BUTTERWORTH - Functions to design and apply Butterworth filters:

bfdesign	design a Butterworth filter
bfhighpass	apply a high-pass Butterworth filter 
bflowpass	apply a low-pass Butterworth filter 

Function Prototypes:
void bfhighpass (int npoles, float f3db, int n, float p[], float q[]);
void bflowpass (int npoles, float f3db, int n, float p[], float q[]);
void bfdesign (float fpass, float apass, float fstop, float astop,
	int *npoles, float *f3db);

bfdesign:
Input:
fpass		frequency in pass band at which amplitude is >= apass
apass		amplitude in pass band corresponding to frequency fpass
fstop 		frequency in stop band at which amplitude is <= astop
astop		amplitude in stop band corresponding to frequency fstop

Output:
npoles		number of poles
f3db		frequency at which amplitude is sqrt(0.5) (-3 db)

bfhighpass and bflowpass:
Input:
npoles		number of poles (and zeros); npoles>=0 is required
f3db		3 db frequency; nyquist = 0.5; 0.0<=f3db<=0.5 is required
n		length of p and q
p		array[n] to be filtered

Output:
q		filtered array[n] (may be equivalent to p)

Notes:
(1) Nyquist frequency equals 0.5

(2) The following conditions must be true:
	(0.0<fpass && fpass<0.5) &&
	(0.0<fstop && fstop<0.5) &&
	(fpass!=fstop) &&
	(0.0<astop && astop<apass && apass<1.0)

(3) if (fpass<fstop)

bfdesign:
Butterworth filter:  compute number of poles and -3 db frequency
for a low-pass or high-pass filter, given a frequency response
constrained at two frequencies.

Author:  Dave Hale, Colorado School of Mines, 06/02/89