I'm a newbie to Signal Processing - my apologies if this question is too obvious (I'm a financial trader trying to use DSP techniques).
For a linear filter:
$y[n] = (1-p) x[n]+p y[n-1]$
we can the write Transfer Function as
$H(z) = \frac{1-p}{1-pz^{-1}}$
But instead, suppose I have a non-linear filter:
$y[n] = y[n-1]+(1-p)\frac{1}{2}(x[n]e^{-2 y[n-1]}-1)$
How can I write a Transfer Function ?
For example, if I simply replace $y[n-1]$ by $y[n]z^{-1}$ and rewrite I get:
$H(z) = \frac{(1-p)\frac{1}{2}(x[n]e^{-2 z^{-1} y[n]}-1)}{1-z^{-1}}$
which is a function of $x[n]$ and $y[n]$ in addition to being a function of $z$?
Can this be written merely as a function of $z$?