A digital filter may be described by the difference equation
\(\boxed{y[n] + A_{1}\,y[n - 1] + \cdots + A_{N}\,y[n - N] = B_{0}\,x[n] + B_{1}\,x[n - 1] + \cdots + B_{M}\,x[n - M]}\)
Digital Filter Realization
Digital filters described by difference equations can be realized by using the symbolic elements: gain (scalar multiplier), delay (shift), and summer (or adder).