## Filter operations

Filter operations can be represented mathematically by one
or more difference equations. A general difference equation can be written
as:

This equation represents the relationship between the
*k*^{th} sample of the output to the *N* previous values of
the output, the *M* previous values of the input, and the current value of
the input. If all the coefficients *b*_{j} are 0, the resulting
filter is called a non-recursive or Finite Impulse Response (FIR) filter.
Recursive filters are also known as Infinite Impulse Response (IIR) filters.

In FIR filters, the output is simply the weighted sum of
the current and previous inputs. In contrast, in IIR filters, the output is the
weighted sum of the current and previous inputs, and the previous
outputs.