Two-Box-Model of a nonlinear amplifier
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 is the same as an infinite-impulse response (IIR) filter, 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.

An ARMA (or IIR) filter is a discrete-time (linear time-invariant) filter whose response $y[n]$ to an input sequence $x[n]$ is computed as follows:

$$y[n]=\sum_{m=0}^Mb_mx[n-m]+\sum_{l=1}^Na_ly[n-l]\tag{1}$$

where $b_m$ and $a_l$ are the filter coefficients, which are chosen such that a certain desired filter characteristic (e.g., low pass, high pass, etc.) is achieved.