# What is the z-domain transfer function of variable delay?

Is it possible to obtain the transfer function of a signal that has a variable delay?

For instance, I have a signal consisting of 10 samples: 0,1,1,1,1,0,0,0,0,1

If I would apply a unit delay to the signal, the transfer function would be z^-1 and the signal is now:

0,0,1,1,1,1,0,0,0,0

What would be the effect e.g. transfer function if I delay the rising edge of the pulse by 1 delay as above, but the falling edge would be delayed by 2 samples? The signal then would be:

0,0,1,1,1,1,1,0,0,0

Could this be derrived as a combination of z^(-1) and z^(-2) or this transfer function is non-linear?

$$H(z)=\sum_{n=-\infty}^{\infty}h[n]z^{-n}\tag{1}$$
where $$h[n]$$ is the impulse response of the system. Only linear time-invariant (LTI) systems can be described by a transfer function as given in $$(1)$$.