TSP_BUTTER Butterworth digital and analog filter design.
[B,A] = TSP_BUTTER(N,Wn) designs an Nth order lowpass digital
Butterworth filter and returns the filter coefficients in length
N+1 vectors B (numerator) and A (denominator). The coefficients
are listed in descending powers of z. The cut-off frequency
Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to
half the sample rate.

If Wn is a two-element vector, Wn = [W1 W2], BUTTER returns an   
order 2N bandpass filter with passband  W1 < W < W2.   
[B,A] = BUTTER(N,Wn,'high') designs a highpass filter.   
[B,A] = BUTTER(N,Wn,'stop') is a bandstop filter if Wn = [W1 W2].   

When used with three left-hand arguments, as in   
[Z,P,K] = BUTTER(...), the zeros and poles are returned in   
length N column vectors Z and P, and the gain in scalar K.   

When used with four left-hand arguments, as in   
[A,B,C,D] = BUTTER(...), state-space matrices are returned.   

BUTTER(N,Wn,'s'), BUTTER(N,Wn,'high','s') and BUTTER(N,Wn,'stop','s')   
design analog Butterworth filters.  In this case, Wn can be bigger   
than 1.0.   

See also BUTTORD, BESSELF, CHEBY1, CHEBY2, ELLIP, FREQZ, FILTER.