/// <summary>
/// 高速フーリエ変換を行います
/// </summary>
/// <param name="sampleN"></param>
/// <param name="srcArr">データバッファ、データの並び替えは不要</param>
/// <param name="dstArr">スペクトラムの配列</param>
private static void fft2(int sampleN, Complex[] srcArr, ref Complex[] dstArr, int intWidth = 24, int decWidth = 8)
{
var srcReArr = srcArr.Select(x => new SignedFixedPoint(intWidth, decWidth)
{
DoubleValue = x.Real
}).ToArray();
var ps = new SignedFixedPoint[sampleN];
fftImpl2(sampleN, intWidth, decWidth, srcReArr, ref ps);
for (int i = 0; i < sampleN; ++i)
{
dstArr[i] = new Complex(ps[i].DoubleValue, 0);
}
}
/// <summary>
/// 組み込み向けのFFT実装
/// </summary>
/// <param name="sampleN"></param>
/// <param name="intWidth"></param>
/// <param name="decWidth"></param>
/// <param name="srcReArr"></param>
/// <param name="powerSpectrum"></param>
private static void fftImpl2(int sampleN, int intWidth, int decWidth, SignedFixedPoint[] srcReArr, ref SignedFixedPoint[] powerSpectrum)
{
//元データをビット反転してコピー
var bitWidth = (int)Math.Log(sampleN, 2);
var addressingArr = generateBitReverseArr(bitWidth).ToArray();//アドレッシングテーブル
var dstReArr = new SignedFixedPoint[sampleN];
var dstImArr = new SignedFixedPoint[sampleN];
foreach (var pair in addressingArr.Select((y, x) => new { SrcIndex = x, DstIndex = y }))
{
dstReArr[pair.DstIndex] = srcReArr[pair.SrcIndex];
dstImArr[pair.DstIndex] = new SignedFixedPoint(intWidth, decWidth)
{
RawData = 0x0
};
}
//バタフライ演算回数
int stageN = (int)Math.Log(sampleN, 2);//定数
//回転子の事前計算
var wMax = sampleN / 2;
var wTable = Enumerable.Range(0, wMax).Select(n => Complex.Exp(-Complex.ImaginaryOne * 2 * Math.PI * n / sampleN)).ToArray();
var wReTable = wTable.Select(x => x.Real).Select(x => new SignedFixedPoint(intWidth, decWidth)
{
DoubleValue = x
}).ToArray();
var wImTable = wTable.Select(x => x.Imaginary).Select(x => new SignedFixedPoint(intWidth, decWidth)
{
DoubleValue = x
}).ToArray();
/* バタフライ演算をする */
for (int stage = 0; stage < stageN; ++stage)
{
//0 ~ sampleN / 2まで2個ずつ処理する
for (int i = 0; i < sampleN / 2; ++i)
{
//対象データのインデックス+サブインデックス(2次元配列等価)
int index1 = (i >> stage) << 1;
int index2 = index1 + 1;
int subIndex = i & ~(0xffff << stage);
//実データへのアドレスは {index,subIndex}
int addr1 = (index1 << stage) + subIndex; //元の配列の位置
int addr2 = (index2 << stage) + subIndex; //元の配列の位置
//回転子決定
int wIndex = (((subIndex) & ~(0xffff << stage)) << (stageN - stage - 1));
//Debug.WriteLine($"i:{i}\twIndex:{wIndex}\tdata1[{index1}, {subIndex}](addr:{addr1}) \t data2[{index2}, {subIndex}](addr:{addr2})");
//計算
var srcDataRe1 = dstReArr[addr1];
var srcDataIm1 = dstImArr[addr1];
var srcDataRe2 = dstReArr[addr2];
var srcDataIm2 = dstImArr[addr2];
//w * srcData2
var wRe = wReTable[wIndex];
var wIm = wImTable[wIndex];
var mulRe1Re2 = wRe * srcDataRe2;
var mulIm1Im2 = wIm * srcDataIm2;
var mulRe1Im2 = wRe * srcDataIm2;
var mulRe2Im1 = wIm * srcDataRe2;
var mulRe = mulRe1Re2 - mulIm1Im2;
var mulIm = mulRe1Im2 + mulRe2Im1;
//srcData1 + w * srcData2, srcData1 - w * srcData2
var dstDataRe1 = srcDataRe1 + mulRe;
var dstDataIm1 = srcDataIm1 + mulIm;
var dstDataRe2 = srcDataRe1 - mulRe;
var dstDataIm2 = srcDataIm1 - mulIm;
dstReArr[addr1] = dstDataRe1;
dstImArr[addr1] = dstDataIm1;
dstReArr[addr2] = dstDataRe2;
dstImArr[addr2] = dstDataIm2;
}
}
/* 計算結果をパワースペクトルに直す */
for (int i = 0; i < sampleN; ++i)
{
//最終的な値を符号無しにすれば終わり
powerSpectrum[i] = dstReArr[i].IsSigned ? dstReArr[i].TwoComplementary : dstReArr[i];
}
}
