//======================================================================================
//======================================================================================
/// <summary>
/// Compute a 1D fast Fourier transform of a dataset of complex numbers (as pairs of float's).
/// </summary>
/// <param name="data"></param>
/// <param name="length"></param>
/// <param name="direction"></param>
public static void FFT(float[] data, int length, FourierDirection direction)
{
Debug.Assert(data != null);
Debug.Assert(data.Length >= length * 2);
Debug.Assert(Fourier.IsPowerOf2(length) == true);
Fourier.SyncLookupTableLength(length);
int ln = Fourier.Log2(length);
// reorder array
Fourier.ReorderArray(data);
// successive doubling
int N = 1;
int signIndex = (direction == FourierDirection.Forward) ? 0 : 1;
for (int level = 1; level <= ln; level++)
{
int M = N;
N <<= 1;
float[] uRLookup = _uRLookupF[level, signIndex];
float[] uILookup = _uILookupF[level, signIndex];
for (int j = 0; j < M; j++)
{
float uR = uRLookup[j];
float uI = uILookup[j];
for (int evenT = j; evenT < length; evenT += N)
{
int even = evenT << 1;
int odd = (evenT + M) << 1;
float r = data[odd];
float i = data[odd + 1];
float odduR = r * uR - i * uI;
float odduI = r * uI + i * uR;
r = data[even];
i = data[even + 1];
data[even] = r + odduR;
data[even + 1] = i + odduI;
data[odd] = r - odduR;
data[odd + 1] = i - odduI;
}
}
}
}
/// <summary>
/// Compute a 2D fast fourier transform on a data set of complex numbers
/// </summary>
/// <param name="data"></param>
/// <param name="xLength"></param>
/// <param name="yLength"></param>
/// <param name="direction"></param>
public static void FFT2(Complex[] data, int xLength, int yLength, FourierDirection direction)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
if (data.Length < xLength * yLength)
{
throw new ArgumentOutOfRangeException("data.Length", data.Length, "must be at least as large as 'xLength * yLength' parameter");
}
if (Fourier.IsPowerOf2(xLength) == false)
{
throw new ArgumentOutOfRangeException("xLength", xLength, "must be a power of 2");
}
if (Fourier.IsPowerOf2(yLength) == false)
{
throw new ArgumentOutOfRangeException("yLength", yLength, "must be a power of 2");
}
int xInc = 1;
int yInc = xLength;
if (xLength > 1)
{
Fourier.SyncLookupTableLength(xLength);
for (int y = 0; y < yLength; y++)
{
int xStart = y * yInc;
Fourier.LinearFFT_Quick(data, xStart, xInc, xLength, direction);
}
}
if (yLength > 1)
{
Fourier.SyncLookupTableLength(yLength);
for (int x = 0; x < xLength; x++)
{
int yStart = x * xInc;
Fourier.LinearFFT_Quick(data, yStart, yInc, yLength, direction);
}
}
}
static private void ReorderArray(double[] data)
{
Debug.Assert(data != null);
int length = data.Length / 2;
Debug.Assert(Fourier.IsPowerOf2(length) == true);
Debug.Assert(length >= cMinLength);
Debug.Assert(length <= cMaxLength);
int[] reversedBits = Fourier.GetReversedBits(Fourier.Log2(length));
for (int i = 0; i < length; i++)
{
int swap = reversedBits[i];
if (swap > i)
{
MathUtils.Swap(ref data[i << 1], ref data[swap << 1]);
MathUtils.Swap(ref data[i << 1 + 1], ref data[swap << 1 + 1]);
}
}
}
static private void ReorderArray(Complex[] data)
{
Debug.Assert(data != null);
int length = data.Length;
Debug.Assert(Fourier.IsPowerOf2(length) == true);
Debug.Assert(length >= cMinLength);
Debug.Assert(length <= cMaxLength);
int[] reversedBits = Fourier.GetReversedBits(Fourier.Log2(length));
for (int i = 0; i < length; i++)
{
int swap = reversedBits[i];
if (swap > i)
{
Complex temp = data[i];
data[i] = data[swap];
data[swap] = temp;
}
}
}
/// <summary>
/// Compute a 1D real-symmetric fast fourier transform.
/// </summary>
/// <param name="data"></param>
/// <param name="length"></param>
/// <param name="direction"></param>
public static void RFFT(float[] data, int length, FourierDirection direction)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
if (data.Length < length)
{
throw new ArgumentOutOfRangeException("length", length, "must be at least as large as 'data.Length' parameter");
}
if (Fourier.IsPowerOf2(length) == false)
{
throw new ArgumentOutOfRangeException("length", length, "must be a power of 2");
}
float c1 = 0.5f, c2;
float theta = (float)Math.PI / (length / 2);
if (direction == FourierDirection.Forward)
{
c2 = -0.5f;
FFT(data, length / 2, direction);
}
else
{
c2 = 0.5f;
theta = -theta;
}
float wtemp = (float)Math.Sin(0.5 * theta);
float wpr = -2 * wtemp * wtemp;
float wpi = (float)Math.Sin(theta);
float wr = 1 + wpr;
float wi = wpi;
// do / undo packing
for (int i = 1; i < length / 4; i++)
{
int a = 2 * i;
int b = length - 2 * i;
float h1r = c1 * (data[a] + data[b]);
float h1i = c1 * (data[a + 1] - data[b + 1]);
float h2r = -c2 * (data[a + 1] + data[b + 1]);
float h2i = c2 * (data[a] - data[b]);
data[a] = h1r + wr * h2r - wi * h2i;
data[a + 1] = h1i + wr * h2i + wi * h2r;
data[b] = h1r - wr * h2r + wi * h2i;
data[b + 1] = -h1i + wr * h2i + wi * h2r;
wr = (wtemp = wr) * wpr - wi * wpi + wr;
wi = wi * wpr + wtemp * wpi + wi;
}
if (direction == FourierDirection.Forward)
{
float hir = data[0];
data[0] = hir + data[1];
data[1] = hir - data[1];
}
else
{
float hir = data[0];
data[0] = c1 * (hir + data[1]);
data[1] = c1 * (hir - data[1]);
Fourier.FFT(data, length / 2, direction);
}
}
/// <summary>
/// Compute a 1D fast Fourier transform of a dataset of complex numbers.
/// </summary>
/// <param name="data"></param>
/// <param name="length"></param>
/// <param name="direction"></param>
public static void FFT(Complex[] data, int length, FourierDirection direction)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
if (data.Length < length)
{
throw new ArgumentOutOfRangeException("length", length, "must be at least as large as 'data.Length' parameter");
}
if (Fourier.IsPowerOf2(length) == false)
{
throw new ArgumentOutOfRangeException("length", length, "must be a power of 2");
}
Fourier.SyncLookupTableLength(length);
int ln = Fourier.Log2(length);
// reorder array
Fourier.ReorderArray(data);
// successive doubling
int N = 1;
int signIndex = (direction == FourierDirection.Forward) ? 0 : 1;
for (int level = 1; level <= ln; level++)
{
int M = N;
N <<= 1;
double[] uRLookup = _uRLookup[level, signIndex];
double[] uILookup = _uILookup[level, signIndex];
for (int j = 0; j < M; j++)
{
double uR = uRLookup[j];
double uI = uILookup[j];
for (int even = j; even < length; even += N)
{
int odd = even + M;
double r = data[odd].Re;
double i = data[odd].Im;
double odduR = r * uR - i * uI;
double odduI = r * uI + i * uR;
r = data[even].Re;
i = data[even].Im;
data[even].Re = r + odduR;
data[even].Im = i + odduI;
data[odd].Re = r - odduR;
data[odd].Im = i - odduI;
}
}
}
}