在C语言编程FIR滤波器的实现(FIR filter implementation in C pro

谁能告诉我如何实现用c语言编程的FIR滤波器。

Answer 1:

设计的FIR滤波器不是一个简单的话题，但实施一个已经设计的滤波器（假设你已经拥有了FIR系数）是不是太糟糕。该算法被称为卷积。这里有一个天真的实现...

void convolve (double *p_coeffs, int p_coeffs_n,
               double *p_in, double *p_out, int n)
{
  int i, j, k;
  double tmp;

  for (k = 0; k < n; k++)  //  position in output
  {
    tmp = 0;

    for (i = 0; i < p_coeffs_n; i++)  //  position in coefficients array
    {
      j = k - i;  //  position in input

      if (j >= 0)  //  bounds check for input buffer
      {
        tmp += p_coeffs [k] * p_in [j];
      }
    }

    p_out [i] = tmp;
  }
}

基本上，卷积确实的输入信号的移动加权平均。权重是滤波器系数，其被假定为总和为1.0。如果权重之和为1.0之外的东西，你得到一些放大/衰减以及过滤。

顺便说一句 - 这是可能的这种功能具有系数阵列向后 - 我没有双重检查，它是因为我想这些事情了一会儿。

对于如何计算FIR系数为特定的过滤器，还有背后的数学相当数量的 - 你真的需要数字信号处理一本好书。这一个是免费提供的PDF，但我不知道它有多好。我有Rorabaugh和Orfandis ，都发表在90年代中期，但这些事情没有真正得到过时。

Answer 2:

要合并多个过滤器：

开始与一个单位脉冲（具有在第一位置的1和0其他地方的信号）。应用该第一滤波器。应用第二滤波器。继续，直到应用了所有过滤器。结果示出了组合过滤器如何卷积单位冲激（设置在数组足够没有数据丢失了长），所以在它的值是一个过滤器是其它过滤器的组合物中的系数。

下面是示例代码：

#include <stdio.h>
#include <string.h>


#define NumberOf(a) (sizeof (a) / sizeof *(a))


/*  Convolve Signal with Filter.

    Signal must contain OutputLength + FilterLength - 1 elements.  Conversely,
    if there are N elements in Signal, OutputLength may be at most
    N+1-FilterLength.
*/
static void convolve(
    float *Signal,
    float *Filter, size_t FilterLength,
    float *Output, size_t OutputLength)
{
    for (size_t i = 0; i < OutputLength; ++i)
    {
        double sum = 0;
        for (size_t j = 0; j < FilterLength; ++j)
            sum += Signal[i+j] * Filter[FilterLength - 1 - j];
        Output[i] = sum;
    }
}


int main(void)
{
    //  Define a length for buffers that is long enough for this demonstration.
    #define LongEnough  128


    //  Define some sample filters.
    float Filter0[] = { 1, 2, -1 };
    float Filter1[] = { 1, 5, 7, 5, 1 };

    size_t Filter0Length = NumberOf(Filter0);
    size_t Filter1Length = NumberOf(Filter1);


    //  Define a unit impulse positioned so it captures all of the filters.
    size_t UnitImpulsePosition = Filter0Length - 1 + Filter1Length - 1;
    float UnitImpulse[LongEnough];
    memset(UnitImpulse, 0, sizeof UnitImpulse);
    UnitImpulse[UnitImpulsePosition] = 1;


    //  Calculate a filter that is Filter0 and Filter1 combined.
    float CombinedFilter[LongEnough];

    //  Set N to number of inputs that must be used.
    size_t N = UnitImpulsePosition + 1 + Filter0Length - 1 + Filter1Length - 1;

    //  Subtract to find number of outputs of first convolution, then convolve.
    N -= Filter0Length - 1;
    convolve(UnitImpulse,    Filter0, Filter0Length, CombinedFilter, N);

    //  Subtract to find number of outputs of second convolution, then convolve.
    N -= Filter1Length - 1;
    convolve(CombinedFilter, Filter1, Filter1Length, CombinedFilter, N);

    //  Remember size of resulting filter.
    size_t CombinedFilterLength = N;

    //  Display filter.
    for (size_t i = 0; i < CombinedFilterLength; ++i)
        printf("CombinedFilter[%zu] = %g.\n", i, CombinedFilter[i]);


    //  Define two identical signals.
    float Buffer0[LongEnough];
    float Buffer1[LongEnough];
    for (size_t i = 0; i < LongEnough; ++i)
    {
        Buffer0[i] = i;
        Buffer1[i] = i;
    }


    //  Convolve Buffer0 by using the two filters separately.

    //  Start with buffer length.
    N = LongEnough;

    //  Subtract to find number of outputs of first convolution, then convolve.
    N -= Filter0Length - 1;
    convolve(Buffer0, Filter0, Filter0Length, Buffer0, N);

    //  Subtract to find number of outputs of second convolution, then convolve.
    N -= Filter1Length - 1;
    convolve(Buffer0, Filter1, Filter1Length, Buffer0, N);

    //  Remember the length of the result.
    size_t ResultLength = N;


    //  Convolve Buffer1 with the combined filter.
    convolve(Buffer1, CombinedFilter, CombinedFilterLength, Buffer1, ResultLength);


    //  Show the contents of Buffer0 and Buffer1, and their differences.
    for (size_t i = 0; i < ResultLength; ++i)
    {
        printf("Buffer0[%zu] = %g.  Buffer1[%zu] = %g.  Difference = %g.\n",
            i, Buffer0[i], i, Buffer1[i], Buffer0[i] - Buffer1[i]);
    }

    return 0;
}