+/*****************************************************************************
+** File IDENTIFICATION
+**
+** Name: filter.cpp
+** Purpose: Routines for signal-procesing filters
+** Progammer: Kevin Rosenberg
+** Date Started: Aug 1984
+**
+** This is part of the CTSim program
+** Copyright (C) 1983-2000 Kevin Rosenberg
+**
+** $Id: procsignal.cpp,v 1.1 2000/08/19 23:00:05 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
+** published by the Free Software Foundation.
+**
+** This program is distributed in the hope that it will be useful,
+** but WITHOUT ANY WARRANTY; without even the implied warranty of
+** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+** GNU General Public License for more details.
+**
+** You should have received a copy of the GNU General Public License
+** along with this program; if not, write to the Free Software
+** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+******************************************************************************/
+
+#include "ct.h"
+
+// FilterMethod ID/Names
+const int ProcessSignal::FILTER_METHOD_INVALID = -1;
+const int ProcessSignal::FILTER_METHOD_CONVOLUTION = 0;
+const int ProcessSignal::FILTER_METHOD_FOURIER = 1;
+const int ProcessSignal::FILTER_METHOD_FOURIER_TABLE = 2;
+const int ProcessSignal::FILTER_METHOD_FFT = 3;
+#if HAVE_FFTW
+const int ProcessSignal::FILTER_METHOD_FFTW = 4;
+const int ProcessSignal::FILTER_METHOD_RFFTW =5 ;
+#endif
+const char* ProcessSignal::s_aszFilterMethodName[] = {
+ {"convolution"},
+ {"fourier"},
+ {"fouier_table"},
+ {"fft"},
+#if HAVE_FFTW
+ {"fftw"},
+ {"rfftw"},
+#endif
+};
+const char* ProcessSignal::s_aszFilterMethodTitle[] = {
+ {"Convolution"},
+ {"Direct Fourier"},
+ {"Fouier Trigometric Table Lookout"},
+ {"FFT"},
+#if HAVE_FFTW
+ {"FFTW"},
+ {"Real/Half-Complex FFTW"},
+#endif
+};
+const int ProcessSignal::s_iFilterMethodCount = sizeof(s_aszFilterMethodName) / sizeof(const char*);
+
+// FilterGeneration ID/Names
+const int ProcessSignal::FILTER_GENERATION_INVALID = -1;
+const int ProcessSignal::FILTER_GENERATION_DIRECT = 0;
+const int ProcessSignal::FILTER_GENERATION_INVERSE_FOURIER = 1;
+const char* ProcessSignal::s_aszFilterGenerationName[] = {
+ {"direct"},
+ {"inverse_fourier"},
+};
+const char* ProcessSignal::s_aszFilterGenerationTitle[] = {
+ {"Direct"},
+ {"Inverse Fourier"},
+};
+const int ProcessSignal::s_iFilterGenerationCount = sizeof(s_aszFilterGenerationName) / sizeof(const char*);
+
+
+// CLASS IDENTIFICATION
+// ProcessSignal
+//
+ProcessSignal::ProcessSignal (const char* szFilterName, const char* szFilterMethodName, double dBandwidth, double dSignalIncrement, int nSignalPoints, double dFilterParam, const char* szDomainName, const char* szFilterGenerationName, int iZeropad = 0, int iPreinterpolationFactor = 1)
+ : m_adFourierCosTable(NULL), m_adFourierSinTable(NULL), m_adFilter(NULL), m_fail(false)
+{
+ m_idFilterMethod = convertFilterMethodNameToID (szFilterMethodName);
+ if (m_idFilterMethod == FILTER_METHOD_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid filter method name ";
+ m_failMessage += szFilterMethodName;
+ return;
+ }
+ m_idFilterGeneration = convertFilterGenerationNameToID (szFilterGenerationName);
+ if (m_idFilterGeneration == FILTER_GENERATION_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid frequency filter name ";
+ m_failMessage += szFilterGenerationName;
+ return;
+ }
+ m_idFilter = SignalFilter::convertFilterNameToID (szFilterName);
+ if (m_idFilter == SignalFilter::FILTER_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid Filter name ";
+ m_failMessage += szFilterName;
+ return;
+ }
+ m_idDomain = SignalFilter::convertDomainNameToID (szDomainName);
+ if (m_idDomain == SignalFilter::DOMAIN_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid domain name ";
+ m_failMessage += szDomainName;
+ return;
+ }
+
+ init (m_idFilter, m_idFilterMethod, dBandwidth, dSignalIncrement, nSignalPoints, dFilterParam, m_idDomain, m_idFilterGeneration, iZeropad, iPreinterpolationFactor);
+}
+
+
+void
+ProcessSignal::init (const int idFilter, const int idFilterMethod, double dBandwidth, double dSignalIncrement, int nSignalPoints, double dFilterParam, const int idDomain, const int idFilterGeneration, const int iZeropad, const int iPreinterpolationFactor)
+{
+ m_idFilter = idFilter;
+ m_idDomain = idDomain;
+ m_idFilterMethod = idFilterMethod;
+ m_idFilterGeneration = idFilterGeneration;
+ if (m_idFilter == SignalFilter::FILTER_INVALID || m_idDomain == SignalFilter::DOMAIN_INVALID || m_idFilterMethod == FILTER_METHOD_INVALID || m_idFilterGeneration == FILTER_GENERATION_INVALID) {
+ m_fail = true;
+ return;
+ }
+ m_traceLevel = TRACE_NONE;
+ m_nameFilterMethod = convertFilterMethodIDToName (m_idFilterMethod);
+ m_nameFilterGeneration = convertFilterGenerationIDToName (m_idFilterGeneration);
+ m_dBandwidth = dBandwidth;
+ m_nSignalPoints = nSignalPoints;
+ m_dSignalInc = dSignalIncrement;
+ m_dFilterParam = dFilterParam;
+ m_iZeropad = iZeropad;
+ m_iPreinterpolationFactor = iPreinterpolationFactor;
+
+ 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
+ }
+
+ bool m_bFrequencyFiltering = true;
+ if (m_idFilterMethod == FILTER_METHOD_CONVOLUTION)
+ m_bFrequencyFiltering = false;
+
+ // Spatial-based filtering
+ if (! m_bFrequencyFiltering) {
+
+ if (m_idFilterGeneration == FILTER_GENERATION_DIRECT) {
+ m_nFilterPoints = 2 * m_nSignalPoints - 1;
+ m_dFilterMin = -m_dSignalInc * (m_nSignalPoints - 1);
+ m_dFilterMax = m_dSignalInc * (m_nSignalPoints - 1);
+ m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
+ SignalFilter filter (m_idFilter, m_dFilterMin, m_dFilterMax, m_nFilterPoints, m_dBandwidth, m_dFilterParam, SignalFilter::DOMAIN_SPATIAL);
+ m_adFilter = new double[ m_nFilterPoints ];
+ filter.copyFilterData (m_adFilter, 0, m_nFilterPoints);
+ } else if (m_idFilterGeneration == FILTER_GENERATION_INVERSE_FOURIER) {
+ m_nFilterPoints = m_nSignalPoints;
+ m_dFilterMin = -1. / (2 * m_dSignalInc);
+ m_dFilterMax = 1. / (2 * m_dSignalInc);
+ m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
+ SignalFilter filter (m_idFilter, m_dFilterMin, m_dFilterMax, m_nFilterPoints, m_dBandwidth, m_dFilterParam, SignalFilter::DOMAIN_FREQUENCY);
+ m_adFilter = new double[ m_nFilterPoints ];
+ double adFrequencyFilter [m_nFilterPoints];
+ double adInverseFilter [m_nFilterPoints];
+ filter.copyFilterData (adFrequencyFilter, 0, m_nFilterPoints);
+ shuffleNaturalToFourierOrder (adFrequencyFilter, m_nFilterPoints);
+ ProcessSignal::finiteFourierTransform (adFrequencyFilter, adInverseFilter, m_nFilterPoints, 1);
+ for (int i = 0; i < m_nFilterPoints; i++)
+ m_adFilter [i] = adInverseFilter[i];
+ }
+ }
+
+ // Frequency-based filtering
+ else if (m_bFrequencyFiltering) {
+
+ // calculate number of filter points with zeropadding
+ m_nFilterPoints = m_nSignalPoints;
+ if (m_iZeropad > 0) {
+ double logBase2 = log(m_nSignalPoints) / log(2);
+ int nextPowerOf2 = static_cast<int>(floor(logBase2));
+ if (logBase2 != floor(logBase2))
+ nextPowerOf2++;
+ nextPowerOf2 += (m_iZeropad - 1);
+ m_nFilterPoints = 1 << nextPowerOf2;
+ if (m_traceLevel >= TRACE_TEXT)
+ cout << "nFilterPoints = " << m_nFilterPoints << endl;
+ }
+ m_nOutputPoints = m_nFilterPoints * m_iPreinterpolationFactor;
+
+ if (m_idFilterGeneration == FILTER_GENERATION_DIRECT) {
+ m_dFilterMin = -1. / (2 * m_dSignalInc);
+ m_dFilterMax = 1. / (2 * m_dSignalInc);
+ m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
+ SignalFilter filter (m_idFilter, m_dFilterMin, m_dFilterMax, m_nFilterPoints, m_dBandwidth, m_dFilterParam, SignalFilter::DOMAIN_FREQUENCY);
+ m_adFilter = new double [m_nFilterPoints];
+ filter.copyFilterData (m_adFilter, 0, m_nFilterPoints);
+ shuffleNaturalToFourierOrder (m_adFilter, m_nFilterPoints);
+ } else if (m_idFilterGeneration == FILTER_GENERATION_INVERSE_FOURIER) {
+ m_nFilterPoints = 2 * m_nSignalPoints - 1;
+ m_dFilterMin = -m_dSignalInc * (m_nSignalPoints - 1);
+ m_dFilterMax = m_dSignalInc * (m_nSignalPoints - 1);
+ m_dFilterInc = (m_dFilterMax - m_dFilterMin) / (m_nFilterPoints - 1);
+ double adSpatialFilter [m_nFilterPoints];
+ double adInverseFilter [m_nFilterPoints];
+ SignalFilter filter (m_idFilter, m_dFilterMin, m_dFilterMax, m_nFilterPoints, m_dBandwidth, m_dFilterParam, SignalFilter::DOMAIN_SPATIAL);
+ filter.copyFilterData (adSpatialFilter, 0, m_nFilterPoints);
+ m_adFilter = new double [m_nFilterPoints];
+ finiteFourierTransform (adSpatialFilter, adInverseFilter, m_nFilterPoints, -1);
+ for (int i = 0; i < m_nFilterPoints; i++)
+ m_adFilter [i] = adInverseFilter[i];
+ }
+ }
+
+ // 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_adFourierCosTable = new double[ nFourier ];
+ m_adFourierSinTable = new double[ nFourier ];
+ double angle = 0;
+ for (int i = 0; i < nFourier; i++) {
+ m_adFourierCosTable[i] = cos (angle);
+ m_adFourierSinTable[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_adFilter[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_adRealFftInput = new fftw_real [ m_nFilterPoints ];
+ m_adRealFftSignal = new fftw_real [ m_nOutputPoints ];
+ for (int i = 0; i < m_nFilterPoints; i++)
+ m_adRealFftInput[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_adComplexFftInput = new fftw_complex [ m_nFilterPoints ];
+ m_adComplexFftSignal = new fftw_complex [ m_nOutputPoints ];
+ for (int i = 0; i < m_nFilterPoints; i++)
+ m_adComplexFftInput[i].re = m_adComplexFftInput[i].im = 0;
+ for (int i = 0; i < m_nOutputPoints; i++)
+ m_adComplexFftSignal[i].re = m_adComplexFftSignal[i].im = 0;
+ }
+#endif
+
+}
+
+ProcessSignal::~ProcessSignal (void)
+{
+ delete [] m_adFourierSinTable;
+ delete [] m_adFourierCosTable;
+
+#if HAVE_FFTW
+ if (m_idFilterMethod == FILTER_METHOD_FFTW) {
+ fftw_destroy_plan(m_complexPlanForward);
+ fftw_destroy_plan(m_complexPlanBackward);
+ delete [] m_adComplexFftInput;
+ delete [] m_adComplexFftSignal;
+ }
+ if (m_idFilterMethod == FILTER_METHOD_RFFTW) {
+ rfftw_destroy_plan(m_realPlanForward);
+ rfftw_destroy_plan(m_realPlanBackward);
+ delete [] m_adRealFftInput;
+ delete [] m_adRealFftSignal;
+ }
+#endif
+}
+
+int
+ProcessSignal::convertFilterMethodNameToID (const char* const filterMethodName)
+{
+ int fmID = FILTER_METHOD_INVALID;
+
+ for (int i = 0; i < s_iFilterMethodCount; i++)
+ if (strcasecmp (filterMethodName, s_aszFilterMethodName[i]) == 0) {
+ fmID = i;
+ break;
+ }
+
+ return (fmID);
+}
+
+const char *
+ProcessSignal::convertFilterMethodIDToName (const int fmID)
+{
+ static const char *name = "";
+
+ if (fmID >= 0 && fmID < s_iFilterMethodCount)
+ return (s_aszFilterMethodName [fmID]);
+
+ return (name);
+}
+
+const char *
+ProcessSignal::convertFilterMethodIDToTitle (const int fmID)
+{
+ static const char *title = "";
+
+ if (fmID >= 0 && fmID < s_iFilterMethodCount)
+ return (s_aszFilterMethodTitle [fmID]);
+
+ return (title);
+}
+
+
+int
+ProcessSignal::convertFilterGenerationNameToID (const char* const fgName)
+{
+ int fgID = FILTER_GENERATION_INVALID;
+
+ for (int i = 0; i < s_iFilterGenerationCount; i++)
+ if (strcasecmp (fgName, s_aszFilterGenerationName[i]) == 0) {
+ fgID = i;
+ break;
+ }
+
+ return (fgID);
+}
+
+const char *
+ProcessSignal::convertFilterGenerationIDToName (const int fgID)
+{
+ static const char *name = "";
+
+ if (fgID >= 0 && fgID < s_iFilterGenerationCount)
+ return (s_aszFilterGenerationName [fgID]);
+
+ return (name);
+}
+
+const char *
+ProcessSignal::convertFilterGenerationIDToTitle (const int fgID)
+{
+ static const char *name = "";
+
+ if (fgID >= 0 && fgID < s_iFilterGenerationCount)
+ return (s_aszFilterGenerationTitle [fgID]);
+
+ return (name);
+}
+
+void
+ProcessSignal::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_dSignalInc, 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<double> fftSignal[m_nFilterPoints];
+ finiteFourierTransform (inputSignal, fftSignal, m_nFilterPoints, -1);
+ for (int i = 0; i < m_nFilterPoints; i++)
+ fftSignal[i] *= m_adFilter[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<double> fftSignal[m_nFilterPoints];
+ finiteFourierTransform (inputSignal, fftSignal, -1);
+ for (int i = 0; i < m_nFilterPoints; i++)
+ fftSignal[i] *= m_adFilter[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_adRealFftInput[i] = input[i];
+
+ fftw_real fftOutput [ m_nFilterPoints ];
+ rfftw_one (m_realPlanForward, m_adRealFftInput, fftOutput);
+ for (int i = 0; i < m_nFilterPoints; i++)
+ m_adRealFftSignal[i] = m_adFilter[i] * fftOutput[i];
+ for (int i = m_nFilterPoints; i < m_nOutputPoints; i++)
+ m_adRealFftSignal[i] = 0;
+
+ fftw_real ifftOutput [ m_nOutputPoints ];
+ rfftw_one (m_realPlanBackward, m_adRealFftSignal, ifftOutput);
+ for (int i = 0; i < m_nSignalPoints * m_iPreinterpolationFactor; i++)
+ output[i] = ifftOutput[i];
+ } else if (m_idFilterMethod == FILTER_METHOD_FFTW) {
+ for (int i = 0; i < m_nSignalPoints; i++)
+ m_adComplexFftInput[i].re = input[i];
+
+ fftw_complex fftOutput [ m_nFilterPoints ];
+ fftw_one (m_complexPlanForward, m_adComplexFftInput, fftOutput);
+ for (int i = 0; i < m_nFilterPoints; i++) {
+ m_adComplexFftSignal[i].re = m_adFilter[i] * fftOutput[i].re;
+ m_adComplexFftSignal[i].im = m_adFilter[i] * fftOutput[i].im;
+ }
+ fftw_complex ifftOutput [ m_nOutputPoints ];
+ fftw_one (m_complexPlanBackward, m_adComplexFftSignal, ifftOutput);
+ for (int i = 0; i < m_nSignalPoints * m_iPreinterpolationFactor; i++)
+ output[i] = ifftOutput[i].re;
+ }
+#endif
+}
+
+
+/* NAME
+ * convolve Discrete convolution of two functions
+ *
+ * SYNOPSIS
+ * r = convolve (f1, f2, dx, n, np, func_type)
+ * double r Convolved result
+ * double f1[], f2[] Functions to be convolved
+ * double dx Difference between successive x values
+ * int n Array index to center convolution about
+ * int np Number of points in f1 array
+ * int func_type EVEN or ODD or EVEN_AND_ODD function f2
+ *
+ * NOTES
+ * f1 is the projection data, its indices range from 0 to np - 1.
+ * The index for f2, the filter, ranges from -(np-1) to (np-1).
+ * There are 3 ways to handle the negative vertices of f2:
+ * 1. If we know f2 is an EVEN function, then f2[-n] = f2[n].
+ * All filters used in reconstruction are even.
+ * 2. If we know f2 is an ODD function, then f2[-n] = -f2[n]
+ * 3. If f2 is both ODD AND EVEN, then we must store the value of f2
+ * for negative indices. Since f2 must range from -(np-1) to (np-1),
+ * if we add (np - 1) to f2's array index, then f2's index will
+ * range from 0 to 2 * (np - 1), and the origin, x = 0, will be
+ * stored at f2[np-1].
+ */
+
+double
+ProcessSignal::convolve (const double func[], const double dx, const int n, const int np) const
+{
+ double sum = 0.0;
+
+#if UNOPTIMIZED_CONVOLUTION
+ for (int i = 0; i < np; i++)
+ sum += func[i] * m_adFilter[n - i + (np - 1)];
+#else
+ double* f2 = m_adFilter + n + (np - 1);
+ for (int i = 0; i < np; i++)
+ sum += *func++ * *f2--;
+#endif
+
+ return (sum * dx);
+}
+
+
+double
+ProcessSignal::convolve (const float func[], const double dx, const int n, const int np) const
+{
+ double sum = 0.0;
+
+#if UNOPTIMIZED_CONVOLUTION
+for (int i = 0; i < np; i++)
+ sum += func[i] * m_adFilter[n - i + (np - 1)];
+#else
+double* f2 = m_adFilter + n + (np - 1);
+for (int i = 0; i < np; i++)
+ sum += *func++ * *f2--;
+#endif
+
+ return (sum * dx);
+}
+
+
+void
+ProcessSignal::finiteFourierTransform (const double input[], double output[], const int n, int direction)
+{
+ complex<double> complexOutput[n];
+
+ finiteFourierTransform (input, complexOutput, n, direction);
+ for (int i = 0; i < n; i++)
+ output[i] = abs(complexOutput[n]);
+}
+
+void
+ProcessSignal::finiteFourierTransform (const double input[], complex<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;
+ 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<double> (sumReal, sumImag);
+ }
+}
+
+
+void
+ProcessSignal::finiteFourierTransform (const complex<double> input[], complex<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++) {
+ complex<double> sum (0,0);
+ for (int j = 0; j < n; j++) {
+ double angle = i * j * angleIncrement;
+ complex<double> exponentTerm (cos(angle), sin(angle));
+ sum += input[j] * exponentTerm;
+ }
+ if (direction < 0) {
+ sum /= n;
+ }
+ output[i] = sum;
+ }
+}
+
+void
+ProcessSignal::finiteFourierTransform (const complex<double> 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;
+ }
+}
+
+// Table-based routines
+
+void
+ProcessSignal::finiteFourierTransform (const double input[], complex<double> 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_adFourierCosTable[tableIndex];
+ sumImag += input[j] * m_adFourierSinTable[tableIndex];
+ } else {
+ sumReal += input[j] * m_adFourierCosTable[tableIndex];
+ sumImag -= input[j] * m_adFourierSinTable[tableIndex];
+ }
+ }
+ if (direction < 0) {
+ sumReal /= m_nFilterPoints;
+ sumImag /= m_nFilterPoints;
+ }
+ output[i] = complex<double> (sumReal, sumImag);
+ }
+}
+
+// (a+bi) * (c + di) = (ac - bd) + (ad + bc)i
+void
+ProcessSignal::finiteFourierTransform (const complex<double> input[], complex<double> 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_adFourierCosTable[tableIndex]
+ - input[j].imag() * m_adFourierSinTable[tableIndex];
+ sumImag += input[j].real() * m_adFourierSinTable[tableIndex]
+ + input[j].imag() * m_adFourierCosTable[tableIndex];
+ } else {
+ sumReal += input[j].real() * m_adFourierCosTable[tableIndex]
+ - input[j].imag() * -m_adFourierSinTable[tableIndex];
+ sumImag += input[j].real() * -m_adFourierSinTable[tableIndex]
+ + input[j].imag() * m_adFourierCosTable[tableIndex];
+ }
+ }
+ if (direction < 0) {
+ sumReal /= m_nFilterPoints;
+ sumImag /= m_nFilterPoints;
+ }
+ output[i] = complex<double> (sumReal, sumImag);
+ }
+}
+
+void
+ProcessSignal::finiteFourierTransform (const complex<double> 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_adFourierCosTable[tableIndex]
+ - input[j].imag() * m_adFourierSinTable[tableIndex];
+ } else {
+ sumReal += input[j].real() * m_adFourierCosTable[tableIndex]
+ - input[j].imag() * -m_adFourierSinTable[tableIndex];
+ }
+ }
+ if (direction < 0) {
+ sumReal /= m_nFilterPoints;
+ }
+ output[i] = sumReal;
+ }
+}
+
+// Odd Number of Points
+// Natural Frequency Order: -(n-1)/2...-1,0,1...(n-1)/2
+// Fourier Frequency Order: 0, 1..(n-1)/2,-(n-1)/2...-1
+// Even Number of Points
+// Natural Frequency Order: -n/2...-1,0,1...((n/2)-1)
+// Fourier Frequency Order: 0,1...((n/2)-1),-n/2...-1
+
+void
+ProcessSignal::shuffleNaturalToFourierOrder (double* pdVector, const int n)
+{
+ double* pdTemp = new double [n];
+ if (n % 2) { // Odd
+ int iHalfN = (n - 1) / 2;
+
+ pdTemp[0] = pdVector[iHalfN];
+ for (int i = 1; i <= iHalfN; i++)
+ pdTemp[i] = pdVector[i+iHalfN];
+ for (int i = iHalfN+1; i < n; i++)
+ pdTemp[i] = pdVector[i-iHalfN];
+ } else { // Even
+ int iHalfN = n / 2;
+ pdTemp[0] = pdVector[iHalfN];
+ }
+
+ for (int i = 0; i < n; i++)
+ pdVector[i] = pdTemp[i];
+ delete pdTemp;
+}
+
+
+void
+ProcessSignal::shuffleFourierToNaturalOrder (double* pdVector, const int n)
+{
+ double* pdTemp = new double [n];
+ if (n % 2) { // Odd
+ int iHalfN = (n - 1) / 2;
+
+ pdTemp[iHalfN] = pdVector[0];
+ for (int i = 1; i <= iHalfN; i++)
+ pdTemp[i] = pdVector[i+iHalfN];
+ for (int i = iHalfN+1; i < n; i++)
+ pdTemp[i] = pdVector[i-iHalfN];
+ } else { // Even
+ int iHalfN = n / 2;
+ pdTemp[iHalfN] = pdVector[0];
+ }
+
+ for (int i = 0; i < n; i++)
+ pdVector[i] = pdTemp[i];
+ delete pdTemp;
+}
+
projects / ctsim.git / commitdiff