gusucode.com > 信号处理工具箱 - signal源码程序 > signal\signal\signal\firrcos.m
function [b,a]=firrcos(varargin) %FIRRCOS Raised Cosine FIR Filter design. % B=FIRRCOS(N,F0,DF,Fs) returns an order N low pass linear phase FIR % filter with a raised cosine transition band. The filter has cutoff % frequency F0, sampling frequency Fs and transition bandwidth DF % (all in Hz). % % F0 +/- DF/2 must be in the range [0,Fs/2]. % % The coefficients of B are normalized so that the nominal passband % gain is always equal to one. % % FIRRCOS(N,F0,DF) uses a default sampling frequency of Fs = 2. % % B=FIRRCOS(N,F0,R,Fs,'rolloff') interprets the third argument as the % rolloff factor instead of as a transition bandwidth. % % R must be in the range [0,1]. % % B=FIRRCOS(N,F0,DF,Fs,TYPE) or B=FIRRCOS(N,F0,R,Fs,'rolloff',TYPE) % will design a regular FIR raised cosine filter when TYPE is % 'normal' or set to an empty matrix. If TYPE is 'sqrt', B is the % square root FIR raised cosine filter. % % B=FIRRCOS(...,TYPE,DELAY) allows for a variable integer delay to be % specified. When omitted or left empty, DELAY defaults to N/2 or % (N+1)/2 depending on whether N is even or odd. % % DELAY must be an integer in the range [0, N+1] % % B=FIRRCOS(...,DELAY,WINDOW) applies a length N+1 window to the % designed filter in order to reduce the ripple in the frequency % response. WINDOW must be a N+1 long column vector. If no window % is specified a boxcar (rectangular) window is used. % % WARNING: Care must be exercised when using a window with a delay % other than the default. % % [B,A]=FIRRCOS(...) will always return A = 1. % % See also FIRLS, FIR1, FIR2. % Author(s): R. Losada and D. Orofino % Copyright (c) 1988-98 by The MathWorks, Inc. % $Revision: 1.2 $ $Date: 1998/06/17 20:33:49 $ error(nargchk(3,8,nargin)); N = varargin{1}+1; if round(N) ~= N, error('Order must be an integer') end fc = varargin{2}; if fc <= 0, error('Cutoff frequency must be greater than zero') end R = varargin{3}; % DF or R % If optional arguments are not passed, substitute with empty: for i = nargin+1:8, varargin{i}=[]; end arg5opts = {'rolloff','sqrt','normal'}; % map 5th arg to one of 3 possible choices: if isempty(varargin{5}), varargin{5} = arg5opts{3}; else idx = strmatch(lower(varargin{5}), arg5opts); if isempty(idx) | length(idx)>1, error('Argument 5 is unknown - must be one of: rolloff, sqrt, or normal'); end varargin{5} = arg5opts{idx}; end % Apply defaults as appropriate: % % Set up default values fs = 2; type = arg5opts{3}; if rem(N,2), delay = (N-1)/2; else delay = N/2; end window = []; % Setup arg translation: params = {'fs','type','delay','window'}; is_rolloff = strcmp(varargin{5},'rolloff'); if is_rolloff, xlat = [4 6:8]; else xlat = 4:7; end % Override defaults when needed: for i=1:length(xlat), arg = varargin{xlat(i)}; if ~isempty(arg), eval([params{i} '=arg;']); end end % Check for validity of fs if ischar(fs), error('Fs must be a number'); end % Fill in defaults if empty matrices are passed: if is_rolloff, % check if input arguments are valid if R < 0 | R > 1, error('R must satisfy 0 <= R <= 1'); end % check for range of input arguments if fc - R.*fc < 0 | fc + R.*fc > fs/2 error('F0 +/- F0*R must satisfy 0 <= F0 +/- F0*R <= Fs/2'); end else % sqrt or normal % check for range of input arguments if fc - R/2 < 0 | fc + R/2 > fs/2 error('F0 +/- DF/2 must satisfy 0 <= F0 +/- DF/2 <= Fs/2'); end % interpret third argument as a bandwidth and convert to rolloff: R = R / (2*fc); end if delay < 0 | delay > N error('DELAY must be in the range [0, N+1]'); elseif round(delay) ~= delay error('DELAY must be an integer'); end % R is now always a rolloff factor - DF has been converted if R == 0, R = realmin; end %n = -delay/fs : 1/fs : (N-delay-1)/fs; n = ((0:N-1)-delay) ./ fs; if is_rolloff, % 6th argument, if present, is type arg6opts = {'sqrt','normal'}; % map 6th arg to one of 2 possible choices: if isempty(varargin{6}), type = arg6opts{2}; else idx = strmatch(lower(varargin{6}), arg6opts); if isempty(idx) | length(idx)>1, error('Argument 6 is unknown - must be one of:sqrt, normal or []'); end type = arg6opts{idx}; end end switch type case 'normal' %normal raised cosine design ind1 = find(abs(4.*R.*fc.*n) ~= 1.0); if ~isempty(ind1), nind = n(ind1); b(ind1) = sinc(2.*fc.*nind)./fs ... .* cos(2.*pi.*R.*fc.*nind) ... ./ (1.0 - (4.*R.*fc.*nind).^2); end ind = 1:length(n); ind(ind1) = []; b(ind) = R ./ (2.*fs) .* sin(pi ./ (2.*R)); b = 2.*fc.*b; case 'sqrt' % square root raised cosine design ind1 = find(n == 0); if ~isempty(ind1), b(ind1) = - sqrt(2.*fc) ./ (pi.*fs) .* (pi.*(R-1) - 4.*R ); end ind2 = find(abs(8.*R.*fc.*n) == 1.0); if ~isempty(ind2), b(ind2) = sqrt(2.*fc) ./ (2.*pi.*fs) ... * ( pi.*(R+1) .* sin(pi.*(R+1)./(4.*R)) ... - 4.*R .* sin(pi.*(R-1)./(4.*R)) ... + pi.*(R-1) .* cos(pi.*(R-1)./(4.*R)) ... ); end ind = 1:length(n); ind([ind1 ind2]) = []; nind = n(ind); b(ind) = -4.*R./fs .* ( cos((1+R).*2.*pi.*fc.*nind) + ... sin((1-R).*2.*pi.*fc.*nind) ./ (8.*R.*fc.*nind) ) ... ./ (pi .* sqrt(1./(2.*fc)) .* ((8.*R.*fc.*nind).^2 - 1)); b = sqrt(2.*fc) .* b; end if ~isempty(window), if length(window) ~= N, error('WINDOW must be of the same length as the filter'); else b = b .* window(:).'; end end if nargout > 1 a = 1.0; end