//======================================================================================
/// <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="direction"></param>
public static void FFT(float[] data, FourierDirection direction)
{
int length = data.Length;
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;
}
}
}
}
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 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 fast Fourier transform of a dataset of complex numbers.
/// </summary>
/// <param name="data"></param>
/// <param name="direction"></param>
public static void FFT(Complex[] data, FourierDirection direction)
{
int length = data.Length;
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;
}
}
}
}
