Accumulator

The accumulator is a DT LTI System system that computes the running sum of an input signal.

• It is the Discrete-Time equivalent of Integration
• It is a Feedback system
• Its Impulse Response is the Unit Step $u[n]$

Forms

Difference Equation

$$y[n]=x[n]+y[n-1]$$

Block Diagram

Operator Form

Implicit Operator Form

$$(1-\mathcal{R})Y=X$$

Explicit Operator Form

$$Y=\frac{1}{1-\mathcal{R}}X=\sum _{k=0}^{\infty }{\mathcal{R}}^{k}X$$