * filter_spatial_response_calc Calculate filter by discrete inverse fourier
417 * transform of filters's frequency
421 * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
422 * double y Filter's response in spatial domain
423 * int filt_type Type of filter (definitions in ct.h)
424 * double x Spatial position to evaluate filter
425 * double m_bw Bandwidth of window
426 * double param General parameter for various filters
427 * int n Number of points to calculate integrations
431 SignalFilter::spatialResponseCalc (double x, double param, int nIntegral) const
433 return (spatialResponseCalc (m_idFilter, m_bw, x, param, nIntegral));
437 SignalFilter::spatialResponseCalc (FilterID filterID, double bw, double x, double param, int n)
441 if (filterID == FILTER_TRIANGLE) {
448 double zinc = (zmax - zmin) / (n - 1);
452 for (int i = 0; i < n; i++, z += zinc)
453 q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
455 double y = 2 * integrateSimpson (zmin, zmax, q, n);
462 * filter_frequency_response Return filter frequency response
465 * h = filter_frequency_response (filt_type, u, m_bw, param)
466 * double h Filters frequency response at u
467 * int filt_type Type of filter
468 * double u Frequency to evaluate filter at
469 * double m_bw Bandwidth of filter
470 * double param General input parameter for various filters
474 SignalFilter::frequencyResponse (double u, double param) const
476 return frequencyResponse (m_idFilter, m_bw, u, param);
481 SignalFilter::frequencyResponse (FilterID filterID, double bw, double u, double param)
484 double au = fabs (u);
487 case FILTER_BANDLIMIT:
493 case FILTER_ABS_BANDLIMIT:
499 case FILTER_TRIANGLE:
509 q = cos(PI * u / bw);
511 case FILTER_ABS_COSINE:
515 q = au * cos(PI * u / bw);
518 q = bw * sinc (PI * bw * u, 1.);
520 case FILTER_ABS_SINC:
521 q = au * bw * sinc (PI * bw * u, 1.);
523 case FILTER_G_HAMMING:
527 q = param + (1 - param) * cos (TWOPI * u / bw);
529 case FILTER_ABS_G_HAMMING:
533 q = au * (param + (1 - param) * cos(TWOPI * u / bw));
537 sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
546 * filter_spatial_response_analytic Calculate filter by analytic inverse fourier
547 * transform of filters's frequency
551 * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
552 * double y Filter's response in spatial domain
553 * int filt_type Type of filter (definitions in ct.h)
554 * double x Spatial position to evaluate filter
555 * double m_bw Bandwidth of window
556 * double param General parameter for various filters
560 SignalFilter::spatialResponseAnalytic (double x, double param) const
562 return spatialResponseAnalytic (m_idFilter, m_bw, x, param);
566 SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, double param)
569 double u = TWOPI * x;
572 double b2 = TWOPI / bw;
575 case FILTER_BANDLIMIT:
576 q = bw * sinc(u * w, 1.0);
578 case FILTER_TRIANGLE:
579 temp = sinc (u * w, 1.0);
580 q = bw * temp * temp;
583 q = sinc(b-u,w) + sinc(b+u,w);
585 case FILTER_G_HAMMING:
586 q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
588 case FILTER_ABS_BANDLIMIT:
589 q = 2 * integral_abscos (u, w);
591 case FILTER_ABS_COSINE:
592 q = integral_abscos(b-u,w) + integral_abscos(b+u,w);
594 case FILTER_ABS_G_HAMMING:
595 q = 2 * param * integral_abscos(u,w) +
596 (1-param)*(integral_abscos(u-b2,w)+integral_abscos(u+b2,w));
600 q = 4. / (PI * bw * bw);
602 q = fabs ((2 / bw) * sin (u * w)) * sinc (u * w, 1.) * sinc (u * w, 1.);
605 if (fabs (x) < bw / 2)
610 case FILTER_ABS_SINC:
612 sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
622 * sinc Return sin(x)/x function
626 * double v sinc value
630 * v = sin(x * mult) / x;
635 * integral_abscos Returns integral of u*cos(u)
638 * q = integral_abscos (u, w)
639 * double q Integral value
640 * double u Integration variable
641 * double w Upper integration boundary
644 * Returns the value of integral of u*cos(u)*dV for V = 0 to w
648 SignalFilter::integral_abscos (double u, double w)
650 return (fabs (u) > F_EPSILON
651 ? (cos(u * w) - 1) / (u * u) + w / u * sin (u * w)
657 * convolve Discrete convolution of two functions
660 * r = convolve (f1, f2, dx, n, np, func_type)
661 * double r Convolved result
662 * double f1[], f2[] Functions to be convolved
663 * double dx Difference between successive x values
664 * int n Array index to center convolution about
665 * int np Number of points in f1 array
666 * int func_type EVEN or ODD or EVEN_AND_ODD function f2
669 * f1 is the projection data, its indices range from 0 to np - 1.
670 * The index for f2, the filter, ranges from -(np-1) to (np-1).
671 * There are 3 ways to handle the negative vertices of f2:
672 * 1. If we know f2 is an EVEN function, then f2[-n] = f2[n].
673 * All filters used in reconstruction are even.
674 * 2. If we know f2 is an ODD function, then f2[-n] = -f2[n]
675 * 3. If f2 is both ODD AND EVEN, then we must store the value of f2
676 * for negative indices. Since f2 must range from -(np-1) to (np-1),
677 * if we add (np - 1) to f2's array index, then f2's index will
678 * range from 0 to 2 * (np - 1), and the origin, x = 0, will be
679 * stored at f2[np-1].
683 SignalFilter::convolve (const double func[], const double dx, const int n, const int np) const
687 #if UNOPTIMIZED_CONVOLUTION
688 for (int i = 0; i < np; i++)
689 sum += func[i] * m_vecFilter[n - i + (np - 1)];
691 double* f2 = m_vecFilter + n + (np - 1);
692 for (int i = 0; i < np; i++)
693 sum += *func++ * *f2--;
701 SignalFilter::convolve (const float func[], const double dx, const int n, const int np) const
705 #if UNOPTIMIZED_CONVOLUTION
706 for (int i = 0; i < np; i++)
707 sum += func[i] * m_vecFilter[n - i + (np - 1)];
709 double* f2 = m_vecFilter + n + (np - 1);
710 for (int i = 0; i < np; i++)
711 sum += *func++ * *f2--;
719 SignalFilter::finiteFourierTransform (const float input[], complex<double> output[], const int n, int direction)
726 double angleIncrement = 2 * PI / n;
727 for (int i = 0; i < n; i++) {
730 for (int j = 0; j < n; j++) {
731 double angle = i * j * angleIncrement * direction;
732 sumReal += input[j] * cos(angle);
733 sumImag += input[j] * sin(angle);
739 output[i] = complex<double> (sumReal, sumImag);
745 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], const int n, int direction)
752 double angleIncrement = 2 * PI / n;
753 for (int i = 0; i < n; i++) {
754 complex<double> sum (0,0);
755 for (int j = 0; j < n; j++) {
756 double angle = i * j * angleIncrement * direction;
757 complex<double> exponentTerm (cos(angle), sin(angle));
758 sum += input[j] * exponentTerm;
768 SignalFilter::finiteFourierTransform (const float input[], complex<double> output[], int direction) const
775 for (int i = 0; i < m_nSignalPoints; i++) {
776 double sumReal = 0, sumImag = 0;
777 for (int j = 0; j < m_nSignalPoints; j++) {
778 int tableIndex = i * j;
780 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
781 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
783 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
784 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
788 sumReal /= m_nSignalPoints;
789 sumImag /= m_nSignalPoints;
791 output[i] = complex<double> (sumReal, sumImag);
795 // (a+bi) * (c + di) = (ac - db) + (bc + da)i
798 SignalFilter::finiteFourierTransform (const complex<double> input[], complex<double> output[], int direction) const
805 for (int i = 0; i < m_nSignalPoints; i++) {
806 double sumReal = 0, sumImag = 0;
807 for (int j = 0; j < m_nSignalPoints; j++) {
808 int tableIndex = i * j;
810 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
811 sumImag += input[i] * m_vecFourierSinTable[tableIndex];
813 sumReal += input[i] * m_vecFourierCosTable[tableIndex];
814 sumImag -= input[i] * m_vecFourierSinTable[tableIndex];
818 sumReal /= m_nSignalPoints;
819 sumImag /= m_nSignalPoints;
821 output[i] = complex<double> (sumReal, sumImag);
827 SignalFilter::dotProduct (const double v1[], const complex<double> v2[], complex<double> output[], const int n)
829 for (int i = 0; i < n; i++)
830 output[i] = v1[i] * v2[i];