Why nb in Hammerstein-Wiener models require to be "zeros + 1"

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ed rey
ed rey 2020-9-4
Sorry if this is a very basic question. The documentation says: "Orders" is a vector of positive integers [nb nf nk] (in SISO models), where:
  • nb is the number of zeros plus 1
  • nf is the number of poles,
  • and nk is the input delay.
Why nb has to be zeros plus 1?
Also I know that the number of zeros can't be more than the number of poles, so if I had:
for ceros=1:num_it
for poles=1:num_it
num_zeros = ceros + 1;
%to ensure that the number of zeros is less than or equal to the number of poles
if num_zeros > poles % (*)
continue
end
Orders=[num_zeros poles 1];
%% the rest of code
end
end
the if statement (*) shoud be before adding 1 to the number of zeros or is it ok? I don't know if Matlab add an extra zero or it doesn't

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