Recursive, non-recursive systems; FIR, IIR systems I am confused with the classifications of an LTI system as recursive or non-recursive systems and FIR or IIR systems.
I understood what the FIR and an IIR systems are, but is it correct to say that FIR system is always non-recursive?

We could express an finite accumulator up to past N inputs (FIR system) in both non-recursive and recursive forms.
Also is it correct to say that a non-recursive system is always an IIR system or vice versa?
The logical implications are the following:
&quot;non-recursive&quot; $\Longrightarrow$ FIR
IIR $\Longrightarrow$ &quot;recursive&quot;
But the opposites are not necessarily true because a FIR system can be implemented recursively (transfer function poles can be cancelled by zeros).

Of course, when referring to "recursive" or "non-recursive" we always talk about implementations with finitely many operations per output sample. Clearly, any discrete-time LTI system can be described by a generally infinite convolution sum, but that is not what we mean by "non-recursive".