X-Git-Url: http://git.kpe.io/?a=blobdiff_plain;f=libctsim%2Ffilter.cpp;h=d7d8b973c61a41f233d5a03a7c1dd3b894a5f8fc;hb=d158a6da6ec776fe98961f73f2ea74cf55de4700;hp=30d47185e3cd08120a9c66c826d6946afb105f71;hpb=99dd1d6ed10db1f669a5fe6af71225a50fc0ddfb;p=ctsim.git

diff --git a/libctsim/filter.cpp b/libctsim/filter.cpp
index 30d4718..d7d8b97 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 1.1 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
@@ -27,61 +27,598 @@
 
 #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
@@ -89,21 +626,27 @@ filter_generate (const FilterType filt_type, double bw, double xmin, double xmax
  *  		 		        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 {
@@ -115,7 +658,7 @@ filter_spatial_response_calc (int filt_type, double x, double bw, double param,
   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);
   
@@ -127,21 +670,28 @@ filter_spatial_response_calc (int filt_type, double x, double bw, double param,
  *    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.;
@@ -192,9 +742,7 @@ filter_frequency_response (int filt_type, double u, double bw, double param)
     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);
@@ -208,16 +756,46 @@ filter_frequency_response (int filt_type, double u, double bw, double param)
  *				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;
@@ -225,7 +803,7 @@ filter_spatial_response_analytic (int filt_type, double x, double bw, double par
   double b = PI / bw;
   double b2 = TWOPI / bw;
 
-  switch (filt_type) {
+  switch (filterID) {
   case FILTER_BANDLIMIT:
     q = bw * sinc(u * w, 1.0);
     break;
@@ -237,8 +815,7 @@ filter_spatial_response_analytic (int filt_type, double x, double bw, double par
     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);
@@ -264,9 +841,7 @@ filter_spatial_response_analytic (int filt_type, double x, double bw, double par
     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;
   }
@@ -287,12 +862,6 @@ filter_spatial_response_analytic (int filt_type, double x, double bw, double par
  *   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)
@@ -308,12 +877,233 @@ sinc (double x, double mult)
  */
 
 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;
+  }
 }