public INumberTable Transform(INumberTable inTable)
{
INumberTable rMatrix = matrixReal.SelectColumns(selectReal);
INumberTable iMatrix = matrixImg.SelectColumns(selectImg);
IList <IColumnSpec> cs = iMatrix.ColumnSpecList;
for (int i = 0; i < cs.Count; i++)
{
cs[i].Id += "_i";
}
return(MatrixProduct(inTable, rMatrix.AppendColumns(iMatrix)));
}
public static INumberTable Filter(INumberTable inTable, double lowFreq, double highFreq, int dimension, INumberTable baseTable)
{
int lowIdx = (int)(lowFreq * dimension);
int hiIdx = (int)(highFreq * dimension);
List <int> columns = new List <int>();
for (int i = 0; i < dimension; i++)
{
if ((i >= lowIdx) && (i <= hiIdx))
{
columns.Add(i);
}
}
INumberTable B = baseTable.SelectColumns(columns);
INumberTable Bt = B.Transpose2();
int b = B.Columns;
int r = inTable.Rows;
int m = inTable.Columns;
INumberTable outTable = null;
//Depending on the size of m relative to r and b, we can
//optimize the calculation by arrange the matrix multiplication.
if (2 * r * b < m * (r + b))
{
// The complexity in this arrangement is 2*m*r*b.
outTable = FourierTransform.MatrixProduct(FourierTransform.MatrixProduct(inTable, B), Bt);
}
else
{
// The complexity in this arrangement is m*m*(r+b).
outTable = FourierTransform.MatrixProduct(inTable, FourierTransform.MatrixProduct(B, Bt));
}
IList <IColumnSpec> oSpecList = outTable.ColumnSpecList;
IList <IColumnSpec> iSpecList = inTable.ColumnSpecList;
for (int col = 0; col < outTable.Columns; col++)
{
oSpecList[col].CopyFrom(iSpecList[col]);
}
return(outTable);
}
public INumberTable Filter(INumberTable inTable, double lowFreq, double highFreq)
{
INumberTable freqTable = Transform(inTable);
//
// Since the frequency vectors are half vector (the other half are mirred and not stored)
// we need to duplicate the vector except the first and, in case n is even, the n/2 th element.
// Notice that the Fourier matrixes have the same mirred structure.
//
for (int row = 0; row < freqTable.Rows; row++)
{
for (int col = 0; col < freqTable.Columns; col++)
{
int c = col % tDim; // c is the index within the repeat interval.
if (c == 0)
{
continue;
}
if ((tDim % 2 == 0) && (c == tDim / 2))
{
// In case tDim is even, the n/2-th element is at the centre of the symmetry
// and must not be duplciated.
continue;
}
freqTable.Matrix[row][col] *= 2;
}
}
// Calculate the filter indexes to pick up bases vectors
// with frequency (stored as column group)falling between give range.
int lFreq = (int)(lowFreq * (tDim / 2 + 1));
int hFreq = (int)(highFreq * (tDim / 2 + 1));
List <int> filterReal = new List <int>();
List <int> filterImg = new List <int>();
List <int> filterFreq = new List <int>();
IList <IColumnSpec> mrSpecList = matrixReal.ColumnSpecList;
foreach (int idx in selectReal)
{
int freq = mrSpecList[idx].Group;
if ((lFreq <= freq) && (freq <= hFreq))
{
filterReal.Add(idx);
filterFreq.Add(idx);
}
}
IList <IColumnSpec> miSpecList = matrixImg.ColumnSpecList;
foreach (int idx in selectImg)
{
int freq = miSpecList[idx].Group;
if ((lFreq <= freq) && (freq <= hFreq))
{
filterImg.Add(idx);
filterFreq.Add(tDim / 2 + idx);
}
}
int repeats = freqTable.Columns / tDim;
if (repeats > 1)
{
// the transformation has been repeated. We need to add the repeated coefficient here.
for (int r = 1; r < repeats; r++)
{
for (int n = 0; n < tDim; n++)
{
filterFreq.Add(r * tDim + filterFreq[n]);
}
}
}
freqTable = freqTable.SelectColumns(filterFreq);
INumberTable revMatrix = matrixReal.SelectRows(filterReal).Append(matrixImg.SelectRows(filterImg));
INumberTable outTable = MatrixProduct(freqTable, revMatrix);
IList <IColumnSpec> oSpecList = outTable.ColumnSpecList;
IList <IColumnSpec> iSpecList = inTable.ColumnSpecList;
for (int col = 0; col < outTable.Columns; col++)
{
if (col < inTable.Columns)
{
oSpecList[col].CopyFrom(iSpecList[col]);
}
}
return(outTable);
}