/// <summary>
/// Two dimensional Fast Fourier Transform.
/// </summary>
///
/// <param name="data">Data to transform.</param>
/// <param name="direction">Transformation direction.</param>
///
/// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
/// only in each dimension, where <b>n</b> may vary in the [1, 14] range. For example, 16x16 array
/// is valid, but 15x15 is not.</note></para></remarks>
///
/// <exception cref="ArgumentException">Incorrect data length.</exception>
///
public void FFT2(ComplexNumber[,] data, Direction direction)
{
int k = data.GetLength(0);
int n = data.GetLength(1);
// check data size
if (
(!Tools.IsPowerOf2(k)) ||
(!Tools.IsPowerOf2(n)) ||
(k < minLength) || (k > maxLength) ||
(n < minLength) || (n > maxLength)
)
{
throw new ArgumentException("Incorrect data length.");
}
// process rows
ComplexNumber[] row = new ComplexNumber[n];
for (int i = 0; i < k; i++)
{
// copy row
for (int j = 0; j < n; j++)
row[j] = data[i, j];
// transform it
FFT(row, direction);
// copy back
for (int j = 0; j < n; j++)
data[i, j] = row[j];
}
// process columns
ComplexNumber[] col = new ComplexNumber[k];
for (int j = 0; j < n; j++)
{
// copy column
for (int i = 0; i < k; i++)
col[i] = data[i, j];
// transform it
FFT(col, direction);
// copy back
for (int i = 0; i < k; i++)
data[i, j] = col[i];
}
}
/// <summary>
/// Two dimensional Discrete Fourier Transform.
/// </summary>
///
/// <param name="data">Data to transform.</param>
/// <param name="direction">Transformation direction.</param>
///
public void DFT2(ComplexNumber[,] data, Direction direction)
{
int n = data.GetLength(0); // rows
int m = data.GetLength(1); // columns
double arg, cos, sin;
ComplexNumber[] dst = new ComplexNumber[System.Math.Max(n, m)];
// process rows
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
dst[j] = ComplexNumberConstants.Zero;
arg = -(int)direction * 2.0 * System.Math.PI * (double)j / (double)m;
// sum source elements
for (int k = 0; k < m; k++)
{
cos = System.Math.Cos(k * arg);
sin = System.Math.Sin(k * arg);
dst[j].Re += (data[i, k].Re * cos - data[i, k].Im * sin);
dst[j].Im += (data[i, k].Re * sin + data[i, k].Im * cos);
}
}
// copy elements
if (direction == Direction.Forward)
{
// devide also for forward transform
for (int j = 0; j < m; j++)
{
data[i, j].Re = dst[j].Re / m;
data[i, j].Im = dst[j].Im / m;
}
}
else
{
for (int j = 0; j < m; j++)
{
data[i, j].Re = dst[j].Re;
data[i, j].Im = dst[j].Im;
}
}
}
// process columns
for (int j = 0; j < m; j++)
{
for (int i = 0; i < n; i++)
{
dst[i] = ComplexNumberConstants.Zero;
arg = -(int)direction * 2.0 * System.Math.PI * (double)i / (double)n;
// sum source elements
for (int k = 0; k < n; k++)
{
cos = System.Math.Cos(k * arg);
sin = System.Math.Sin(k * arg);
dst[i].Re += (data[k, j].Re * cos - data[k, j].Im * sin);
dst[i].Im += (data[k, j].Re * sin + data[k, j].Im * cos);
}
}
// copy elements
if (direction == Direction.Forward)
{
// devide also for forward transform
for (int i = 0; i < n; i++)
{
data[i, j].Re = dst[i].Re / n;
data[i, j].Im = dst[i].Im / n;
}
}
else
{
for (int i = 0; i < n; i++)
{
data[i, j].Re = dst[i].Re;
data[i, j].Im = dst[i].Im;
}
}
}
}
