Recursive IIR Filter (Infinite Impulse Response Filter)
Filter for which the output depends on previous inputs and outputs;
An impulse extinguishes them after an indefinite period of time.
We'll implement it by simply following the difference equation:
\(y\left(n\right)=-\sum_{k=1}^{N}{a_ky\left(n-k\right)}+\sum_{k=0}^{M}{b_kx\left(n-k\right)}\) (3)
\(\rightarrow\) Presence of poles, risk of instability.
\(\rightarrow\) Minimum phase systems exist if all the zeros of the numerator are inside the unit circle.
\(\rightarrow\) Rational filters cannot have a linear phase.