Question

I have obtained some Z coefficients in MatLAB. Now I need to implement the filter in C.
How do I do this?
The coefficients in Z domain:

num = [0.2557 -0.5115 -0.2557 1.0230 -0.2557 -0.5115 0.2557];

den = [1.0000 -4.0196 6.1894 -4.4532 1.4208 -0.1418 0.0044];

Any help is appreciated.

(I tried googling, but didn’t find anything clear and easy to understand.)

Answer 1

I’m guessing that the main issue is translating from Z domain to time.

Y(z) = H(z)*X(z)

H(z) = B(z)/A(z) = Y(z)/X(z)

B(z)*X(z) = A(z)*Y(z)

Then from the documentation:

B(z) = b(1)*z^-n + … + b(n+1)
A(z) = z^-n + … + a(n+1)

Converting to time domain:

b(1)*x(t) + b(2)*x(t-1) + … + b(n+1)*x(t-n) = a(1)y(t) + … + a(n+1)*y(t-n)

Then ‘solving’ for y(t), given that a(1) is 1:

y(t) = b(1)*x(t) + b(2)*x(t-1) + … + b(n+1)*x(t-n) – a(2)*y(t-1) … – a(n+1)*y(t-n)

where n = 7. So, say you have to arrays in which you store the last 6 values of the input x and the filter output y:

/* Warning Warning Warning: 
   This has not been tested,
   for illustration purposes only */
double filter_data(double x)
{
  static double x_prev[6] = {0};
  static double y_prev[6] = {0};
  /* x is newest input value */
  double y;  /* output to be calculated */
  int ii;

  /* let's just keep it really simple for now, you can get more sophisticated later */
  y = 0.2557*x[0] + -0.5115*x_prev[0] + -0.2557*x_prev[1] + 1.0230*x_prev[2] + 
      -0.2557*x_prev[3] + -0.5115*x_prev[4] + 0.2557*x_prev[5] - -4.0196*y_prev[0] - 
      6.1894*y_prev[1] - -4.4532*y_prev[2] - 1.4208*y_prev[3] - -0.1418*y_prev[4] - 
      0.0044*y_prev[5];

  /* really really wasteful, but simple shift of previous values */
  for(ii=5;ii>0;ii--)
  {
    y_prev[ii] = y_prev[ii-1]
    x_prev[ii] = x_prev[ii-1]
  }
  y_prev[0] = y;
  x_prev[0] = x;
  return y;
}

It’s not great, but I think that ought to get you going. Let me know if something isn’t clear!