webrtc傅里叶变换实现

1.实傅里叶变换

说明

    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            rdft(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            rdft(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (float *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            rdft(n, 1, a, ip, w);
        is
            rdft(n, -1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .

参数说明:

n:数组长度

isgn:1：傅里叶变换 -1：反傅里叶变换

a:傅里叶变换结果生成与传输(isgn决定)

ip:位反转空间

w:cos/sin 空间

ip[0] = 0时进行初始化

void WebRtc_rdft(int n, int isgn, float *a, int *ip, float *w)
{
    int nw, nc;
    float 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 (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, ip + 2, 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] = 0.5f * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4) {
            rftbsub(n, a, nc, w + nw);
            bitrv2(n, ip + 2, a);
            cftbsub(n, a, w);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
    }
}

//计算cos和sin对应值的结果。
static void makewt(int nw, int *ip, float *w)
{
    int j, nwh;
    float delta, x, y;

    ip[0] = nw;
    ip[1] = 1;
    if (nw > 2) {
        nwh = nw >> 1;// nw/2
        delta = (float)atan(1.0f) / nwh; //
        w[0] = 1;//2j cos(0)
        w[1] = 0;//2j+1 sin(0)
        w[nwh] = (float)cos(delta * nwh);
        w[nwh + 1] = w[nwh];
        //对称性赋值
        if (nwh > 2) {
            for (j = 2; j < nwh; j += 2) {
                x = (float)cos(delta * j);
                y = (float)sin(delta * j);
                w[j] = x;
                w[j + 1] = y;
                w[nw - j] = y;
                w[nw - j + 1] = x;
            }
            bitrv2(nw, ip + 2, w);
        }
    }
}

static void bitrv2(int n, int *ip, float *a)
{
    int j, j1, k, k1, l, m, m2;
    float xr, xi, yr, yi;

    ip[0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
            ip[m + j] = ip[j] + 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];
                k1 = 2 * k + ip[j];
                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];
            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];
                k1 = 2 * k + ip[j];
                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;
            }
        }
    }
}