Differencer

The differencer is a DT LTI System system that computes the first difference of an input signal.

• It is the Discrete-Time equivalent of a Derivative
• This system is Feed-Forward
• Its Impulse Response is $\delta [n]-\delta [n-1]$, a difference of the Unit Sample

$$\begin{array}{rl}y[n]& =x[n]-x[n-1]\\ Y& =(1-\mathcal{R})X\end{array}$$