general form of difference equation

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 ?

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migrated from electronics.stackexchange.comOct 18 '12 at 15:12

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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.