A nonlinearity with memory can be modelled by a two-box-model, which consists of a filter and a memoryless nonlinearity. I am referring to chapter 5.3.2 of the book "Simulation of Communication Systems" by M.C.Jeruchim et. al. here's a link to Google books
I am given the AM-AM- and the AM-PM-characteristic of an amplifier. I want to model the behavior of the amplifier to a two-tone input signal. To do so, I want to set up a two-box-model. The memoryless nonlinearity should be described by the given characteristics.
- But what does a filter before the memoryless nonlinearity do?
- What does an ARMA filter do?
- Can an ARMA filter be used to filter an analog signal (sine-waves) ?
Answer
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.
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