使用 MATLAB 中的系数在 C++ 中设计 FIR 滤波器，滤波器没有给出正确的结果

Question

我正在开发 OpenCV 的一个项目，因为我是这个领域的新手，我面临着一些问题。我必须设计一个 128 阶 FIR 带通滤波器，为此我使用了通过 MATLAB 计算的系数。我在网上找到了以下代码。

const int taps = 129;
double buffer[129] = {0.0};
int offset = 0;
double input;

double coefficients[] =

{
    0.0005,0.0004,0.0002,0.0000,-0.0001,-0.0000,0.0001,0.0004,0.0007,0.0011,
    0.0015,0.0017,0.0018,0.0016,0.0011,0.0006,0.0001,-0.0003,-0.0002,0.0003,
    0.0011,0.0022,0.0032,0.0038,0.0038,0.0031,0.0015,-0.0005,-0.0026,-0.0044,
    -0.0053,-0.0050,-0.0037,-0.0016,0.0007,0.0023,0.0027,0.0012,-0.0022,-0.0072,
    -0.0127,-0.0178,-0.0212,-0.0220,-0.0199,-0.0153,-0.0093,-0.0036,-0.0001,-0.0003,
    -0.0053,-0.0147,-0.0274,-0.0408,-0.0519,-0.0573,-0.0545,-0.0419,-0.0197,0.0102,
    0.0442,0.0779,0.1064,0.1254,0.1321,0.1254,0.1064,0.0779,0.0442,0.0102,-0.0197,
    -0.0419,-0.0545,-0.0573,-0.0519,-0.0408,-0.0274,-0.0147,-0.0053,-0.0003,-0.0001,-0.0036,
    -0.0093,-0.0153,-0.0199,-0.0220,-0.0212,-0.0178,-0.0127,-0.0072,-0.0022,0.0012,0.0027,
    0.0023,0.0007,-0.0016,-0.0037,-0.0050,-0.0053,-0.0044,-0.0026,-0.0005,0.0015,0.0031,
    0.0038,0.0038,0.0032,0.0022,0.0011,0.0003,-0.0002,-0.0003,0.0001,0.0006,0.0011,
    0.0016,0.0018,0.0017,0.0015,0.0011,0.0007, 0.0004,0.0001,-0.0000,-0.0001,0.0000,
    0.0002,0.0004,0.0005
};


double filter( double input)

{
    double output = 0;


    for(int i= taps-1; i>0 ; i-- )
    {
       buffer[i] = buffer[i-1];
    }

       buffer[0] = input;


    for(int j = 0; j<taps; j++ )
    {

        output += (coefficients[j]*buffer[j]);

    }
    return output; 
}

我尝试使用下面代码 sn-p 中描述的过滤器。 filtersTrajectory 是向量的向量，我想在其中存储过滤后的值。 YCoordinates 是包含要过滤的数据的向量的向量。 YCoordinates的尺寸是[1000x266]

// Calling FIR filter function filter
// filtering all 266 values across 1000 frames.

const int numFrames = 1000;

//featuresPrevious.size() = 266 (predefined fixed value)

vector<vector<double>> filteredTrajectory;
filteredTrajectory.resize(numFrames-1);

   for (int i = 0; i<numFrames-1; i++)

    {

       filteredTrajectory[i].resize(featuresPrevious.size());

       for (int j = 0; j<featuresPrevious.size(); j++)

        {

            filteredTrajectory[i][j] = filter (Ycoordinates[i][j]); 

     }

    }

当我运行此代码时，过滤后的值与 MATLAB 的值不匹配。但是，如果我在所有 1000 帧中只过滤一个值，我会得到与 MATLAB 匹配的结果（参见下面的代码）。

// Filtering value at index Ycoordinates[i][0] across all frames 

filteredTrajectory.resize(numFrames-1);

   for (int i = 0; i<numFrames-1; i++)

    {

     filteredTrajectory[i].resize(1);

     filteredTrajectory[i][0] = filter (Ycoordinates[i][0]);

} 

代码中可能存在哪些缺陷，在过滤循环内的所有轨迹时提供错误结果，但在单独过滤时匹配结果。

Answer 1

Matlab 的filter 是一维滤波器。当提供一个二维矩阵的输入时，它会独立过滤每一列（如果 dim 参数未设置或设置为 1，则为默认值；将 dim 设置为 2 将执行相同的操作，但在每一行上），本质上是在每个处理的列（或行）之间重置 FIR 状态。

因此，为了获得正确的结果，您还必须通过将缓冲区重置为零来重置您存储在buffer 中的每组要过滤的值之间的过滤器状态：

void reset_buffer()
{
  for(int i=0; i<taps ; i++ )
  {
    buffer[i] = 0.0;
  }
}

此外，过滤器必须按顺序查看属于同一集合的每个值（即不要将值交错到过滤函数），因此循环的顺序很重要。根据您是要沿数据的列维度还是行维度进行过滤，您可以使用以下任一函数：

// Filter along columns, similar to Matlab's filter(coefficients, 1, data, [], 1)
void filterDim1()
{
  for (int i = 0; i<numFrames-1; i++)
  {
    filteredTrajectory[i].resize(featuresPrevious.size());
  }
  for (int j = 0; j<featuresPrevious.size(); j++)
  {
    for (int i = 0; i<numFrames-1; i++)
    {
      filteredTrajectory[i][j] = filter (Ycoordinates[i][j]); 
    }
    reset_buffer();
  }
}
// Filter along rows, similar to Matlab's filter(coefficients, 1, data, [], 2)
void filterDim2()
{
  for (int i = 0; i<numFrames-1; i++)
  {
    filteredTrajectory[i].resize(featuresPrevious.size());
    for (int j = 0; j<featuresPrevious.size(); j++)
    {
      filteredTrajectory[i][j] = filter (Ycoordinates[i][j]); 
    }
    reset_buffer();
  }
}