private static void SyncLookupTableLength(int length)
{
Debug.Assert(length < 1024 * 10);
Debug.Assert(length >= 0);
if (length > _lookupTabletLength)
{
int level = (int)Math.Ceiling(Math.Log(length, 2));
Fourier.InitializeReverseBits(level);
Fourier.InitializeComplexRotations(level);
//_cFFTData = new Complex[ Math2.CeilingBase( length, 2 ) ];
//_cFFTDataF = new ComplexF[ Math2.CeilingBase( length, 2 ) ];
_lookupTabletLength = length;
}
}
/// <summary>
/// Compute a 2D fast fourier transform on a data set of complex numbers (represented as pairs of floats)
/// </summary>
/// <param name="data"></param>
/// <param name="xLength"></param>
/// <param name="yLength"></param>
/// <param name="direction"></param>
public static void FFT2(float[] data, int xLength, int yLength, FourierDirection direction)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
if (data.Length < xLength * yLength * 2)
{
throw new ArgumentOutOfRangeException("data.Length", data.Length, "must be at least as large as 'xLength * yLength * 2' 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)
{
Fourier.Swap(ref data[i << 1], ref data[swap << 1]);
Fourier.Swap(ref data[i << 1 + 1], ref data[swap << 1 + 1]);
}
}
}
static private int[] GetReversedBits(int numberOfBits)
{
Debug.Assert(numberOfBits >= cMinBits);
Debug.Assert(numberOfBits <= cMaxBits);
if (_reversedBits[numberOfBits - 1] == null)
{
int maxBits = Fourier.Pow2(numberOfBits);
int[] reversedBits = new int[maxBits];
for (int i = 0; i < maxBits; i++)
{
int oldBits = i;
int newBits = 0;
for (int j = 0; j < numberOfBits; j++)
{
newBits = (newBits << 1) | (oldBits & 1);
oldBits = (oldBits >> 1);
}
reversedBits[i] = newBits;
}
_reversedBits[numberOfBits - 1] = reversedBits;
}
return(_reversedBits[numberOfBits - 1]);
}
/// <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);
}
}