/// <summary>
/// 注：compensationが指定しないとき、結果をNで割りません。
/// </summary>
/// <param name="aFrom">時間ドメイン値x[n] 0≦n＜N</param>
/// <param name="compensation">倍率。指定しないとき1.0f倍となる。</param>
/// <returns>周波数ドメイン値X^m(q)</returns>
public WWComplexF[] ForwardFft(WWComplexF[] aFrom, float?compensation = null)
{
if (aFrom == null || aFrom.Length != mNumPoints)
{
throw new ArgumentOutOfRangeException("aFrom");
}
var aTo = new WWComplexF[aFrom.Length];
var aTmp0 = new WWComplexF[mNumPoints];
for (int i = 0; i < aTmp0.Length; ++i)
{
aTmp0[i] = aFrom[mBitReversalTable[i]];
}
var aTmp1 = new WWComplexF[mNumPoints];
for (int i = 0; i < aTmp1.Length; ++i)
{
aTmp1[i] = WWComplexF.Zero();
}
var aTmps = new WWComplexF[2][];
aTmps[0] = aTmp0;
aTmps[1] = aTmp1;
for (int i = 0; i < mNumStage - 1; ++i)
{
FftStageN(i, aTmps[((i & 1) == 1) ? 1 : 0], aTmps[((i & 1) == 0) ? 1 : 0]);
}
FftStageN(mNumStage - 1, aTmps[(((mNumStage - 1) & 1) == 1) ? 1 : 0], aTo);
float c = 1.0f;
if (compensation != null)
{
c = (float)compensation;
}
if (c != 1.0f)
{
var aToC = new WWComplexF[aTo.Length];
for (int i = 0; i < aTo.Length; ++i)
{
aToC[i] = new WWComplexF(aTo[i].real * c, aTo[i].imaginary * c);
}
return(aToC);
}
else
{
return(aTo);
}
}
private void FftStageN(int stageNr, WWComplexF[] x, WWComplexF[] y)
{
/*
* stage0: 2つの入力データにバタフライ演算 (length=8の時) 4回 (nRepeat=4, nSubRepeat=2)
* y[0] = x[0] + w_n^(0*4) * x[1]
* y[1] = x[0] + w_n^(1*4) * x[1]
*
* y[2] = x[2] + w_n^(0*4) * x[3]
* y[3] = x[2] + w_n^(1*4) * x[3]
*
* y[4] = x[4] + w_n^(0*4) * x[5]
* y[5] = x[4] + w_n^(1*4) * x[5]
*
* y[6] = x[6] + w_n^(0*4) * x[7]
* y[7] = x[6] + w_n^(1*4) * x[7]
*/
/*
* stage1: 4つの入力データにバタフライ演算 (length=8の時) 2回 (nRepeat=2, nSubRepeat=4)
* y[0] = x[0] + w_n^(0*2) * x[2]
* y[1] = x[1] + w_n^(1*2) * x[3]
* y[2] = x[0] + w_n^(2*2) * x[2]
* y[3] = x[1] + w_n^(3*2) * x[3]
*
* y[4] = x[4] + w_n^(0*2) * x[6]
* y[5] = x[5] + w_n^(1*2) * x[7]
* y[6] = x[4] + w_n^(2*2) * x[6]
* y[7] = x[5] + w_n^(3*2) * x[7]
*/
/*
* stage2: 8つの入力データにバタフライ演算 (length=8の時) 1回 (nRepeat=1, nSubRepeat=8)
* y[0] = x[0] + w_n^(0*1) * x[4]
* y[1] = x[1] + w_n^(1*1) * x[5]
* y[2] = x[2] + w_n^(2*1) * x[6]
* y[3] = x[3] + w_n^(3*1) * x[7]
* y[4] = x[0] + w_n^(4*1) * x[4]
* y[5] = x[1] + w_n^(5*1) * x[5]
* y[6] = x[2] + w_n^(6*1) * x[6]
* y[7] = x[3] + w_n^(7*1) * x[7]
*/
/*
* stageN:
*/
int nRepeat = Pow2(mNumStage - stageNr - 1);
int nSubRepeat = mNumPoints / nRepeat;
var t = WWComplexF.Zero();
for (int i = 0; i < nRepeat; ++i)
{
int offsBase = i * nSubRepeat;
bool allZero = true;
for (int j = 0; j < nSubRepeat / 2; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
if (Double.Epsilon < x[offs].Magnitude())
{
allZero = false;
break;
}
if (Double.Epsilon < x[offs + nSubRepeat / 2].Magnitude())
{
allZero = false;
break;
}
}
if (allZero)
{
for (int j = 0; j < nSubRepeat; ++j)
{
y[j + offsBase] = WWComplexF.Zero();
}
}
else
{
for (int j = 0; j < nSubRepeat; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
var v1 = x[offs];
var v2 = WWComplexF.Mul(mWn[j * nRepeat], x[offs + nSubRepeat / 2]);
y[j + offsBase] = WWComplexF.Add(v1, v2);
}
}
}
}