public WWRadix2FftF(int numPoints)
{
if (!Functions.IsPowerOfTwo(numPoints) || numPoints < 2)
{
throw new ArgumentException("numPoints must be power of two integer and larger than 2");
}
mNumPoints = numPoints;
mWn = new WWComplexF[mNumPoints];
for (int i = 0; i < mNumPoints; ++i)
{
double angle = -2.0 * Math.PI * i / mNumPoints;
mWn[i] = new WWComplexF((float)Math.Cos(angle), (float)Math.Sin(angle));
}
// mNumStage == log_2(mNumPoints)
int t = mNumPoints;
for (int i = 0; 0 < t; ++i)
{
t >>= 1;
mNumStage = i;
}
mBitReversalTable = new uint[mNumPoints];
for (uint i = 0; i < mNumPoints; ++i)
{
mBitReversalTable[i] = BitReversal(mNumStage, i);
}
}
public static WWComplexF Reciprocal(WWComplexF uni)
{
float sq = uni.real * uni.real + uni.imaginary * uni.imaginary;
float real = uni.real / sq;
float imaginary = -uni.imaginary / sq;
return(new WWComplexF(real, imaginary));
}
/// <summary>
/// 複素数の配列をWWComplexComparerでソートする。
/// </summary>
public static WWComplexF[] SortArray(WWComplexF[] inp)
{
var outp = new WWComplexF[inp.Length];
Array.Copy(inp, outp, inp.Length);
Array.Sort(outp, new WWComplexComparer());
return(outp);
}
/// <summary>
/// すべての要素値が0の複素数配列をnewして戻す。
/// </summary>
/// <param name="count">配列の要素数。</param>
public static WWComplexF[] ZeroArray(int count)
{
var r = new WWComplexF[count];
for (int i = 0; i < r.Length; ++i)
{
r[i] = Zero();
}
return(r);
}
public static WWComplexF[] FromRealArray(double[] r)
{
var c = new WWComplexF[r.Length];
for (int i = 0; i < c.Length; ++i)
{
c[i] = new WWComplexF((float)r[i], 0);
}
return(c);
}
/// <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);
}
}
public static WWComplexF[] Mul(WWComplexF[] a, WWComplexF[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("input array length mismatch");
}
var c = new WWComplexF[a.Length];
for (int i = 0; i < a.Length; ++i)
{
c[i] = WWComplexF.Mul(a[i], b[i]);
}
return(c);
}
/// <summary>
/// create copy and copy := L * R, returns copy.
/// </summary>
public static WWComplexF Mul(WWComplexF lhs, WWComplexF rhs)
{
#if false
// straightforward but slow
float tR = real * rhs.real - imaginary * rhs.imaginary;
float tI = real * rhs.imaginary + imaginary * rhs.real;
real = tR;
imaginary = tI;
#else
// more efficient way
float k1 = lhs.real * (rhs.real + rhs.imaginary);
float k2 = rhs.imaginary * (lhs.real + lhs.imaginary);
float k3 = rhs.real * (lhs.imaginary - lhs.real);
float real = k1 - k2;
float imaginary = k1 + k3;
#endif
return(new WWComplexF(real, imaginary));
}
/// <summary>
/// 逆FFTします。結果をcompensation倍します(compensationを指定しないとき1.0f/N倍)
/// </summary>
/// <param name="aFrom">周波数ドメイン値X^m(q) 0≦m≦N</param>
/// <param name="compensation">倍率。指定しないとき1.0f/Nとなる。</param>
/// <returns></returns>
public WWComplexF[] InverseFft(WWComplexF[] aFrom, float?compensation = null)
{
for (int i = 0; i < aFrom.Length; ++i)
{
aFrom[i] = new WWComplexF(aFrom[i].real, -aFrom[i].imaginary);
}
var aTo = ForwardFft(aFrom);
float c = 1.0f / mNumPoints;
if (compensation != null)
{
c = (float)compensation;
}
for (int i = 0; i < aTo.Length; ++i)
{
aTo[i] = new WWComplexF(aTo[i].real * c, -aTo[i].imaginary * c);
}
return(aTo);
}
/// <summary>
/// create copy and copy := complex conjugate of uni, returns copy.
/// </summary>
public static WWComplexF ComplexConjugate(WWComplexF uni)
{
return(new WWComplexF(uni.real, -uni.imaginary));
}
public static WWComplexF Add(WWComplexF a, WWComplexF b, WWComplexF c, WWComplexF d, WWComplexF e)
{
return(new WWComplexF(
a.real + b.real + c.real + d.real + e.real,
a.imaginary + b.imaginary + c.imaginary + d.imaginary + e.imaginary));
}
/// <summary>
/// create copy and copy := L - R, returns copy.
/// </summary>
public static WWComplexF Sub(WWComplexF lhs, WWComplexF rhs)
{
return(new WWComplexF(lhs.real - rhs.real, lhs.imaginary - rhs.imaginary));
}
public static WWComplexF Mul(WWComplexF lhs, float v)
{
return(new WWComplexF(lhs.real * v, lhs.imaginary * v));
}
/// <summary>
/// create copy and copy := L + R, returns copy.
/// </summary>
public static WWComplexF Add(WWComplexF lhs, WWComplexF rhs)
{
return(new WWComplexF(lhs.real + rhs.real, lhs.imaginary + rhs.imaginary));
}
/// <summary>
/// 内容が全く同じときtrue
/// </summary>
public bool EqualValue(WWComplexF rhs)
{
return(real == rhs.real && imaginary == rhs.imaginary);
}
/// <summary>
/// returns reciprocal. this instance is not changed.
/// </summary>
public WWComplexF Reciplocal()
{
return(WWComplexF.Reciprocal(this));
}
public static float Distance(WWComplexF a, WWComplexF b)
{
var s = WWComplexF.Sub(a, b);
return(s.Magnitude());
}
/// <summary>
/// create copy and copy := L / R, returns copy.
/// </summary>
public static WWComplexF Div(WWComplexF lhs, WWComplexF rhs)
{
var recip = Reciprocal(rhs);
return(Mul(lhs, recip));
}
public static WWComplexF Div(WWComplexF lhs, float rhs)
{
var recip = 1.0f / rhs;
return(Mul(lhs, recip));
}
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);
}
}
}
}
/// <summary>
/// create copy and copy := -uni, returns copy.
/// argument value is not changed.
/// </summary>
public static WWComplexF Minus(WWComplexF uni)
{
return(new WWComplexF(-uni.real, -uni.imaginary));
}