# This version is correct!
# length 19 (-9,...,9) linear phase FIR filter

param n := 10;
param N := 300;
param pi := 4*atan(1);
param eps := 1.0e-6;

set NU_P := {0.0..0.2 by 1/N} union {0.8..1.0 by 1/N};
set NU_S := {0.3..0.7 by 1/N};
set NU_I := {0.2..0.3 by 1/N} union {0.7..0.8 by 1/N};
set NU   := NU_P union NU_S union NU_I;

var rho >= 0;
var h_real {0..n-1};
var h_imag {1..n-1};

var H {nu in NU} =
    h_real[0] + 
    2*
    sum {k in 1..n-1} (h_real[k]*cos(-2*pi*k*nu) - h_imag[k]*sin(-2*pi*k*nu));

minimize power_bnd: rho;

subject to passband: sqrt(sum {nu in NU_P} (H[nu]-1)^2) <= sqrt(0.4*N)*rho;

subject to stopband: sqrt(sum {nu in NU_S} H[nu]^2) <= sqrt(0.4*N*eps);

let h_real[0] := 2;

solve;

printf {nu in NU}: "%7.4f %10.3e \n", 
    nu, 20*log10(abs(H[nu])) > 2.out;