fftw_complex *genenerate_fft_noise(uint width, uint height, double power, double lower, double upper) {
    fftw_plan plan;
    uint size = width * height;
    fftw_complex *in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex) * size);
    fftw_complex *out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex) * size);
    fftw_complex *in_end = in + size;
    fftw_complex *out_end = out + size;
    fftw_complex *p;

    for (p = in; p < in_end; p++) {
        double a = 2. * PI * Random() / UINT32_MAX;
        (*p)[0] = std::cos(a);
        (*p)[1] = std::sin(a);
    }

    plan = fftw_plan_dft_2d(MapSizeY(), MapSizeX(), in, out, FFTW_FORWARD, FFTW_ESTIMATE);
    fftw_execute(plan);
    fftw_destroy_plan(plan);

    p = out;
    for (size_t y = 0; y < height; y++) {
        auto fy = fftfreq(y, height);
        for (size_t x = 0; x < width; x++, p++) {
            auto f = std::hypot(fy, fftfreq(x, width));
            auto e = (f > lower ? std::pow(f, power) : 0.);
            (*p)[0] *= e;
            (*p)[1] *= e;
        }
    }

    plan = fftw_plan_dft_2d(height, width, out, in, FFTW_BACKWARD, FFTW_ESTIMATE);
    fftw_execute(plan);
    fftw_destroy_plan(plan);

    fftw_free(out);

    normalize(in, in_end);

    return in;
}