function [f,H]=lp_butterworth_oN_dft(fc,K,fmax,N,Norder)

%determine odd or even length
%to specify a specific discrete frequency let
%fc=kc and fmax= N/2 for N even and (N-1)/2 for N odd
%K = dc gain
%N = vector length
%Norder = order of filter (1,2,3,...)
% Example code:
% fc=20;K=1;N=256;fmax=N/2;Norder=10;
% [f H]=lp_butterworth_oN_dft(fc,K,fmax,N,Norder);
% plot(f,real(H)); or plot (real(H)) for discrete version

temp=floor(N/2); temp=temp*2; % test for odd or even

evenodd=0; % guess odd

if temp==N,

   evenodd=1; % even

end;

% determine the frequency vector

if evenodd==1

   n0=-((N/2)-1);

else

   n0=-((N-1)/2);

end;

n1=n0+N-1;

na=n0:1:-1; % index vector

nb=0:1:n1;

n=[nb,na];

df=fmax/n1; % frequency increment

f=n*df; % frequency vector

w=2*pi*f;

wc=2*pi*fc;

H=(K^0.5)*(1 + (w/wc).^(2*Norder)).^(-0.5)+i*0;