This is the mkfilter code from
https://github.com/university-of-york/cs-www-users-fisher slightly
hacked so it will compile with the more pernickety up to date Gnu C++
compiler and produce .png plot files.
mkfilter -Bu -Lp -o 4 -a 0.2
Generate a 4-pole Butterworth lowpass filter with corner frequency 0.2 fs; display pole & zero positions and filter recurrence relation
Command line: ./mkfilter -Bu -Lp -o 4 -a 0.2
raw alpha1 = 0.2000000000
raw alpha2 = 0.2000000000
warped alpha1 = 0.2312656694
warped alpha2 = 0.2312656694
gain at dc : mag = 2.146710182e+01 phase = 0.0000000000 pi
gain at centre: mag = 1.517953327e+01 phase = -1.0000000000 pi
gain at hf : mag = 0.000000000e+00
S-plane zeros:
S-plane poles:
-0.5560715768 + j 1.3424755422
-1.3424755422 + j 0.5560715768
-1.3424755422 + j -0.5560715768
-0.5560715768 + j -1.3424755422
Z-plane zeros:
-1.0000000000 + j 0.0000000000 4 times
Z-plane poles:
0.2265597603 + j 0.6442020225
0.1644878387 + j 0.1937302399
0.1644878387 + j -0.1937302399
0.2265597603 + j -0.6442020225
Recurrence relation:
y[n] = ( 1 * x[n- 4])
+ ( 4 * x[n- 3])
+ ( 6 * x[n- 2])
+ ( 4 * x[n- 1])
+ ( 1 * x[n- 0])
+ ( -0.0301188750 * y[n- 4])
+ ( 0.1826756978 * y[n- 3])
+ ( -0.6799785269 * y[n- 2])
+ ( 0.7820951980 * y[n- 1])
mkfilter -Bu -Lp -o 4 -a 0.2 -l | gencode
Generate C code for the above filter
/* Digital filter designed by mkfilter/mkshape/gencode A.J. Fisher
Command line: ./mkfilter -Bu -Lp -o 4 -a 0.2 -l */
#define NZEROS 4
#define NPOLES 4
#define GAIN 2.146710182e+01
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]
+ ( -0.0301188750 * yv[0]) + ( 0.1826756978 * yv[1])
+ ( -0.6799785269 * yv[2]) + ( 0.7820951980 * yv[3]);
`next output value' = yv[4];
}
}mkfilter -Bu -Lp -o 4 -a 0.2 -l | genplot graph.png
Generate phase & magnitude graphs for the above filter
mkfilter -Re 1000 -Bp -a 0.3
Generate a bandpass resonator with Q = 1000 and centre frequency 0.3 fs; display pole & zero positions and filter recurrence relation
See doc.pdf for original documentation.