====== Octave Filter Design Example ======

<code matlab>
# do this one time
pkg install control-3.1.0.tar.gz
pkg install signal-1.4.0.tar.gz

pkg list
pkg update

</code>

=== Filter design ===

<code matlab>
pkg load signal

% Simple but has a large transition band and only about 50 to 60 db attenuation
freqz(fir1(63,0.125))
</code>

The parks McClellan algorithm incorporates both the Remez exchange algorithm and the Chebyshev approximation theorem to achieve an optimal fit between your desired and actual filter response. 

<code matlab>
% --- Parks-McClellan lowpass Filter
n = 64
f = [0.0 0.3 0.4 1.0 ];
a = [1.0 1.0 0.0 0.0];
w = [1.0 0.1];
b = remez(n, f, a, w);

[h,w] = freqz(b,1,512);
plot(f,a,w/pi,abs(h))
legend('Ideal','remez Design')
xlabel 'Radian Frequency (\omega/\pi)', ylabel 'Magnitude'
</code>

=== Example of 100dB filter ===
<code matlab>
% example of 100dB filter
f = [0.0 0.1 0.2 1.0 ];
a = [1.0 1.0 0.0 0.0];
freqz(remez(128,f,a));
</code>
{{:ref:octave:remez_100db.png|}}