/*****************************************************************************
-** FILE IDENTIFICATION
+** File IDENTIFICATION
**
** Name: filter.cpp
** Purpose: Routines for signal-procesing filters
** This is part of the CTSim program
** Copyright (C) 1983-2000 Kevin Rosenberg
**
-** $Id: filter.cpp,v 1.1 2000/06/19 02:59:34 kevin Exp $
+** $Id: filter.cpp,v 1.24 2000/08/03 09:57:33 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
#include "ct.h"
+int SignalFilter::N_INTEGRAL=500; //static member
+
+const int SignalFilter::FILTER_INVALID = -1 ;
+const int SignalFilter::FILTER_ABS_BANDLIMIT = 0; // filter times |x = |
+const int SignalFilter::FILTER_ABS_SINC = 1;
+const int SignalFilter::FILTER_ABS_G_HAMMING = 2;
+const int SignalFilter::FILTER_ABS_COSINE = 3;
+const int SignalFilter::FILTER_SHEPP = 4;
+const int SignalFilter::FILTER_BANDLIMIT = 5;
+const int SignalFilter::FILTER_SINC = 6;
+const int SignalFilter::FILTER_G_HAMMING = 7;
+const int SignalFilter::FILTER_COSINE = 8;
+const int SignalFilter::FILTER_TRIANGLE = 9;
+
+const char* SignalFilter::s_aszFilterName[] = {
+ {"abs_bandlimit"},
+ {"abs_sinc"},
+ {"abs_hamming"},
+ {"abs_cosine"},
+ {"shepp"},
+ {"bandlimit"},
+ {"sinc"},
+ {"hamming"},
+ {"cosine"},
+ {"triangle"},
+};
+
+const char* SignalFilter::s_aszFilterTitle[] = {
+ {"Abs(w) * Bandlimit"},
+ {"Abs(w) * Sinc"},
+ {"Abs(w) * Hamming"},
+ {"Abs(w) * Cosine"},
+ {"Shepp"},
+ {"Bandlimit"},
+ {"Sinc"},
+ {"Hamming"},
+ {"Cosine"},
+ {"Triangle"},
+};
+
+const int SignalFilter::s_iFilterCount = sizeof(s_aszFilterName) / sizeof(const char*);
+
+const int SignalFilter::FILTER_METHOD_INVALID = -1;
+const int SignalFilter::FILTER_METHOD_CONVOLUTION = 0;
+const int SignalFilter::FILTER_METHOD_FOURIER = 1;
+const int SignalFilter::FILTER_METHOD_FOURIER_TABLE = 2;
+const int SignalFilter::FILTER_METHOD_FFT = 3;
+#if HAVE_FFTW
+const int SignalFilter::FILTER_METHOD_FFTW = 4;
+const int SignalFilter::FILTER_METHOD_RFFTW =5 ;
+#endif
+
+const char* SignalFilter::s_aszFilterMethodName[] = {
+ {"convolution"},
+ {"fourier"},
+ {"fouier_table"},
+ {"fft"},
+#if HAVE_FFTW
+ {"fftw"},
+ {"rfftw"},
+#endif
+};
+
+const char* SignalFilter::s_aszFilterMethodTitle[] = {
+ {"Convolution"},
+ {"Direct Fourier"},
+ {"Fouier Trigometric Table Lookout"},
+ {"FFT"},
+#if HAVE_FFTW
+ {"FFTW"},
+ {"Real/Half-Complex FFTW"},
+#endif
+};
+
+const int SignalFilter::s_iFilterMethodCount = sizeof(s_aszFilterMethodName) / sizeof(const char*);
+
+
+const int SignalFilter::DOMAIN_INVALID = -1;
+const int SignalFilter::DOMAIN_FREQUENCY = 0;
+const int SignalFilter::DOMAIN_SPATIAL = 1;
+
+const char* SignalFilter::s_aszDomainName[] = {
+ {"frequency"},
+ {"spatial"},
+};
+
+const char* SignalFilter::s_aszDomainTitle[] = {
+ {"Frequency"},
+ {"Spatial"},
+};
+
+const int SignalFilter::s_iDomainCount = sizeof(s_aszDomainName) / sizeof(const char*);
+
+
+const int SignalFilter::FREQUENCY_FILTER_INVALID = -1;
+const int SignalFilter::FREQUENCY_FILTER_DIRECT_FREQUENCY = 0;
+const int SignalFilter::FREQUENCY_FILTER_INVERSE_SPATIAL = 1;
+
+const char* SignalFilter::s_aszFrequencyFilterName[] = {
+ {"direct_frequency"},
+ {"inverse_spatial"},
+};
+
+const char* SignalFilter::s_aszFrequencyFilterTitle[] = {
+ {"Direct Frequency"},
+ {"Inverse Spatial"},
+};
+
+const int SignalFilter::s_iFrequencyFilterCount = sizeof(s_aszFrequencyFilterName) / sizeof(const char*);
+
/* NAME
- * filter_generate Generate a filter
+ * SignalFilter::SignalFilter Construct a signal
*
* SYNOPSIS
- * f = filter_generate (filt_type, bw, xmin, xmax, 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 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
+ * 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 filterMin, filterMax Filter limits
+ * int nSignalPoints Number of points in signal
+ * double param General input parameter to filters
+ * int domain FREQUENCY or SPATIAL domain wanted
*/
-double *
-filter_generate (const FilterType filt_type, double bw, double xmin, double xmax, int n, double param, const DomainType domain, int numint)
+SignalFilter::SignalFilter (const char* filterName, const char* filterMethodName, double bw, double signalIncrement, int nSignalPoints, double param, const char* domainName, const char* frequencyFilterName, int zeropad = 0, int preinterpolationFactor = 1)
+ : m_vecFilter(NULL), m_vecFourierCosTable(NULL), m_vecFourierSinTable(NULL), m_fail(false)
+{
+ m_idFilter = convertFilterNameToID (filterName);
+ if (m_idFilter == FILTER_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid Filter name ";
+ 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;
+ m_failMessage = "Invalid domain name ";
+ m_failMessage += domainName;
+ return;
+ }
+ m_idFrequencyFilter = convertFrequencyFilterNameToID (frequencyFilterName);
+ if (m_idFrequencyFilter == FREQUENCY_FILTER_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid frequency filter name ";
+ m_failMessage += frequencyFilterName;
+ return;
+ }
+ init (m_idFilter, m_idFilterMethod, bw, signalIncrement, nSignalPoints, param, m_idDomain, m_idFrequencyFilter, zeropad, preinterpolationFactor);
+}
+
+SignalFilter::SignalFilter (const int filterID, const int filterMethodID, double bw, double signalIncrement, int nSignalPoints, double param, const int domainID, int frequencyFilterID, int zeropad = 0, int preinterpolationFactor = 1)
+ : m_vecFilter(NULL), m_vecFourierCosTable(NULL), m_vecFourierSinTable(NULL), m_fail(false)
+{
+ init (filterID, filterMethodID, bw, signalIncrement, nSignalPoints, param, domainID, frequencyFilterID, zeropad, preinterpolationFactor);
+}
+
+SignalFilter::SignalFilter (const char* filterName, const char* domainName, double bw, double param)
+ : m_vecFilter(NULL), m_vecFourierCosTable(NULL), m_vecFourierSinTable(NULL), m_fail(false)
+{
+ m_bw = bw;
+ m_nSignalPoints = 0;
+ m_nFilterPoints = 0;
+ m_filterParam = param;
+ m_idFilter = convertFilterNameToID (filterName);
+ if (m_idFilter == FILTER_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid Filter name ";
+ m_failMessage += filterName;
+ return;
+ }
+ m_idDomain = convertDomainNameToID (domainName);
+ if (m_idDomain == DOMAIN_INVALID) {
+ m_fail = true;
+ m_failMessage = "Invalid domain name ";
+ m_failMessage += domainName;
+ return;
+ }
+}
+
+void
+SignalFilter::init (const int filterID, const int filterMethodID, double bw, double signalIncrement, int nSignalPoints, double filterParam, const int domainID, const int frequencyFilterID, int zeropad, int preinterpolationFactor)
{
- double *f = new double [n];
- double xinc = (xmax - xmin) / (n - 1);
+ m_bw = bw;
+ m_idFilter = filterID;
+ m_idDomain = domainID;
+ m_idFilterMethod = filterMethodID;
+ m_idFrequencyFilter = frequencyFilterID;
+ if (m_idFilter == FILTER_INVALID || m_idDomain == DOMAIN_INVALID || m_idFilterMethod == FILTER_METHOD_INVALID || m_idFrequencyFilter == FREQUENCY_FILTER_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_nameFrequencyFilter = convertFrequencyFilterIDToName (m_idFrequencyFilter);
+ 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 (filt_type == FILTER_SHEPP) {
- double a = 2 * bw;
- double c = - 4. / (a * a);
- int center = (n - 1) / 2;
- int sidelen = center;
- f[center] = 4. / (a * a);
+ 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<int>(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<double>(i) / halfFilter/ (2. * m_signalInc);
+ for (int i = 1; i <= halfFilter; i++)
+ m_vecFilter[m_nFilterPoints - i] = static_cast<double>(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 ];
- for (int i = 1; i <= sidelen; i++ )
- f [center + i] = f [center - i] = c / (4 * (i * i) - 1);
- } else if (domain == D_FREQ) {
- double x;
- int i;
- for (x = xmin, i = 0; i < n; x += xinc, i++)
- f[i] = filter_frequency_response (filt_type, x, bw, param);
- } else if (domain == D_SPATIAL) {
- double x;
- int i;
- for (x = xmin, i = 0; i < n; x += xinc, i++)
- if (numint == 0)
- f[i] = filter_spatial_response_analytic (filt_type, x, bw, param);
- else
- f[i] = filter_spatial_response_calc (filt_type, x, bw, param, numint);
- } else {
- sys_error (ERR_WARNING, "Illegal domain %d [filt_generate]", domain);
- return (NULL);
+ 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);
+#if LIMIT_BANDWIDTH_TRIAL
+ if (i < m_nFilterPoints / 4 || i > (m_nFilterPoints * 3) / 4)
+ m_vecFilter[i] = 0;
+#endif
+ }
+ } else {
+ m_failMessage = "Illegal domain name ";
+ m_failMessage += m_idDomain;
+ m_fail = true;
+ }
}
-
- return (f);
}
+SignalFilter::~SignalFilter (void)
+{
+ 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
+}
+
+
+int
+SignalFilter::convertFilterNameToID (const char *filterName)
+{
+ int filterID = FILTER_INVALID;
+
+ for (int i = 0; i < s_iFilterCount; i++)
+ if (strcasecmp (filterName, s_aszFilterName[i]) == 0) {
+ filterID = i;
+ break;
+ }
+
+ return (filterID);
+}
+
+const char *
+SignalFilter::convertFilterIDToName (const int filterID)
+{
+ static const char *name = "";
+
+ if (filterID >= 0 && filterID < s_iFilterCount)
+ return (s_aszFilterName [filterID]);
+
+ return (name);
+}
+
+const char *
+SignalFilter::convertFilterIDToTitle (const int filterID)
+{
+ static const char *title = "";
+
+ if (filterID >= 0 && filterID < s_iFilterCount)
+ return (s_aszFilterTitle [filterID]);
+
+ return (title);
+}
+
+int
+SignalFilter::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 *
+SignalFilter::convertFilterMethodIDToName (const int fmID)
+{
+ static const char *name = "";
+
+ if (fmID >= 0 && fmID < s_iFilterMethodCount)
+ return (s_aszFilterMethodName [fmID]);
+
+ return (name);
+}
+
+const char *
+SignalFilter::convertFilterMethodIDToTitle (const int fmID)
+{
+ static const char *title = "";
+
+ if (fmID >= 0 && fmID < s_iFilterMethodCount)
+ return (s_aszFilterTitle [fmID]);
+
+ return (title);
+}
+
+int
+SignalFilter::convertDomainNameToID (const char* const domainName)
+{
+ int dID = DOMAIN_INVALID;
+
+ for (int i = 0; i < s_iDomainCount; i++)
+ if (strcasecmp (domainName, s_aszDomainName[i]) == 0) {
+ dID = i;
+ break;
+ }
+
+ return (dID);
+}
+
+const char *
+SignalFilter::convertDomainIDToName (const int domainID)
+{
+ static const char *name = "";
+
+ if (domainID >= 0 && domainID < s_iDomainCount)
+ return (s_aszDomainName [domainID]);
+
+ return (name);
+}
+
+const char *
+SignalFilter::convertDomainIDToTitle (const int domainID)
+{
+ static const char *title = "";
+
+ if (domainID >= 0 && domainID < s_iDomainCount)
+ return (s_aszDomainTitle [domainID]);
+
+ return (title);
+}
+
+int
+SignalFilter::convertFrequencyFilterNameToID (const char* const ffName)
+{
+ int ffID = FREQUENCY_FILTER_INVALID;
+
+ for (int i = 0; i < s_iFrequencyFilterCount; i++)
+ if (strcasecmp (ffName, s_aszFrequencyFilterName[i]) == 0) {
+ ffID = i;
+ break;
+ }
+
+ return (ffID);
+}
+
+const char *
+SignalFilter::convertFrequencyFilterIDToName (const int ffID)
+{
+ static const char *name = "";
+
+ if (ffID >= 0 && ffID < s_iFrequencyFilterCount)
+ return (s_aszFrequencyFilterName [ffID]);
+
+ return (name);
+}
+
+const char *
+SignalFilter::convertFrequencyFilterIDToTitle (const int ffID)
+{
+ static const char *name = "";
+
+ if (ffID >= 0 && ffID < s_iFrequencyFilterCount)
+ return (s_aszFrequencyFilterTitle [ffID]);
+
+ 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<double> 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<double> 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)
+{
+ double response = 0;
+
+ if (m_idDomain == DOMAIN_SPATIAL)
+ 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);
+}
+
+
+double
+SignalFilter::spatialResponse (int filterID, double bw, double x, double param)
+{
+ if (haveAnalyticSpatial(filterID))
+ return spatialResponseAnalytic (filterID, bw, x, param);
+ else
+ return spatialResponseCalc (filterID, bw, x, param, N_INTEGRAL);
+}
/* NAME
* filter_spatial_response_calc Calculate filter by discrete inverse fourier
* response
*
* SYNOPSIS
- * y = filter_spatial_response_calc (filt_type, x, bw, param, n)
+ * y = filter_spatial_response_calc (filt_type, x, m_bw, param, n)
* double y Filter's response in spatial domain
* int filt_type Type of filter (definitions in ct.h)
* double x Spatial position to evaluate filter
- * double bw Bandwidth of window
+ * double m_bw Bandwidth of window
* double param General parameter for various filters
* int n Number of points to calculate integrations
*/
double
-filter_spatial_response_calc (int filt_type, double x, double bw, double param, int n)
+SignalFilter::spatialResponseCalc (double x, double param) const
+{
+ return (spatialResponseCalc (m_idFilter, m_bw, x, param, N_INTEGRAL));
+}
+
+double
+SignalFilter::spatialResponseCalc (int filterID, double bw, double x, double param, int n)
{
double zmin, zmax;
- if (filt_type == FILTER_TRIANGLE) {
+ if (filterID == FILTER_TRIANGLE) {
zmin = 0;
zmax = bw;
} else {
double z = zmin;
double q [n];
for (int i = 0; i < n; i++, z += zinc)
- q[i] = filter_frequency_response (filt_type, z, bw, param) * cos (TWOPI * z * x);
+ q[i] = frequencyResponse (filterID, bw, z, param) * cos (TWOPI * z * x);
double y = 2 * integrateSimpson (zmin, zmax, q, n);
* filter_frequency_response Return filter frequency response
*
* SYNOPSIS
- * h = filter_frequency_response (filt_type, u, bw, param)
+ * h = filter_frequency_response (filt_type, u, m_bw, param)
* double h Filters frequency response at u
* int filt_type Type of filter
* double u Frequency to evaluate filter at
- * double bw Bandwidth of filter
+ * double m_bw Bandwidth of filter
* double param General input parameter for various filters
*/
double
-filter_frequency_response (int filt_type, double u, double bw, double param)
+SignalFilter::frequencyResponse (double u, double param) const
+{
+ return frequencyResponse (m_idFilter, m_bw, u, param);
+}
+
+
+double
+SignalFilter::frequencyResponse (int filterID, double bw, double u, double param)
{
double q;
double au = fabs (u);
- switch (filt_type) {
+ switch (filterID) {
case FILTER_BANDLIMIT:
if (au >= bw / 2)
q = 0.;
break;
default:
q = 0;
- sys_error (ERR_WARNING,
- "Frequency response for filter %d not implemented [filter_frequency_response]",
- filt_type);
+ sys_error (ERR_WARNING, "Frequency response for filter %d not implemented [filter_frequency_response]", filterID);
break;
}
return (q);
* response
*
* SYNOPSIS
- * y = filter_spatial_response_analytic (filt_type, x, bw, param)
+ * y = filter_spatial_response_analytic (filt_type, x, m_bw, param)
* double y Filter's response in spatial domain
* int filt_type Type of filter (definitions in ct.h)
* double x Spatial position to evaluate filter
- * double bw Bandwidth of window
+ * double m_bw Bandwidth of window
* double param General parameter for various filters
*/
double
-filter_spatial_response_analytic (int filt_type, double x, double bw, double param)
+SignalFilter::spatialResponseAnalytic (double x, double param) const
+{
+ return spatialResponseAnalytic (m_idFilter, m_bw, x, param);
+}
+
+const bool
+SignalFilter::haveAnalyticSpatial (int 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 (int filterID, double bw, double x, double param)
{
double q, temp;
double u = TWOPI * x;
double b = PI / bw;
double b2 = TWOPI / bw;
- switch (filt_type) {
+ switch (filterID) {
case FILTER_BANDLIMIT:
q = bw * sinc(u * w, 1.0);
break;
q = sinc(b-u,w) + sinc(b+u,w);
break;
case FILTER_G_HAMMING:
- q = 2 * param * sin(u*w)/u + (1-param) *
- (sinc(b2-u, w) + sinc(b2+u, w));
+ q = 2 * param * sin(u*w)/u + (1-param) * (sinc(b2-u, w) + sinc(b2+u, w));
break;
case FILTER_ABS_BANDLIMIT:
q = 2 * integral_abscos (u, w);
break;
case FILTER_ABS_SINC:
default:
- sys_error (ERR_WARNING,
- "Analytic filter type %d not implemented [filter_spatial_response_analytic]",
- filt_type);
+ sys_error (ERR_WARNING, "Analytic filter type %d not implemented [filter_spatial_response_analytic]", filterID);
q = 0;
break;
}
* v = sin(x * mult) / x;
*/
-double
-sinc (double x, double mult)
-{
- return (fabs(x) > F_EPSILON ? (sin (x * mult) / x) : 1.0);
-}
-
/* NAME
* integral_abscos Returns integral of u*cos(u)
*/
double
-integral_abscos (double u, double w)
+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));
+}
+
+
+/* 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
+SignalFilter::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_vecFilter[n - i + (np - 1)];
+#else
+ double* f2 = m_vecFilter + n + (np - 1);
+ for (int i = 0; i < np; i++)
+ sum += *func++ * *f2--;
+#endif
+
+ return (sum * dx);
+}
+
+
+double
+SignalFilter::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_vecFilter[n - i + (np - 1)];
+#else
+double* f2 = m_vecFilter + n + (np - 1);
+for (int i = 0; i < np; i++)
+ sum += *func++ * *f2--;
+#endif
+
+ return (sum * dx);
+}
+
+
+void
+SignalFilter::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
+SignalFilter::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
+SignalFilter::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;
+ }
+}
+
+void
+SignalFilter::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_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<double> (sumReal, sumImag);
+ }
+}
+
+// (a+bi) * (c + di) = (ac - bd) + (ad + bc)i
+void
+SignalFilter::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_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<double> (sumReal, sumImag);
+ }
+}
+
+void
+SignalFilter::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_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;
+ }
}
projects / ctsim.git / blobdiff