I have some basic doubts about IIR digital filters.
My first question is about its definition. IIR means Infinite impulse response, so my question is: is it physically possible to realize such filters? Does infinite impulse response means that it is different from 0 for all negative and positive times (from - infinite to + infinite)?
My second question is about the input - output relation in time domain, which is the following one:
Which is its meaning? "A linear combination of the output samples is equal to a certain linear combination of the input samples"?
If we apply Z - Transform to the previous expression in time domain, we get:
This is due to the time - shift properties of the Z - transforms. What I do not understand is how we have many output terms (for different k) in time domain, while we have only 1 output term (Y(z)) in Z - domain, and the same for the input.