IIR filters are one of two primary types of digital filters used in Digital Signal Processing (DSP) applications (the other type being FIR). "IIR" means "Infinite Impulse Response".
The impulse response is "infinite" because there is feedback in the filter; if you put in an impulse (a single "1" sample followed by many "0" samples), an infinite number of non-zero values will come out (theoretically).
DSP filters can also be "Finite Impulse Response" (FIR). FIR filters do not use feedback, so for a FIR filter with N coefficients, the output always becomes zero after putting in N samples of an impulse response.
IIR filters can achieve a given filtering characteristic using less memory and calculations than a similar FIR filter.
- They are more susceptable to problems of finite-length arithmetic, such as noise generated by calculations, and limit cycles. (This is a direct consequence of feedback: when the output isn't computed perfectly and is fed back, the imperfection can compound.)
- They are harder (slower) to implement using fixed-point arithmetic.
- They don't offer the computational advantages of FIR filters for multirate (decimation and interpolation) applications.