Take the tour ×  The general form of diff equation for an LTi
system is :  $$ y(n) = - \sum_{k=1}^N a_k \cdot y(n-k) +
\sum_{k=0}^M b_k \cdot x(n-k) $$  My questions are:  1) why is
the first term negative ? 2) why limits of $k$ are from $1$ to
$N$ and not $0$ to $N$ ? 3) what does $M$ represent if $N$
represents the order of the system ?  share|improve this
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electronics.stackexchange.com Oct 18 '12 at 15:12   1 Answer
1. The first sum is the feedback from previous outputs. If the
feedback wouldn't be negative you would always add more positive
values to your output, and the transfer function would diverge
to infinity; your system would be unstable. Feedback must be
negative.    2. If you would also consider k = 0 then your first
term would be $a_0 \cdot y(n)$. Which is the output you're
actually calculating right now, you can't use that in your
calculation because it doesn't exist yet.  share|improve this
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