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function [DH,DW] = lowpass(N, F, GF, W, delay) %LOWPASS Desired frequency response for lowpass filters. % CREMEZ(N,F,'lowpass', ...) designs a linear-phase lowpass filter % response using CREMEZ. % % CREMEZ(N,F,{'lowpass', D}, ...) specifies group-delay offset D such % that the filter response will have a group delay of N/2 + D in % units of the sample interval, where N is the filter order. % Negative values create less delay, while positive values create % more delay. By default, D=0. % % The symmetry option SYM defaults to 'even' if unspecified in the % call to CREMEZ, and if no negative band edge frequencies are % specified in F. % % EXAMPLE: Design a 31-tap, complex lowpass filter % b = cremez(30,[-1 -.5 -.4 .7 .8 1],'lowpass'); % freqz(b,1,512,'whole'); % % EXAMPLE: Reduced group delay filter response: % b = cremez(30,[0 .6 .7 1],{'lowpass',-1}); % % See also CREMEZ. % Authors: L. Karam, J. McClellan % Revised: October 1996, D. Orofino % % Copyright (c) 1988-98 by The MathWorks, Inc. % $Revision: 1.1 $ $Date: 1998/06/03 16:14:46 $ % [DH,DW]=LOWPASS(N,F,GF,W,DELAY) % N: filter order (length minus one) % F: vector of band edges % GF: vector of interpolated grid frequencies % W: vector of weights, one per band % DELAY: negative slope of the phase. % N/2=(L-1)/2 for exact linear phase. % % DH: vector of desired filter response (mag & phase) % DW: vector of weights (positive) % % NOTE: DH(GF) and DW(GF) are specified as functions of frequency % Support query by CREMEZ for the default symmetry option: if nargin==2, % Return symmetry default: if strcmp(N,'defaults'), % Second arg (F) is cell-array of args passed later to function: num_args = length(F); % Get they delay value: if num_args<5, delay=0; else delay=F{5}; end % Use delay arg to base symmetry decision: if isequal(delay,0), DH = 'even'; else DH='real'; end return end end % Standard call: error(nargchk(4,5,nargin)); if nargin < 5, delay = 0; end delay = delay + N/2; % adjust for linear phase Le = length(F); if (Le == 4), if any(F < 0), error('Band edges must be non-negative for 2-band Lowpass designs.'); end elseif (Le == 6), if F(3)*F(4) > 0, error('Passband must include DC for 3-band Lowpass designs.'); end else error('There must be either 4 or 6 band edges for Lowpass designs.') end % Optimization weighting: W = [1;1]*(W(:).'); W = W(:); % Construct "lowpass" magnitude response: mags = zeros(size(W)); mags(Le-3:Le-2) = 1; % Unity in 2nd-to-last band DH = table1([F(:), mags], GF) .* exp(-1i*pi*GF*delay); DW = table1([F(:), W], GF); % end of lowpass.m