Infinite impulse response (IIR) filters have several attractive properties:
• They only require a few delay elements and math operations.
• You can design them directly in the z-plane.
• You can use existing analog designs and convert them to digital with the Bilinear z-Transform (BZT); the fact that IIR topologies somewhat resemble the signal flow in analog filters emphasizes their relationship.
• You can get extreme resonance/gain by placing poles very near the unit circle.
• You can make filters, EQs, and so on with controls that link to the coefficients directly or indirectly for real-time manipulation of the plug-in.
Their main drawback is that they can become unstable and blow up, or oscillate. ...