Difference Equation
A filtering-equation defined in terms of the current input and the output of the filter at an earlier point in time. For [see page 3, example]: \[ y[n] = ay[n-1] + x[n] \] where \( y[n] \) is the output of the filter at time \( n \), \( x \) is the signal and \( m \) is some scalar we use in this specific equation applied to the output of the filter at an earlier time \( y[n-1] \).
The \( n-1 \) part of this equation is defined as the delay and the \( a \) is the gain. It must be noted that we ALWAYS have to have a delay before the gain.