public static IEnumerable <Complex> TransformReverse(IEnumerable <Complex> values)
{
if (!reverseTransformations.ContainsKey(values.Count()))
{
reverseTransformations[values.Count()] = GetReverseTransformation(values.Count());
}
MatrixComplex transformation = reverseTransformations[values.Count()];
MatrixComplex vector = MatrixComplex.FromRowVectors(values.Select(MatrixComplex.CreateSingleton));
return((transformation * vector).Columns.Single());
}
// Intended for synthesis
// Input \ Output | Real | Imaginary
// ---------------|------|----------
// Real | + | -
// Imaginary | + | +
static MatrixComplex GetReverseTransformation(int size)
{
MatrixComplex transformation = new MatrixComplex(size, size);
Complex factor = (2 * Math.PI / size) * Complex.ImaginaryOne;
for (int row = 0; row < transformation.RowCount; row++)
{
for (int column = 0; column < transformation.ColumnCount; column++)
{
transformation[row, column] = Scalars.Exponentiate(-factor * row * column);
}
}
return((1 / Scalars.SquareRoot(size)) * transformation);
}
