Have you tried calculating the filter's impulse response, to see if it's finite?
– MBazDec 14 '17 at 15:48
I did answer the exact same question a few years ago. If a filter is recursive (previous values of y[n-k] are being used), it doesn't necessarily imply that the impulse response is infinite. You must calculate the IR first.
– jojeckDec 14 '17 at 15:51
y[n-k]are being used), it doesn't necessarily imply that the impulse response is infinite. You must calculate the IR first. – jojeck Dec 14 '17 at 15:51