// Copyright(C) 1996-2001 Takuya Ooura // C# port by J.D. Purcell // You may use, copy, modify this code for any purpose and without fee. using System; namespace Nikse.SubtitleEdit.Core { public class RealFFT { private readonly int _length; private readonly int[] _ip; private readonly double[] _w; public readonly double ForwardScaleFactor; public readonly double ReverseScaleFactor; public RealFFT(int length) { if (length < 2 || (length & (length - 1)) != 0) { throw new ArgumentException("length", "FFT length must be at least 2 and a power of 2."); } _length = length; _ip = new int[2 + (1 << (Convert.ToInt32(Math.Log(Math.Max(length / 4, 1), 2)) / 2))]; _w = new double[length / 2]; ForwardScaleFactor = length; ReverseScaleFactor = 0.5; } public void ComputeForward(double[] buff) { Compute(buff, false); } public void ComputeReverse(double[] buff) { Compute(buff, true); } private void Compute(double[] buff, bool reverse) { if (buff.Length < _length) { throw new ArgumentException("buff", "Buffer length must be greater than or equal to the FFT length."); } rdft(_length, reverse, buff, _ip, _w); } private static void rdft(int n, bool rev, double[] a, int[] ip, double[] w) { int nw, nc; double xi; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 2)) { nc = n >> 2; makect(nc, ip, w, nw); } if (!rev) { if (n > 4) { bitrv2(n, ip, a); cftfsub(n, a, w); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a, w); } xi = a[0] - a[1]; a[0] += a[1]; a[1] = xi; } else { a[1] = 0.5 * (a[0] - a[1]); a[0] -= a[1]; if (n > 4) { rftbsub(n, a, nc, w, nw); bitrv2(n, ip, a); cftbsub(n, a, w); } else if (n == 4) { cftfsub(n, a, w); } } } /* -------- initializing routines -------- */ private static void makewt(int nw, int[] ip, double[] w) { int j, nwh; double delta, x, y; ip[0] = nw; ip[1] = 1; if (nw > 2) { nwh = nw >> 1; delta = Math.Atan(1.0) / nwh; w[0] = 1; w[1] = 0; w[nwh] = Math.Cos(delta * nwh); w[nwh + 1] = w[nwh]; if (nwh > 2) { for (j = 2; j < nwh; j += 2) { x = Math.Cos(delta * j); y = Math.Sin(delta * j); w[j] = x; w[j + 1] = y; w[nw - j] = y; w[nw - j + 1] = x; } bitrv2(nw, ip, w); } } } private static void makect(int nc, int[] ip, double[] c, int nw) { int j, nch; double delta; ip[1] = nc; if (nc > 1) { nch = nc >> 1; delta = Math.Atan(1.0) / nch; c[nw] = Math.Cos(delta * nch); c[nw + nch] = 0.5 * c[nw]; for (j = 1; j < nch; j++) { c[nw + j] = 0.5 * Math.Cos(delta * j); c[nw + nc - j] = 0.5 * Math.Sin(delta * j); } } } /* -------- child routines -------- */ private static void bitrv2(int n, int[] ip, double[] a) { int j, j1, k, k1, l, m, m2; double xr, xi, yr, yi; ip[2] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[m + j + 2] = ip[j + 2] + l; } m <<= 1; } m2 = 2 * m; if ((m << 3) == l) { for (k = 0; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k + 2]; k1 = 2 * k + ip[j + 2]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 -= m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } j1 = 2 * k + m2 + ip[k + 2]; k1 = j1 + m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } else { for (k = 1; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k + 2]; k1 = 2 * k + ip[j + 2]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } } } private static void cftfsub(int n, double[] a, double[] w) { int j, j1, j2, j3, l; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(n, a, w); l = 8; while ((l << 2) < n) { cftmdl(n, l, a, w); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = a[j + 1] - a[j1 + 1]; a[j] += a[j1]; a[j + 1] += a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } private static void cftbsub(int n, double[] a, double[] w) { int j, j1, j2, j3, l; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(n, a, w); l = 8; while ((l << 2) < n) { cftmdl(n, l, a, w); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = -a[j + 1] - a[j1 + 1]; x1r = a[j] - a[j1]; x1i = -a[j + 1] + a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i - x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i + x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i - x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i + x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = -a[j + 1] + a[j1 + 1]; a[j] += a[j1]; a[j + 1] = -a[j + 1] - a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } private static void cft1st(int n, double[] a, double[] w) { int j, k1, k2; double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[2]; x0i = a[1] + a[3]; x1r = a[0] - a[2]; x1i = a[1] - a[3]; x2r = a[4] + a[6]; x2i = a[5] + a[7]; x3r = a[4] - a[6]; x3i = a[5] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[4] = x0r - x2r; a[5] = x0i - x2i; a[2] = x1r - x3i; a[3] = x1i + x3r; a[6] = x1r + x3i; a[7] = x1i - x3r; wk1r = w[2]; x0r = a[8] + a[10]; x0i = a[9] + a[11]; x1r = a[8] - a[10]; x1i = a[9] - a[11]; x2r = a[12] + a[14]; x2i = a[13] + a[15]; x3r = a[12] - a[14]; x3i = a[13] - a[15]; a[8] = x0r + x2r; a[9] = x0i + x2i; a[12] = x2i - x0i; a[13] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[10] = wk1r * (x0r - x0i); a[11] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[14] = wk1r * (x0i - x0r); a[15] = wk1r * (x0i + x0r); k1 = 0; for (j = 16; j < n; j += 16) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; x0r = a[j] + a[j + 2]; x0i = a[j + 1] + a[j + 3]; x1r = a[j] - a[j + 2]; x1i = a[j + 1] - a[j + 3]; x2r = a[j + 4] + a[j + 6]; x2i = a[j + 5] + a[j + 7]; x3r = a[j + 4] - a[j + 6]; x3i = a[j + 5] - a[j + 7]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 4] = wk2r * x0r - wk2i * x0i; a[j + 5] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 2] = wk1r * x0r - wk1i * x0i; a[j + 3] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 6] = wk3r * x0r - wk3i * x0i; a[j + 7] = wk3r * x0i + wk3i * x0r; wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; x0r = a[j + 8] + a[j + 10]; x0i = a[j + 9] + a[j + 11]; x1r = a[j + 8] - a[j + 10]; x1i = a[j + 9] - a[j + 11]; x2r = a[j + 12] + a[j + 14]; x2i = a[j + 13] + a[j + 15]; x3r = a[j + 12] - a[j + 14]; x3i = a[j + 13] - a[j + 15]; a[j + 8] = x0r + x2r; a[j + 9] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 12] = -wk2i * x0r - wk2r * x0i; a[j + 13] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 10] = wk1r * x0r - wk1i * x0i; a[j + 11] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 14] = wk3r * x0r - wk3i * x0i; a[j + 15] = wk3r * x0i + wk3i * x0r; } } private static void cftmdl(int n, int l, double[] a, double[] w) { int j, j1, j2, j3, k, k1, k2, m, m2; double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; m = l << 2; for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } wk1r = w[2]; for (j = m; j < l + m; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x2i - x0i; a[j2 + 1] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * (x0r - x0i); a[j1 + 1] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[j3] = wk1r * (x0i - x0r); a[j3 + 1] = wk1r * (x0i + x0r); } k1 = 0; m2 = 2 * m; for (k = m2; k < n; k += m2) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; for (j = k; j < l + k; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = wk2r * x0r - wk2i * x0i; a[j2 + 1] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; for (j = k + m; j < l + (k + m); j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = -wk2i * x0r - wk2r * x0i; a[j2 + 1] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } } } private static void rftfsub(int n, double[] a, int nc, double[] c, int nw) { int j, k, kk, ks, m; double wkr, wki, xr, xi, yr, yi; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5 - c[nw + nc - kk]; wki = c[nw + kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr - wki * xi; yi = wkr * xi + wki * xr; a[j] -= yr; a[j + 1] -= yi; a[k] += yr; a[k + 1] -= yi; } } private static void rftbsub(int n, double[] a, int nc, double[] c, int nw) { int j, k, kk, ks, m; double wkr, wki, xr, xi, yr, yi; a[1] = -a[1]; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5 - c[nw + nc - kk]; wki = c[nw + kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr + wki * xi; yi = wkr * xi - wki * xr; a[j] -= yr; a[j + 1] = yi - a[j + 1]; a[k] += yr; a[k + 1] = yi - a[k + 1]; } a[m + 1] = -a[m + 1]; } } }