# Direct Form 2 IIR filter input values

In the filter graph below:

• where circle with 'X' inside is a multiplication
• circle with 'Σ' inside addition
• and the triangle is a delay element

What could be the values x(k) in this type of filter? There is a rule? There is a range? I can understand the matrix of coefficients but i don't know about the x(k) values.

$x[k]$ is the input signal to the filter; it could be anything. There is no "rule" for what signal you can input to a linear filter. With that said, the stability of filters is usually talked about in a bounded-in, bounded-out (BIBO) sense. If the input signal is unbounded, then it's likely that the output signal will be also. So if anything, the "rule" that you're looking for would be to only apply signals $x[k]$ whose magnitude $|x[k]|$ is bounded below some value $B < \infty$.

• I know this is being very picky but in principle it should be $|x[k]|$ instead of just $x[k]$. Not only does that take into account negative values but also complex valued inputs. Jun 3, 2013 at 9:03