Infinite Impulse Response Filter

Infinite impulse response filters are like finite impulse response filters (FIR filter), the difference lies in the fact that IIR filters use feedback, for example $y(n)=0.5y(n-1))$ which results in an infinite impulse response.

IIR filters can be very powerful, but it can also be more difficult to design them properly (IIR filters are prone to instability for example, because they are recursive filters).