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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    $\begingroup$ That depends on your definition of "digital filter"; for me, the definition of digital filter is pretty much "a system that implements a z-Domain transfer function", so for me, these two are pretty much equivalent. If your definition of filter is something else, for example "any system that shows deterministic frequency-selective behaviour", then, no, the things that you can represent as a transfer function also cover non-selective systems. $\endgroup$ – Marcus Müller Mar 28 at 10:36

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

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  • $\begingroup$ Transfer function cannot be defined for non-Lti systems?? $\endgroup$ – Man Mar 28 at 11:44
  • $\begingroup$ that is correct, Man. $\endgroup$ – Marcus Müller Mar 28 at 11:44
  • $\begingroup$ Non causal and unstable filters are realizable? $\endgroup$ – Man Mar 28 at 11:45
  • $\begingroup$ Man, re-read Hilmar's answer. He specifically addressed that. $\endgroup$ – Marcus Müller Mar 28 at 12:14

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