A difference equation is a mathematical equation that describes the evolution of a sequence of values over time. It relates the value of a variable at one point in time to its value at a previous point in time, as well as any inputs or external factors that may affect it. A difference equation can *implicitly* specify a causal [[discrete-time LTI system]] with input $x(n)$ and output $y(n)$: $\sum_{k=0}^{N} a_k y(n-k) = \sum_{k=0}^{M} b_k x(n-k)$ Example: $ y(n) = x(n) + b x(n-1) + a y(n-1) $ This system can be represented in the following block diagram where the blocks with $z^{-1}$ are [[unit delay]]s: ![[grafobl.svg]] or in a graph: ![[grafofl.svg]]