- Infinite Impulse Response (IIR) filters include delayed and scaled versions of the output signal that are fed back into the current output.
- IIR filters are described by the following difference equation:
*n*< 0. - An IIR filter can be represented by a block diagram as shown in Fig. 2 below.
- With respect to the filter block diagram, IIR filters make use of both feed-forward and feedback terms.
- Given these feedback terms, IIR filters can become unstable based on the values of the feedback coefficients (
*a*_{k}terms). - Because of this constructive feedback, an IIR filter can produce strong peaks, or resonances, in its frequency magnitude response.
- The feedback terms also result in a long filter impulse response. Though a stable filter's impulse response will decay toward zero over time, it technically never exactly reaches zero (ignoring issues of finite precision arithmetic).
- The order of an IIR filter is equivalent to the greater of the number of its delayed input or output terms.

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