in my notes for DSP they have the difference equation general form as:
y(k) + a1*y(k-1) + a2*y(k-2) + ... + an*y(k-N) = b0*x(k) + b1*x(k-1) + ... + bm*x(k-M)
with the claim that for the output to not depend on future values of the input then M<=N.
Why is this the case?
In fact, if I'm not missing something here I think I can provide a counterexample:
y(k) = x(k-1)
which has N = 0 and M = 1. But this is just a unit delay, the output is just the previous value of the input.
What's going on here?