buttord.m

matlabDigitalSigalProcess内有文件若干

function [order,wn] = buttord(wp,ws,rp,rs,opt)
%BUTTORD Butterworth filter order selection.
%   [N, Wn] = BUTTORD(Wp, Ws, Rp, Rs) returns the order N of the lowest 
%   order digital Butterworth filter that loses no more than Rp dB in 
%   the passband and has at least Rs dB of attenuation in the stopband.  
%   Wp and Ws are the passband and stopband edge frequencies, normalized 
%   from 0 to 1 (where 1 corresponds to pi radians). For example,
%       Lowpass:    Wp = .1,      Ws = .2
%       Highpass:   Wp = .2,      Ws = .1
%       Bandpass:   Wp = [.1 .8], Ws = [.2 .7]
%       Bandstop:   Wp = [.2 .7], Ws = [.1 .8]
%   BUTTORD also returns Wn, the Butterworth natural frequency (or, 
%   the "3 dB frequency") to use with BUTTER to achieve the specifications. 
%
%   [N, Wn] = BUTTORD(Wp, Ws, Rp, Rs, 's') does the computation for an 
%   analog filter, in which case Wp and Ws are in radians/second.
%
%   When Rp is chosen as 3 dB, the Wn in BUTTER is equal to Wp in BUTTORD.  
%
%   See also BUTTER, CHEB1ORD, CHEB2ORD, ELLIPORD.

%   Author(s): L. Shure, 6-9-88
%              T. Krauss, 11-13-92, revised
%   Copyright (c) 1988-98 by The MathWorks, Inc.
%   $Revision: 1.11 $  $Date: 1997/11/26 20:13:21 $

%   Reference(s):
%     [1] Rabiner and Gold, p 241.

if nargin == 4
	opt = 'z';
elseif nargin == 5
	if ~strcmp(opt,'z') & ~strcmp(opt,'s')
		error('Invalid option for final argument.');
	end
end
np1 = length(wp);
ns1 = length(ws);
if (np1 ~= ns1)
	error('The frequency vectors must both be the same length.')
end
ftype = 2*(np1 - 1);
if wp(1) < ws(1)
	ftype = ftype + 1;	% low (1) or reject (3)
else
	ftype = ftype + 2;	% high (2) or pass (4)
end

% first, prewarp frequencies from digital (unit circle) to analog (imag. axis):
if strcmp(opt,'z')	% digital
	WP=tan(pi*wp/2);
	WS=tan(pi*ws/2);
else  % don't have to if analog already
	WP=wp;
	WS=ws;
end
%note - on old systems that are NOT case sensitive, this will still work OK

% next, transform to low pass prototype with passband edge of 1 and stopband
% edges determined by the following: (see Rabiner and Gold, p.258)
if ftype == 1	% low
	WA=WS/WP;
elseif ftype == 2	% high
	WA=WP/WS;
elseif ftype == 3	% stop
	fo = foptions;
	wp1 = fmin('bscost',WP(1),WS(1)-1e-12,fo,1,WP,WS,rs,rp,'butter');
	WP(1) = wp1;
	wp2 = fmin('bscost',WS(2)+1e-12,WP(2),fo,2,WP,WS,rs,rp,'butter');
	WP(2) = wp2;
	WA=(WS*(WP(1)-WP(2)))./(WS.^2 - WP(1)*WP(2));
elseif ftype == 4	% pass
	WA=(WS.^2 - WP(1)*WP(2))./(WS*(WP(1)-WP(2)));
end


% find the minimum order b'worth filter to meet the more demanding spec:
WA=min(abs(WA));
order = ceil( log10( (10 .^ (0.1*abs(rs)) - 1)./ ...
	(10 .^ (0.1*abs(rp)) - 1) ) / (2*log10(WA)) );

% next find the butterworth natural frequency W0 (or, the "3dB frequency")
% to give exactly rs dB at WA.  W0 will be between 1 and WA:
W0 = WA / ( (10^(.1*abs(rs)) - 1)^(1/(2*order)) );

% now convert this frequency back from lowpass prototype 
% to the original analog filter:
if ftype == 1	% low
	WN=W0*WP;
elseif ftype == 2	% high
	WN=WP/W0;
elseif ftype == 3	% stop
	WN(1) = ( (WP(2)-WP(1)) + sqrt((WP(2)-WP(1))^2 + ...
		4*W0.^2*WP(1)*WP(2)))./(2*W0);
	WN(2) = ( (WP(2)-WP(1)) - sqrt((WP(2)-WP(1))^2 + ...
		4*W0.^2*WP(1)*WP(2)))./(2*W0);
	WN=sort(abs(WN)); 
elseif ftype == 4	% pass
	W0=[-W0 W0];  % need both left and right 3dB frequencies
	WN= -W0*(WP(2)-WP(1))/2 + sqrt( W0.^2/4*(WP(2)-WP(1))^2 + WP(1)*WP(2) );
	WN=sort(abs(WN)); 
end

% finally, transform frequencies from analog to digital if necessary:
if strcmp(opt,'z')	% digital
	wn=(2/pi)*atan(WN);  % bilinear transform
else
	wn=WN;
end