public static Complex[] RealFastFourierTransform(double[] src, double amplitude = 1.0)
{
int n4 = 1 << (Mt.Log2Int(src.Length) - 2);
int n = n4 * 4, n2 = n4 * 2, n3 = n4 * 3;
int n2mask = n2 - 1;
Complex[] Data = new Complex[n2 + 1];
for (int i = n2; --i >= 0;)
{
Data[i] = new Complex(src[i * 2], src[i * 2 + 1]);
}
Complex[] Dst = FastFourierTransform_(Data, true);
TriangularTable Triangle = TriangularTable.Get(n);
for (int i = n4; i >= 0; --i)
{
int j = n2 - i;
Complex g1 = Dst[i];
Complex g2 = Complex.Conjugate(Dst[j & n2mask]);
Complex h1 = (g1 + g2);
Complex h2 = (g1 - g2) * Triangle.Complex(n3 - i);
Data[i] = (h1 + h2);
Data[j] = Complex.Conjugate(h1 - h2);
}
LetMul(Data, amplitude / 2);
return(Data);
}
public static TriangularTable Get(int size)
{
for (int i = Stocks.Count; --i >= 0;)
{
var s = Stocks[i];
if (s.size == size)
{
if (i < Stocks.Count - 1)
{
Stocks.RemoveAt(i);
Stocks.Add(s);
}
return(s);
}
}
{
var s = new TriangularTable(size);
if (Stocks.Count >= 8)
{
Stocks.RemoveAt(0);
}
Stocks.Add(s);
return(s);
}
}
static Complex[] FastFourierTransform_(Complex[] src, bool sw)
{
int l = Mt.Log2Int(src.Length);
int n = 1 << l;
Complex[] Data = new Complex[n];
for (int j = -(n >> 1), i = 0; i < n; i++)
{
int k = n;
while ((k >>= 1) <= j)
{
j -= k;
}
j += k;
Data[i] = src[j];
}
int sign = sw ? -1 : 1;
TriangularTable Triangle = TriangularTable.Get(n);
for (int m = 0; m < l; m++)
{
int step = 1 << m;
int rotw = sign * (1 << (l - 1 - m));
for (int k = 0; k < step; k++)
{
Complex u = Triangle.Complex(rotw * k); // (2 * Math.PI / n) * rotw * k
for (int i = k; i < n; i += step * 2)
{
Complex t = Data[i + step] * u;
Data[i + step] = Data[i] - t;
Data[i] += t;
}
}
}
return(Data);
}
public static double[] RealFastFourierTransform(Complex[] src, double amplitude = 1.0)
{
int n4 = 1 << (Mt.Log2Int(src.Length) - 1);
int n = n4 * 4, n2 = n4 * 2, n3 = n4 * 3;
int n2mask = n2 - 1;
Complex[] Data = new Complex[n2];
TriangularTable Triangle = TriangularTable.Get(n);
for (int i = n4; i >= 0; --i)
{
int j = n2 - i;
Complex g1 = src[i];
Complex g2 = Complex.Conjugate(src[j]);
Complex h1 = (g1 + g2);
Complex h2 = (g1 - g2) * Triangle.Complex(n4 + i);
Data[i] = (h1 + h2);
Data[j & n2mask] = Complex.Conjugate(h1 - h2);
}
Data = FastFourierTransform_(Data, false);
LetMul(Data, amplitude / n);
double[] Dst = New.Array(n, i => (i & 1) == 0 ? Data[i / 2].Real : Data[i / 2].Imaginary);
return(Dst);
}
