The filter is a linear time-invariant (LTI) system that adds memory to the model. Combined with a memoryless nonlinearity, the filter allows to model non-linear systems *with* memory, unlike a pure AM-AM and AM-PM model, which models a *memoryless* nonlinearity. An [ARMA-filter](https://en.wikibooks.org/wiki/Signal_Processing/Digital_Filters#ARMA_Filters) is the same as an [infinite-impulse response (IIR) filter](https://en.wikipedia.org/wiki/Infinite_impulse_response), which computes its output as a linear combination of weighted and delayed versions of the input and output signal. IIR filters need to be implemented by recursive structures.