% COEF generiert IIR-Tiefpass Koeffizienten für geradzahlige Ordnung
% [b,a] = coef(fa,fg,Q,N)
%
% fa   : Abtastfrequenz [Hz]
% fg   : Grenzfrequenz  [Hz]  fg <= fa/2
% Q    : Polgüte (Q=1.0 für Butterworth)
% N    : Filterordnung (durch zwei teilbar)
% Type : 'Lowpass', 'Highpass', 'Bandpass', 'Bandstop'
%
function [b,a] = coef(fa,fg,Q,N,Type)

if (rem(N,2) > 0)
  error('Filterordnung muss z.Zt. noch durch zwei teilbar sein!');
end;

if (strcmp(Type,'Bandstop'))
  TF = 4;
end;

TF
sn = sin(2*pi*fg/fa);
cs = cos(2*pi*fg/fa);
ak = ones(N/2,3);
bk = ones(N/2,3);
a  = 1;
b  = 1;

if (strcmp(Type,'Lowpass'))
  for n = 1:N/2,
    Qp      = 1/(2*sin(pi*(n-0.5)/N))
    alpha   = sn/(2*Q*Qp);
    a0      = 1+alpha;
    ak(n,2) = -2*cs/a0;
    ak(n,3) = (1-alpha)/a0;
    bk(n,1) = 0.5*(1-cs)/a0;
    bk(n,2) = (1-cs)/a0;
    bk(n,3) = 0.5*(1-cs)/a0;
    a       = conv(a,ak(n,(1:3)));
    b       = conv(b,bk(n,(1:3)));
  end;
end;

if (strcmp(Type,'Highpass'))
  for n = 1:N/2,
    Qp      = 1/(2*sin(pi*(n-0.5)/N))
    alpha   = sn/(2*Q*Qp);
    a0      = 1+alpha;
    ak(n,2) = -2*cs/a0;
    ak(n,3) = (1-alpha)/a0;
    bk(n,1) = 0.5*(1+cs)/a0;
    bk(n,2) = -(1+cs)/a0;
    bk(n,3) = 0.5*(1+cs)/a0;
    a       = conv(a,ak(n,(1:3)));
    b       = conv(b,bk(n,(1:3)));
  end;
end;

if (strcmp(Type,'Bandpass'))
  for n = 1:N/2,
    Qp      = 1/(2*sin(pi*(n-0.5)/N))
    alpha   = sn/(2*Q*Qp);
    a0      = 1+alpha;
    ak(n,2) = -2*cs/a0;
    ak(n,3) = (1-alpha)/a0;
    bk(n,1) = alpha/a0;
    bk(n,2) = 0;
    bk(n,3) = -alpha/a0;
    a       = conv(a,ak(n,(1:3)));
    b       = conv(b,bk(n,(1:3)));
  end;
end;