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Infinite impulse response (IIR) filters are characterized by the fact that they use delayed versions of the input signal and fed-back and delayed versions of the output signal to filter the input to the output. For example, if we take the expression for a general IIR filter below, we can see that the output is a function of a series of delayed, scaled versions of the input and output.
where Ai is the scale factor for the ith delayed version of the input and Bi is the scale factor for the ith delayed version of the output. This is obviously very similar to the FIR example previously given and can be built up using the same basic elements. If we consider the simple example earlier in this chapter, it can be seen that this is in fact a simple first order (single delay) IIR filter, with no delayed versions of the input and a single delayed version of the output.
Figure 9.7
FIR fifilter schematic.
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