/// <summary>
/// One dimensional Fast Fourier Transform.
/// </summary>
///
/// <param name="data">Data to transform.</param>
/// <param name="length">Array length.</param>
/// <param name="direction">Transformation direction.</param>
///
/// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
/// only, where <b>n</b> may vary in the [1, 14] range.</note></para></remarks>
///
/// <exception cref="ArgumentException">Incorrect data length.</exception>
///
public unsafe static void FFT(ComplexF *data, int length, Direction direction)
{
int n = length;
int m = AForge.Math.Tools.Log2(n);
// reorder data first
ReorderData(data, length);
// compute FFT
int tn = 1, tm;
for (int k = 1; k <= m; k++)
{
ComplexF[] rotation = FourierTransform.GetComplexRotation(k, direction);
tm = tn;
tn <<= 1;
for (int i = 0; i < tm; i++)
{
ComplexF t = rotation[i];
for (int even = i; even < n; even += tn)
{
int odd = even + tm;
ComplexF *ce = &data[even];
ComplexF *co = &data[odd];
float tr = co->Re * t.Re - co->Im * t.Im;
float ti = co->Re * t.Im + co->Im * t.Re;
co->Re = ce->Re - tr;
co->Im = ce->Im - ti;
ce->Re += tr;
ce->Im += ti;
}
}
}
if (direction == Direction.Backward)
{
for (int i = 0; i < n; i++)
{
data[i].Re /= n;
data[i].Im /= n;
}
}
}
/*
* /// <summary>
* /// One dimensional Fast Fourier Transform.
* /// </summary>
* /// <param name="data">Data to transform.</param>
* /// <param name="direction">Transformation direction.</param>
* public static void FFT(ComplexF[] data, Direction direction){
* int length = data.Length;
* int n = length;
* int m = AForge.Math.Tools.Log2(n);
*
* // reorder data first
* ReorderData(data, length);
*
* // compute FFT
* int tn = 1, tm;
*
* for (int k = 1; k <= m; k++)
* {
* ComplexF[] rotation = FourierTransform.GetComplexRotation(k, direction);
*
* tm = tn;
* tn <<= 1;
*
* for (int i = 0; i < tm; i++)
* {
* ComplexF t = rotation[i];
*
* for (int even = i; even < n; even += tn)
* {
* int odd = even + tm;
* ComplexF* ce = &data[even];
* ComplexF* co = &data[odd];
*
* float tr = co->Re * t.Re - co->Im * t.Im;
* float ti = co->Re * t.Im + co->Im * t.Re;
*
* co->Re = ce->Re - tr;
* co->Im = ce->Im - ti;
*
* ce->Re += tr;
* ce->Im += ti;
* }
* }
* }
*
* if (direction == Direction.Backward)
* {
* for (int i = 0; i < n; i++)
* {
* data[i].Re /= n;
* data[i].Im /= n;
* }
* }
* }
*
*
* /// <summary>
* /// Two dimensional Fast Fourier Transform.
* /// </summary>
* /// <param name="data">Data to transform.</param>
* /// <param name="direction">Transformation direction.</param>
* public unsafe static void FFT2(ComplexF[,] data, Direction direction)
* {
* int width = data.GetLength(1);
* int height = data.GetLength(0);
*
* fixed (ComplexF* dataPtr = data)
* {
* FFT2(dataPtr, width, height, width, direction);
* }
* }
*
* /// <summary>
* /// Two dimensional Fast Fourier Transform.
* /// </summary>
* /// <param name="width">Image width.</param>
* /// <param name="height">Image height.</param>
* /// <param name="stride">Image stride.</param>
* /// <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 unsafe static void FFT2(ComplexF* data, int width, int height, int stride, Direction direction)
* {
* const int MIN_PATCH_SIZE = 32; //how much rows/columns should one thread process
*
* int k = height;
* int n = width;
*
* // check data size
* if (
* (!AForge.Math.Tools.IsPowerOf2(k)) ||
* (!AForge.Math.Tools.IsPowerOf2(n)) ||
* (k < minLength) || (k > maxLength) ||
* (n < minLength) || (n > maxLength)
* )
* {
* throw new ArgumentException("Incorrect data length.");
* }
*
* // process rows
* var procRow = new ParallelProcessor<bool, bool>(
* new Size(
* 1 // does not matter
* , height
* )
* ,
* () => true,
* (_, __, area) =>
* {
* ComplexF* dataPatchPtr = data + area.Y * stride / sizeof(ComplexF); //get row
*
* for (int i = 0; i < area.Height; i++)
* {
* // transform it
* FourierTransform.FFT(dataPatchPtr, n, direction);
*
* dataPatchPtr += stride / sizeof(ComplexF);
* }
* },
* new ParallelOptions2D {
* ParallelTrigger = (size) => size.Height >= MIN_PATCH_SIZE
* //,ForceSequential = true
* }
* );
*
* // process columns
* //(y and x are swaped => proc thinks it is diving horizontal pacthes but instead we are using them as vertical ones)
* var procCol = new ParallelProcessor<bool, bool>(
* new Size(
* 1 // does not matter
* , width
* )
* ,
* () => true,
* (_, __, area) =>
* {
* ComplexF* dataPatchPtr = &data[area.Y]; //get column
*
* fixed (ComplexF* _col = new ComplexF[k])
* {
* ComplexF* col = _col;
*
* for (int j = 0; j < area.Height; j++)
* {
* // copy column
* ComplexF* dataColPtr = &dataPatchPtr[j];
* for (int i = 0; i < k; i++)
* {
* col[i] = *dataColPtr;
* dataColPtr += stride / sizeof(ComplexF);
* }
*
* // transform it
* FourierTransform.FFT(col, k, direction);
*
* // copy back
* dataColPtr = &dataPatchPtr[j];
* for (int i = 0; i < k; i++)
* {
* dataColPtr = col[i];
* dataColPtr += stride / sizeof(ComplexF);
* }
* }
* }
* },
* new ParallelOptions2D {
* ParallelTrigger = (size) => size.Height >= MIN_PATCH_SIZE
* //,ForceSequential = true
* }
* );
*
* procRow.Process(true);
* procCol.Process(true);
* }
*
#region Private Region
*
* private static ComplexF[,][] complexRotation = new ComplexF[maxBits, 2][];
*
* // Get rotation of complex number
* private static ComplexF[] GetComplexRotation(int numberOfBits, Direction direction)
* {
* int directionIndex = (direction == Direction.Forward) ? 1 : 0;
*
* // check if the array is already calculated
* if (complexRotation[numberOfBits - 1, directionIndex] == null)
* {
* int n = 1 << (numberOfBits - 1);
* float uR = 1.0f;
* float uI = 0.0f;
* double angle = System.Math.PI / n * (-(int)(direction));
* float wR = (float)System.Math.Cos(angle);
* float wI = (float)System.Math.Sin(angle);
* float t;
* ComplexF[] rotation = new ComplexF[n];
*
* for (int i = 0; i < n; i++)
* {
* rotation[i] = new ComplexF { Re = uR, Im = uI};
* t = uR * wI + uI * wR;
* uR = uR * wR - uI * wI;
* uI = t;
* }
*
* complexRotation[numberOfBits - 1, directionIndex] = rotation;
* }
* return complexRotation[numberOfBits - 1, directionIndex];
* }
*
* // Reorder data for FFT using
* private static void ReorderData(ComplexF[] data){
* int length = data.Length;
*
* // check data length
* if ((length < minLength) || (length > maxLength) || (!AForge.Math.Tools.IsPowerOf2(length)))
* throw new ArgumentException("Incorrect data length.");
*
* int[] rBits = GetReversedBits(AForge.Math.Tools.Log2(len));
*
* for (int i = 0; i < len; i++)
* {
* int s = rBits[i];
*
* if (s > i)
* {
* ComplexF t = data[i];
* data[i] = data[s];
* data[s] = t;
* }
* }
* }
#endregion
*/
/// <summary>
/// One 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, where <b>n</b> may vary in the [1, 14] range.</note></para></remarks>
///
/// <exception cref="ArgumentException">Incorrect data length.</exception>
///
public static void FFT(ComplexF[] data, Direction direction)
{
int n = data.Length;
int m = Tools.Log2(n);
// reorder data first
ReorderData(data);
// compute FFT
int tn = 1, tm;
for (int k = 1; k <= m; k++)
{
ComplexF[] rotation = FourierTransform.GetComplexRotation(k, direction);
tm = tn;
tn <<= 1;
for (int i = 0; i < tm; i++)
{
ComplexF t = rotation[i];
for (int even = i; even < n; even += tn)
{
int odd = even + tm;
ComplexF ce = data[even];
ComplexF co = data[odd];
float tr = co.Re * t.Re - co.Im * t.Im;
float ti = co.Re * t.Im + co.Im * t.Re;
data[even].Re += tr;
data[even].Im += ti;
data[odd].Re = ce.Re - tr;
data[odd].Im = ce.Im - ti;
}
}
}
if (direction == Direction.Forward)
{
for (int i = 0; i < n; i++)
{
data[i].Re /= (float)n;
data[i].Im /= (float)n;
}
}
}