See this:
t = 1:30;
x = rand(1, 30); % Some test data
[b, a] = butter(3, 0.8); % A Butterworth filter
x1 = filter(b, a, x) * 4; % Filter and amplify
x2 = filter(b * 4, a, x); % Amplify internally
plot(t, x1, 'ro', t, x2, 'c-')
max(abs(x1-x2)) % 0.0, but some rounding error can be expected
