Filter Design Results

Summary

filtertype	=	Butterworth
passtype	=	Bandpass
ripple	=
order	=	4
samplerate	=	44100
corner1	=	110
corner2	=	2900
adzero	=
logmin	=	-48

Results

Command line: /www/usr/fisher/helpers/mkfilter -Bu -Bp -o 4 -a 2.4943310658e-03 6.5759637188e-02
raw alpha1    =   0.0024943311
raw alpha2    =   0.0657596372
warped alpha1 =   0.0024943821
warped alpha2 =   0.0667114169
gain at dc    :   mag = 0.000000000e+00
gain at centre:   mag = 1.024607115e+03   phase =  -0.3936427349 pi
gain at hf    :   mag = 0.000000000e+00

S-plane zeros:
	  0.0000000000 + j   0.0000000000	4 times

S-plane poles:
	 -0.1487375645 + j   0.3875486640
	 -0.3575061784 + j   0.1612963284
	 -0.3575061784 + j  -0.1612963284
	 -0.1487375645 + j  -0.3875486640
	 -0.0056704282 + j  -0.0147747940
	 -0.0152676916 + j  -0.0068883358
	 -0.0152676916 + j   0.0068883358
	 -0.0056704282 + j   0.0147747940

Z-plane zeros:
	  1.0000000000 + j   0.0000000000	4 times
	 -1.0000000000 + j   0.0000000000	4 times

Z-plane poles:
	  0.8029093188 + j   0.3251747023
	  0.6888028022 + j   0.1155448473
	  0.6888028022 + j  -0.1155448473
	  0.8029093188 + j  -0.3251747023
	  0.9942373850 + j  -0.0146905723
	  0.9848247874 + j  -0.0067842797
	  0.9848247874 + j   0.0067842797
	  0.9942373850 + j   0.0146905723

Recurrence relation:
y[n] = (  1 * x[n- 8])
     + (  0 * x[n- 7])
     + ( -4 * x[n- 6])
     + (  0 * x[n- 5])
     + (  6 * x[n- 4])
     + (  0 * x[n- 3])
     + ( -4 * x[n- 2])
     + (  0 * x[n- 1])
     + (  1 * x[n- 0])

     + ( -0.3510340249 * y[n- 8])
     + (  3.1613912027 * y[n- 7])
     + (-12.5026849109 * y[n- 6])
     + ( 28.3597862198 * y[n- 5])
     + (-40.3532139600 * y[n- 4])
     + ( 36.8786058005 * y[n- 3])
     + (-21.1343989150 * y[n- 2])
     + (  6.9415485867 * y[n- 1])

Ansi ``C'' Code

/* Digital filter designed by mkfilter/mkshape/gencode   A.J. Fisher
   Command line: /www/usr/fisher/helpers/mkfilter -Bu -Bp -o 4 -a 2.4943310658e-03 6.5759637188e-02 -l */

#define NZEROS 8
#define NPOLES 8
#define GAIN   1.024607115e+03

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] = xv[5]; xv[5] = xv[6]; xv[6] = xv[7]; xv[7] = xv[8]; 
        xv[8] = next input value / GAIN;
        yv[0] = yv[1]; yv[1] = yv[2]; yv[2] = yv[3]; yv[3] = yv[4]; yv[4] = yv[5]; yv[5] = yv[6]; yv[6] = yv[7]; yv[7] = yv[8]; 
        yv[8] =   (xv[0] + xv[8]) - 4 * (xv[2] + xv[6]) + 6 * xv[4]
                     + ( -0.3510340249 * yv[0]) + (  3.1613912027 * yv[1])
                     + (-12.5026849110 * yv[2]) + ( 28.3597862200 * yv[3])
                     + (-40.3532139600 * yv[4]) + ( 36.8786058000 * yv[5])
                     + (-21.1343989150 * yv[6]) + (  6.9415485867 * yv[7]);
        next output value = yv[8];
      }
  }

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 22050 Hz)
• y axis (red): magnitude (logarithmic, normalized)
• y axis (blue): phase

For an expanded view, enter frequency limits (as a fraction of the sampling rate) here:

Impulse response

• x axis: time, in samples (i.e. 44100 represents 1 second)
• y axis (red): filter response (linear, normalized)

Step response

• x axis: time, in samples (i.e. 44100 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: