Filter Design ResultsFilter Design Results 
Generated by:   http://www-users.cs.york.ac.uk/~fisher/mkfilter 
Summary 
You specified the following parameters: 
        filtertype = Butterworth 
        passtype = Lowpass 
        ripple = 
        order = 4 
        samplerate = 51065 
        corner1 = 1250 
        corner2 = 
        adzero = 
        logmin = 

Results 
Command line: /www/usr/fisher/helpers/mkfilter -Bu -Lp -o 4 -a 2.4478605699e-02 0.0000000000e+00
raw alpha1    =   0.0244786057
raw alpha2    =   0.0244786057
warped alpha1 =   0.0245269747
warped alpha2 =   0.0245269747
gain at dc    :   mag = 3.468956503e+04   phase =   0.0000000000 pi
gain at centre:   mag = 2.452922667e+04   phase =  -1.0000000000 pi
gain at hf    :   mag = 0.000000000e+00

S-plane zeros:

S-plane poles:
	 -0.0589743974 + j   0.1423767901
	 -0.1423767901 + j   0.0589743974
	 -0.1423767901 + j  -0.0589743974
	 -0.0589743974 + j  -0.1423767901

Z-plane zeros:
	 -1.0000000000 + j   0.0000000000	4 times

Z-plane poles:
	  0.9334696354 + j   0.1336982144
	  0.8656714581 + j   0.0513573758
	  0.8656714581 + j  -0.0513573758
	  0.9334696354 + j  -0.1336982144

Recurrence relation:
y[n] = (  1 * x[n- 4])
     + (  4 * x[n- 3])
     + (  6 * x[n- 2])
     + (  4 * x[n- 1])
     + (  1 * x[n- 0])

     + ( -0.6687309839 * y[n- 4])
     + (  2.9435650706 * y[n- 3])
     + ( -4.8735775075 * y[n- 2])
     + (  3.5982821869 * y[n- 1])

Ansi ``C'' Code 
/* Digital filter designed by mkfilter/mkshape/gencode   A.J. Fisher
   Command line: /www/usr/fisher/helpers/mkfilter -Bu -Lp -o 4 -a 2.4478605699e-02 0.0000000000e+00 -l */

#define NZEROS 4
#define NPOLES 4
#define GAIN   3.468956503e+04

static float xv[NZEROS+1], yv[NPOLES+1];

static void filterloop()
  { for (;;)
      { xv[0] = xv[1]; xv[1] = xv[2]; xv[2] = xv[3]; xv[3] = xv[4]; 
        xv[4] = next input value / GAIN;
        yv[0] = yv[1]; yv[1] = yv[2]; yv[2] = yv[3]; yv[3] = yv[4]; 
        yv[4] =   (xv[0] + xv[4]) + 4 * (xv[1] + xv[3]) + 6 * xv[2]
                     + ( -0.6687309839 * yv[0]) + (  2.9435650706 * yv[1])
                     + ( -4.8735775075 * yv[2]) + (  3.5982821869 * yv[3]);
        next output value = yv[4];
      }
  }

Download code and/or coefficients:     
Magnitude (red) and phase (blue) vs. frequency 
  x axis: frequency, as a fraction of the sampling rate (i.e. 0.5 represents the 
  Nyquist frequency, which is 25532.5 Hz) 
  y axis (red): magnitude (linear, normalized) 
  y axis (blue): phase 
 
For an expanded view, enter frequency limits (as a fraction of the sampling 
rate) here: 

   Lower limit:  Upper limit:   
Impulse response 
  x axis: time, in samples (i.e. 51065 represents 1 second) 
  y axis (red): filter response (linear, normalized) 
 
Step response 
  x axis: time, in samples (i.e. 51065 represents 1 second) 
  y axis (red): filter response (linear, normalized) 
 
For a view on a different scale, enter upper time limit (integer number of 
samples) here: 

  Upper limit:   



Tony Fisher fisher@minster.york.ac.uk  