X-Git-Url: http://git.kpe.io/?p=ctsim.git;a=blobdiff_plain;f=libctsim%2Ffilter.cpp;h=1c9e95bc37c03e372147f3349ea6dea4b75fcad7;hp=e8038aad7203790f5beb15462dcf96272401abd0;hb=e4c1f7f8eb87558c3abf3bf1d20732361f425351;hpb=08f34bf3ba14d4f436f4d2ef0ee5af1d6eb266ac diff --git a/libctsim/filter.cpp b/libctsim/filter.cpp index e8038aa..1c9e95b 100644 --- a/libctsim/filter.cpp +++ b/libctsim/filter.cpp @@ -1,5 +1,5 @@ /***************************************************************************** -** FILE IDENTIFICATION +** File IDENTIFICATION ** ** Name: filter.cpp ** Purpose: Routines for signal-procesing filters @@ -9,7 +9,7 @@ ** This is part of the CTSim program ** Copyright (C) 1983-2000 Kevin Rosenberg ** -** $Id: filter.cpp,v 1.4 2000/06/25 17:32:24 kevin Exp $ +** $Id: filter.cpp,v 1.18 2000/07/15 08:36:13 kevin Exp $ ** ** This program is free software; you can redistribute it and/or modify ** it under the terms of the GNU General Public License (version 2) as @@ -28,25 +28,27 @@ #include "ct.h" +int SignalFilter::N_INTEGRAL=500; //static member + /* NAME * SignalFilter::SignalFilter Construct a signal * * SYNOPSIS - * f = SignalFilter (filt_type, bw, xmin, xmax, n, param, domain, analytic) + * f = SignalFilter (filt_type, bw, filterMin, filterMax, n, param, domain, analytic) * double f Generated filter vector * int filt_type Type of filter wanted * double bw Bandwidth of filter - * double xmin, xmax Filter limits - * int n Number of points in filter + * double filterMin, filterMax Filter limits + * int nSignalPoints Number of points in signal * double param General input parameter to filters - * int domain FREQ or SPATIAL domain wanted - * int numint Number if intervals for calculating discrete inverse fourier xform - * for spatial domain filters. For ANALYTIC solutions, use numint = 0 + * int domain FREQUENCY or SPATIAL domain wanted */ -SignalFilter::SignalFilter (const char* filterName, double bw, double xmin, double xmax, int n, double param, const char* domainName, int numIntegral = 0) +SignalFilter::SignalFilter (const char* filterName, const char* filterMethodName, double bw, double signalIncrement, int nSignalPoints, double param, const char* domainName, int zeropad = 0, int preinterpolationFactor = 1) { m_vecFilter = NULL; + m_vecFourierCosTable = NULL; + m_vecFourierSinTable = NULL; m_idFilter = convertFilterNameToID (filterName); if (m_idFilter == FILTER_INVALID) { m_fail = true; @@ -54,6 +56,13 @@ SignalFilter::SignalFilter (const char* filterName, double bw, double xmin, doub m_failMessage += filterName; return; } + m_idFilterMethod = convertFilterMethodNameToID (filterMethodName); + if (m_idFilterMethod == FILTER_METHOD_INVALID) { + m_fail = true; + m_failMessage = "Invalid filter method name "; + m_failMessage += filterMethodName; + return; + } m_idDomain = convertDomainNameToID (domainName); if (m_idDomain == DOMAIN_INVALID) { m_fail = true; @@ -61,21 +70,23 @@ SignalFilter::SignalFilter (const char* filterName, double bw, double xmin, doub m_failMessage += domainName; return; } - init (m_idFilter, bw, xmin, xmax, n, param, m_idDomain, numIntegral); + init (m_idFilter, m_idFilterMethod, bw, signalIncrement, nSignalPoints, param, m_idDomain, zeropad, preinterpolationFactor); } -SignalFilter::SignalFilter (const FilterID filterID, double bw, double xmin, double xmax, int n, double param, const DomainID domainID, int numIntegral = 0) +SignalFilter::SignalFilter (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const DomainID domainID, int zeropad = 0, int preinterpolationFactor = 1) { - init (filterID, bw, xmin, xmax, n, param, domainID, numIntegral); + init (filterID, filterMethodID, bw, signalIncrement, nSignalPoints, param, domainID, zeropad, preinterpolationFactor); } -SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param, int numIntegral = 0) +SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param) { m_bw = bw; - m_nPoints = 0; + m_nSignalPoints = 0; + m_nFilterPoints = 0; m_vecFilter = NULL; + m_vecFourierCosTable = NULL; + m_vecFourierSinTable = NULL; m_filterParam = param; - m_numIntegral = numIntegral; m_idFilter = convertFilterNameToID (filterName); if (m_idFilter == FILTER_INVALID) { m_fail = true; @@ -93,63 +104,169 @@ SignalFilter::SignalFilter (const char* filterName, const char* domainName, doub } void -SignalFilter::init (const FilterID filterID, double bw, double xmin, double xmax, int n, double param, const DomainID domainID, int numint) +SignalFilter::init (const FilterID filterID, const FilterMethodID filterMethodID, double bw, double signalIncrement, int nSignalPoints, double filterParam, const DomainID domainID, int zeropad, int preinterpolationFactor) { m_bw = bw; m_idFilter = filterID; m_idDomain = domainID; - if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID) { + m_idFilterMethod = filterMethodID; + if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID || m_idFilterMethod == FILTER_METHOD_INVALID) { m_fail = true; return; } + m_traceLevel = TRACE_NONE; m_nameFilter = convertFilterIDToName (m_idFilter); m_nameDomain = convertDomainIDToName (m_idDomain); + m_nameFilterMethod = convertFilterMethodIDToName (m_idFilterMethod); m_fail = false; - m_nPoints = n; - m_xmin = xmin; - m_xmax = xmax; - m_numIntegral = numint; - m_filterParam = param; - m_vecFilter = new double[n]; - - double xinc = (m_xmax - m_xmin) / (m_nPoints - 1); - - if (m_idFilter == FILTER_SHEPP) { - double a = 2 * m_bw; - double c = - 4. / (a * a); - int center = (m_nPoints - 1) / 2; - int sidelen = center; - m_vecFilter[center] = 4. / (a * a); - - for (int i = 1; i <= sidelen; i++ ) - m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1); - } else if (m_idDomain == DOMAIN_FREQ) { - double x; - int i; - for (x = m_xmin, i = 0; i < m_nPoints; x += xinc, i++) - m_vecFilter[i] = frequencyResponse (x, param); - } else if (m_idDomain == DOMAIN_SPATIAL) { - double x; - int i; - for (x = m_xmin, i = 0; i < m_nPoints; x += xinc, i++) - if (numint == 0) - m_vecFilter[i] = spatialResponseAnalytic (x, param); - else - m_vecFilter[i] = spatialResponseCalc (x, param, numint); - } else { + m_nSignalPoints = nSignalPoints; + m_signalInc = signalIncrement; + m_filterParam = filterParam; + m_zeropad = zeropad; + m_preinterpolationFactor = preinterpolationFactor; + + m_vecFourierCosTable = NULL; + m_vecFourierSinTable = NULL; + m_vecFilter = NULL; + + if (m_idFilterMethod == FILTER_METHOD_FFT) { +#if HAVE_FFTW + m_idFilterMethod = FILTER_METHOD_RFFTW; +#else + m_fail = true; + m_failMessage = "FFT not yet implemented"; + return; +#endif + } + + if (m_idFilterMethod == FILTER_METHOD_FOURIER || m_idFilterMethod == FILTER_METHOD_FOURIER_TABLE || m_idFilterMethod == FILTER_METHOD_FFT +#if HAVE_FFTW + || m_idFilterMethod == FILTER_METHOD_FFTW || m_idFilterMethod == FILTER_METHOD_RFFTW +#endif + ) { + m_nFilterPoints = m_nSignalPoints; + if (m_zeropad > 0) { + double logBase2 = log(m_nSignalPoints) / log(2); + int nextPowerOf2 = static_cast(floor(logBase2)); + if (logBase2 != floor(logBase2)) + nextPowerOf2++; + nextPowerOf2 += (m_zeropad - 1); + m_nFilterPoints = 1 << nextPowerOf2; + if (m_traceLevel >= TRACE_TEXT) + cout << "nFilterPoints = " << m_nFilterPoints << endl; + } + m_nOutputPoints = m_nFilterPoints * m_preinterpolationFactor; + m_filterMin = -1. / (2 * m_signalInc); + m_filterMax = 1. / (2 * m_signalInc); + m_filterInc = (m_filterMax - m_filterMin) / m_nFilterPoints; + m_vecFilter = new double [m_nFilterPoints]; + int halfFilter = m_nFilterPoints / 2; + for (int i = 0; i <= halfFilter; i++) + m_vecFilter[i] = static_cast(i) / halfFilter/ (2. * m_signalInc); + for (int i = 1; i <= halfFilter; i++) + m_vecFilter[m_nFilterPoints - i] = static_cast(i) / halfFilter / (2. * m_signalInc); + } + + // precalculate sin and cosine tables for fourier transform + if (m_idFilterMethod == FILTER_METHOD_FOURIER_TABLE) { + int nFourier = max(m_nFilterPoints,m_nOutputPoints) * max(m_nFilterPoints, m_nOutputPoints) + 1; + double angleIncrement = (2. * PI) / m_nFilterPoints; + m_vecFourierCosTable = new double[ nFourier ]; + m_vecFourierSinTable = new double[ nFourier ]; + double angle = 0; + for (int i = 0; i < nFourier; i++) { + m_vecFourierCosTable[i] = cos (angle); + m_vecFourierSinTable[i] = sin (angle); + angle += angleIncrement; + } + } + +#if HAVE_FFTW + if (m_idFilterMethod == FILTER_METHOD_FFTW || m_idFilterMethod == FILTER_METHOD_RFFTW) { + for (int i = 0; i < m_nFilterPoints; i++) //fftw uses unnormalized fft + m_vecFilter[i] /= m_nFilterPoints; + } + + if (m_idFilterMethod == FILTER_METHOD_RFFTW) { + m_realPlanForward = rfftw_create_plan (m_nFilterPoints, FFTW_REAL_TO_COMPLEX, FFTW_ESTIMATE); + m_realPlanBackward = rfftw_create_plan (m_nOutputPoints, FFTW_COMPLEX_TO_REAL, FFTW_ESTIMATE); + m_vecRealFftInput = new fftw_real [ m_nFilterPoints ]; + m_vecRealFftSignal = new fftw_real [ m_nOutputPoints ]; + for (int i = 0; i < m_nFilterPoints; i++) + m_vecRealFftInput[i] = 0; + } else if (m_idFilterMethod == FILTER_METHOD_FFTW) { + m_complexPlanForward = fftw_create_plan (m_nFilterPoints, FFTW_FORWARD, FFTW_ESTIMATE); + m_complexPlanBackward = fftw_create_plan (m_nOutputPoints, FFTW_BACKWARD, FFTW_ESTIMATE); + m_vecComplexFftInput = new fftw_complex [ m_nFilterPoints ]; + m_vecComplexFftSignal = new fftw_complex [ m_nOutputPoints ]; + for (int i = 0; i < m_nFilterPoints; i++) + m_vecComplexFftInput[i].re = m_vecComplexFftInput[i].im = 0; + for (int i = 0; i < m_nOutputPoints; i++) + m_vecComplexFftSignal[i].re = m_vecComplexFftSignal[i].im = 0; + } +#endif + + if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) { + m_nFilterPoints = 2 * m_nSignalPoints - 1; + m_filterMin = -m_signalInc * (m_nSignalPoints - 1); + m_filterMax = m_signalInc * (m_nSignalPoints - 1); + m_filterInc = (m_filterMax - m_filterMin) / (m_nFilterPoints - 1); + m_vecFilter = new double[ m_nFilterPoints ]; + + if (m_idFilter == FILTER_SHEPP) { + double a = 2 * m_bw; + double c = - 4. / (a * a); + int center = (m_nFilterPoints - 1) / 2; + int sidelen = center; + m_vecFilter[center] = 4. / (a * a); + + for (int i = 1; i <= sidelen; i++ ) + m_vecFilter [center + i] = m_vecFilter [center - i] = c / (4 * (i * i) - 1); + } else if (m_idDomain == DOMAIN_FREQUENCY) { + double x; + int i; + for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++) + m_vecFilter[i] = frequencyResponse (x, m_filterParam); + } else if (m_idDomain == DOMAIN_SPATIAL) { + double x; + int i; + for (x = m_filterMin, i = 0; i < m_nFilterPoints; x += m_filterInc, i++) + if (haveAnalyticSpatial(m_idFilter)) + m_vecFilter[i] = spatialResponseAnalytic (x, m_filterParam); + else + m_vecFilter[i] = spatialResponseCalc (x, m_filterParam); + } else { m_failMessage = "Illegal domain name "; m_failMessage += m_idDomain; m_fail = true; + } } } SignalFilter::~SignalFilter (void) { - delete m_vecFilter; + delete [] m_vecFilter; + delete [] m_vecFourierSinTable; + delete [] m_vecFourierCosTable; + +#if HAVE_FFTW + if (m_idFilterMethod == FILTER_METHOD_FFTW) { + fftw_destroy_plan(m_complexPlanForward); + fftw_destroy_plan(m_complexPlanBackward); + delete [] m_vecComplexFftInput; + delete [] m_vecComplexFftSignal; + } + if (m_idFilterMethod == FILTER_METHOD_RFFTW) { + rfftw_destroy_plan(m_realPlanForward); + rfftw_destroy_plan(m_realPlanBackward); + delete [] m_vecRealFftInput; + delete [] m_vecRealFftSignal; + } +#endif } -SignalFilter::FilterID +const SignalFilter::FilterID SignalFilter::convertFilterNameToID (const char *filterName) { FilterID filterID = FILTER_INVALID; @@ -207,6 +324,52 @@ SignalFilter::convertFilterIDToName (const FilterID filterID) return (name); } +const SignalFilter::FilterMethodID +SignalFilter::convertFilterMethodNameToID (const char* const filterMethodName) +{ + FilterMethodID fmID = FILTER_METHOD_INVALID; + + if (strcasecmp (filterMethodName, FILTER_METHOD_CONVOLUTION_STR) == 0) + fmID = FILTER_METHOD_CONVOLUTION; + else if (strcasecmp (filterMethodName, FILTER_METHOD_FOURIER_STR) == 0) + fmID = FILTER_METHOD_FOURIER; + else if (strcasecmp (filterMethodName, FILTER_METHOD_FOURIER_TABLE_STR) == 0) + fmID = FILTER_METHOD_FOURIER_TABLE; + else if (strcasecmp (filterMethodName, FILTER_METHOD_FFT_STR) == 0) + fmID = FILTER_METHOD_FFT; +#if HAVE_FFTW + else if (strcasecmp (filterMethodName, FILTER_METHOD_FFTW_STR) == 0) + fmID = FILTER_METHOD_FFTW; + else if (strcasecmp (filterMethodName, FILTER_METHOD_RFFTW_STR) == 0) + fmID = FILTER_METHOD_RFFTW; +#endif + + return (fmID); +} + +const char * +SignalFilter::convertFilterMethodIDToName (const FilterMethodID fmID) +{ + const char *name = ""; + + if (fmID == FILTER_METHOD_CONVOLUTION) + return (FILTER_METHOD_CONVOLUTION_STR); + else if (fmID == FILTER_METHOD_FOURIER) + return (FILTER_METHOD_FOURIER_STR); + else if (fmID == FILTER_METHOD_FOURIER_TABLE) + return (FILTER_METHOD_FOURIER_TABLE_STR); + else if (fmID == FILTER_METHOD_FFT) + return (FILTER_METHOD_FFT_STR); +#if HAVE_FFTW + else if (fmID == FILTER_METHOD_FFTW) + return (FILTER_METHOD_FFTW_STR); + else if (fmID == FILTER_METHOD_RFFTW) + return (FILTER_METHOD_RFFTW_STR); +#endif + + return (name); +} + const SignalFilter::DomainID SignalFilter::convertDomainNameToID (const char* const domainName) { @@ -214,8 +377,8 @@ SignalFilter::convertDomainNameToID (const char* const domainName) if (strcasecmp (domainName, DOMAIN_SPATIAL_STR) == 0) dID = DOMAIN_SPATIAL; - else if (strcasecmp (domainName, DOMAIN_FREQ_STR) == 0) - dID = DOMAIN_FREQ; + else if (strcasecmp (domainName, DOMAIN_FREQUENCY_STR) == 0) + dID = DOMAIN_FREQUENCY; return (dID); } @@ -227,12 +390,80 @@ SignalFilter::convertDomainIDToName (const DomainID domain) if (domain == DOMAIN_SPATIAL) return (DOMAIN_SPATIAL_STR); - else if (domain == DOMAIN_FREQ) - return (DOMAIN_FREQ_STR); + else if (domain == DOMAIN_FREQUENCY) + return (DOMAIN_FREQUENCY_STR); return (name); } +void +SignalFilter::filterSignal (const float input[], double output[]) const +{ + if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION) { + for (int i = 0; i < m_nSignalPoints; i++) + output[i] = convolve (input, m_signalInc, i, m_nSignalPoints); + } else if (m_idFilterMethod == FILTER_METHOD_FOURIER) { + double inputSignal[m_nFilterPoints]; + for (int i = 0; i < m_nSignalPoints; i++) + inputSignal[i] = input[i]; + for (int i = m_nSignalPoints; i < m_nFilterPoints; i++) + inputSignal[i] = 0; // zeropad + complex fftSignal[m_nFilterPoints]; + finiteFourierTransform (inputSignal, fftSignal, m_nFilterPoints, -1); + for (int i = 0; i < m_nFilterPoints; i++) + fftSignal[i] *= m_vecFilter[i]; + double inverseFourier[m_nFilterPoints]; + finiteFourierTransform (fftSignal, inverseFourier, m_nFilterPoints, 1); + for (int i = 0; i < m_nSignalPoints; i++) + output[i] = inverseFourier[i]; + } else if (m_idFilterMethod == FILTER_METHOD_FOURIER_TABLE) { + double inputSignal[m_nFilterPoints]; + for (int i = 0; i < m_nSignalPoints; i++) + inputSignal[i] = input[i]; + for (int i = m_nSignalPoints; i < m_nFilterPoints; i++) + inputSignal[i] = 0; // zeropad + complex fftSignal[m_nFilterPoints]; + finiteFourierTransform (inputSignal, fftSignal, -1); + for (int i = 0; i < m_nFilterPoints; i++) + fftSignal[i] *= m_vecFilter[i]; + double inverseFourier[m_nFilterPoints]; + finiteFourierTransform (fftSignal, inverseFourier, 1); + for (int i = 0; i < m_nSignalPoints; i++) + output[i] = inverseFourier[i]; + } +#if HAVE_FFTW + else if (m_idFilterMethod == FILTER_METHOD_RFFTW) { + for (int i = 0; i < m_nSignalPoints; i++) + m_vecRealFftInput[i] = input[i]; + + fftw_real fftOutput [ m_nFilterPoints ]; + rfftw_one (m_realPlanForward, m_vecRealFftInput, fftOutput); + for (int i = 0; i < m_nFilterPoints; i++) + m_vecRealFftSignal[i] = m_vecFilter[i] * fftOutput[i]; + for (int i = m_nFilterPoints; i < m_nOutputPoints; i++) + m_vecRealFftSignal[i] = 0; + + fftw_real ifftOutput [ m_nOutputPoints ]; + rfftw_one(m_realPlanBackward, m_vecRealFftSignal, ifftOutput); + for (int i = 0; i < m_nSignalPoints * m_preinterpolationFactor; i++) + output[i] = ifftOutput[i]; + } else if (m_idFilterMethod == FILTER_METHOD_FFTW) { + for (int i = 0; i < m_nSignalPoints; i++) + m_vecComplexFftInput[i].re = input[i]; + + fftw_complex fftOutput [ m_nFilterPoints ]; + fftw_one(m_complexPlanForward, m_vecComplexFftInput, fftOutput); + for (int i = 0; i < m_nFilterPoints; i++) { + m_vecComplexFftSignal[i].re = m_vecFilter[i] * fftOutput[i].re; + m_vecComplexFftSignal[i].im = m_vecFilter[i] * fftOutput[i].im; + } + fftw_complex ifftOutput [ m_nOutputPoints ]; + fftw_one(m_complexPlanBackward, m_vecComplexFftSignal, ifftOutput); + for (int i = 0; i < m_nSignalPoints * m_preinterpolationFactor; i++) + output[i] = ifftOutput[i].re; + } +#endif +} double SignalFilter::response (double x) @@ -240,8 +471,8 @@ SignalFilter::response (double x) double response = 0; if (m_idDomain == DOMAIN_SPATIAL) - response = spatialResponse (m_idFilter, m_bw, x, m_filterParam, m_numIntegral); - else if (m_idDomain == DOMAIN_FREQ) + response = spatialResponse (m_idFilter, m_bw, x, m_filterParam); + else if (m_idDomain == DOMAIN_FREQUENCY) response = frequencyResponse (m_idFilter, m_bw, x, m_filterParam); return (response); @@ -249,12 +480,12 @@ SignalFilter::response (double x) double -SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param, int nIntegral = 0) +SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double param) { - if (nIntegral == 0) + if (haveAnalyticSpatial(filterID)) return spatialResponseAnalytic (filterID, bw, x, param); else - return spatialResponseCalc (filterID, bw, x, param, nIntegral); + return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL); } /* NAME @@ -273,9 +504,9 @@ SignalFilter::spatialResponse (FilterID filterID, double bw, double x, double pa */ double -SignalFilter::spatialResponseCalc (double x, double param, int nIntegral) const +SignalFilter::spatialResponseCalc (double x, double param) const { - return (spatialResponseCalc (m_idFilter, m_bw, x, param, nIntegral)); + return (spatialResponseCalc (m_idFilter, m_bw, x, param, N_INTEGRAL)); } double @@ -407,6 +638,30 @@ SignalFilter::spatialResponseAnalytic (double x, double param) const return spatialResponseAnalytic (m_idFilter, m_bw, x, param); } +const bool +SignalFilter::haveAnalyticSpatial (FilterID filterID) +{ + bool haveAnalytic = false; + + switch (filterID) { + case FILTER_BANDLIMIT: + case FILTER_TRIANGLE: + case FILTER_COSINE: + case FILTER_G_HAMMING: + case FILTER_ABS_BANDLIMIT: + case FILTER_ABS_COSINE: + case FILTER_ABS_G_HAMMING: + case FILTER_SHEPP: + case FILTER_SINC: + haveAnalytic = true; + break; + default: + break; + } + + return (haveAnalytic); +} + double SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, double param) { @@ -492,10 +747,9 @@ SignalFilter::spatialResponseAnalytic (FilterID filterID, double bw, double x, d double SignalFilter::integral_abscos (double u, double w) { - if (fabs (u) > F_EPSILON) - return (cos(u * w) - 1) / (u * u) + w / u * sin (u * w); - else - return (w * w / 2); + return (fabs (u) > F_EPSILON + ? (cos(u * w) - 1) / (u * u) + w / u * sin (u * w) + : (w * w / 2)); } @@ -560,3 +814,164 @@ for (int i = 0; i < np; i++) return (sum * dx); } + +void +SignalFilter::finiteFourierTransform (const double input[], complex output[], const int n, int direction) +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + double angleIncrement = direction * 2 * PI / n; + for (int i = 0; i < n; i++) { + double sumReal = 0; + double sumImag = 0; + for (int j = 0; j < n; j++) { + double angle = i * j * angleIncrement; + sumReal += input[j] * cos(angle); + sumImag += input[j] * sin(angle); + } + if (direction < 0) { + sumReal /= n; + sumImag /= n; + } + output[i] = complex (sumReal, sumImag); + } +} + + +void +SignalFilter::finiteFourierTransform (const complex input[], complex output[], const int n, int direction) +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + double angleIncrement = direction * 2 * PI / n; + for (int i = 0; i < n; i++) { + complex sum (0,0); + for (int j = 0; j < n; j++) { + double angle = i * j * angleIncrement; + complex exponentTerm (cos(angle), sin(angle)); + sum += input[j] * exponentTerm; + } + if (direction < 0) { + sum /= n; + } + output[i] = sum; + } +} + +void +SignalFilter::finiteFourierTransform (const complex input[], double output[], const int n, int direction) +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + double angleIncrement = direction * 2 * PI / n; + for (int i = 0; i < n; i++) { + double sumReal = 0; + for (int j = 0; j < n; j++) { + double angle = i * j * angleIncrement; + sumReal += input[j].real() * cos(angle) - input[j].imag() * sin(angle); + } + if (direction < 0) { + sumReal /= n; + } + output[i] = sumReal; + } +} + +void +SignalFilter::finiteFourierTransform (const double input[], complex output[], int direction) const +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + for (int i = 0; i < m_nFilterPoints; i++) { + double sumReal = 0, sumImag = 0; + for (int j = 0; j < m_nFilterPoints; j++) { + int tableIndex = i * j; + if (direction > 0) { + sumReal += input[j] * m_vecFourierCosTable[tableIndex]; + sumImag += input[j] * m_vecFourierSinTable[tableIndex]; + } else { + sumReal += input[j] * m_vecFourierCosTable[tableIndex]; + sumImag -= input[j] * m_vecFourierSinTable[tableIndex]; + } + } + if (direction < 0) { + sumReal /= m_nFilterPoints; + sumImag /= m_nFilterPoints; + } + output[i] = complex (sumReal, sumImag); + } +} + +// (a+bi) * (c + di) = (ac - bd) + (ad + bc)i +void +SignalFilter::finiteFourierTransform (const complex input[], complex output[], int direction) const +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + for (int i = 0; i < m_nFilterPoints; i++) { + double sumReal = 0, sumImag = 0; + for (int j = 0; j < m_nFilterPoints; j++) { + int tableIndex = i * j; + if (direction > 0) { + sumReal += input[j].real() * m_vecFourierCosTable[tableIndex] + - input[j].imag() * m_vecFourierSinTable[tableIndex]; + sumImag += input[j].real() * m_vecFourierSinTable[tableIndex] + + input[j].imag() * m_vecFourierCosTable[tableIndex]; + } else { + sumReal += input[j].real() * m_vecFourierCosTable[tableIndex] + - input[j].imag() * -m_vecFourierSinTable[tableIndex]; + sumImag += input[j].real() * -m_vecFourierSinTable[tableIndex] + + input[j].imag() * m_vecFourierCosTable[tableIndex]; + } + } + if (direction < 0) { + sumReal /= m_nFilterPoints; + sumImag /= m_nFilterPoints; + } + output[i] = complex (sumReal, sumImag); + } +} + +void +SignalFilter::finiteFourierTransform (const complex input[], double output[], int direction) const +{ + if (direction < 0) + direction = -1; + else + direction = 1; + + for (int i = 0; i < m_nFilterPoints; i++) { + double sumReal = 0; + for (int j = 0; j < m_nFilterPoints; j++) { + int tableIndex = i * j; + if (direction > 0) { + sumReal += input[j].real() * m_vecFourierCosTable[tableIndex] + - input[j].imag() * m_vecFourierSinTable[tableIndex]; + } else { + sumReal += input[j].real() * m_vecFourierCosTable[tableIndex] + - input[j].imag() * -m_vecFourierSinTable[tableIndex]; + } + } + if (direction < 0) { + sumReal /= m_nFilterPoints; + } + output[i] = sumReal; + } +} + +