Given a signal $x[n] = [1, 2, 3, 4, 5]$. How many transfer functions can be found with Padé approximation which have a causal impulse response and start with those five samples. How many of them are stable?
Found this question and I'm not sure if I understood it right. I'd say none of them is stable since Padé can't guarantee stable solutions. The first five samples will be perfectly recreated in the impulse response. Therefor $h(z)$ between $0-4$ looks like $x[n]$. But what about how many? Are there multiple solutions? Is this question badly formulated?
A further question is then: Find the Padé model with exaclty one pole. One pole? Isn't that an all pole model? Or is there some kind of rule like always the same amount of poles and zeros? Can't solve it with the Padé euqations.