// given double[] x as the input signal

    n = x.length;  // assume n is a power of 2
    nu = (int)(Math.log(n)/Math.log(2));
    int n2 = n/2;
    int nu1 = nu - 1;
    double[] xre = new double[n];
    double[] xim = new double[n];
    double[] mag = new double[n2];
    double tr, ti, p, arg, c, s;
    for (int i = 0; i < n; i++) {
        xre[i] = x[i];
        xim[i] = 0.0;
    }
    int k = 0;

    for (int l = 1; l <= nu; l++) {
        while (k < n) {
            for (int i = 1; i <= n2; i++) {
                p = bitrev (k >> nu1);
                arg = 2 * (double) Math.PI * p / n;
                c = (double) Math.cos (arg);
                s = (double) Math.sin (arg);
                tr = xre[k+n2]*c + xim[k+n2]*s;
                ti = xim[k+n2]*c - xre[k+n2]*s;
                xre[k+n2] = xre[k] - tr;
                xim[k+n2] = xim[k] - ti;
                xre[k] += tr;
                xim[k] += ti;
                k++;
            }
            k += n2;
        }
        k = 0;
        nu1--;
        n2 = n2/2;
    }
    k = 0;
    int r;
    while (k < n) {
        r = bitrev (k);
        if (r > k) {
            tr = xre[k];
            ti = xim[k];
            xre[k] = xre[r];
            xim[k] = xim[r];
            xre[r] = tr;
            xim[r] = ti;
        }
        k++;
    }
    // The result
    // -> real part stored in xre
    // -> imaginary part stored in xim