Normally a system transfer function is represented by H(z)
I want to know wether all those system transfer functions are only representing a digital filter?
Or their any other thing/entity in z domain that can be represented by H(z)
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One way to think about this:
Everything that can be represented as a rational function in the Z-domain can also be represented as a linear difference equation in the time domain. As such at can be interpreted (and implemented) as a filter. It may be non-causal or unstable, but it's still a filter.
You can certainly represent things in the z-Domain that are NOT rational functions, however, that would be a system transfer function anymore, because the transfer function is only defined for LTI (Linear Time Invariant) Systems