System visualization

Basic building blocks LTI system

When realizing or implementing a discrete-time system, we need the following basic building blocks: A multiplier, which multiplies signal sample x[n] by a scalar β which results in a sample with value y[n]=βx[n]; An adder which adds two signal samples x1[n] and x2[n] together into y[n]=x1[n]+x2[n] and finally an unit-delay operator which delays a signal sample x[n] by one sample index into y[n]=x[n1]. These basic building blocks are depicted in Fig. 1.

Basic building blocks of a discrete-time system.
Basic building blocks of a discrete-time system.

Realization scheme and Difference Equation LTI system

Fig. 2 shows the realization scheme, or flow diagram, of a basic LTI system.

Signal flow diagram or realization scheme of a basic LTI system.
Signal flow diagram or realization scheme of a basic LTI system.
The LTI systems that we consider in this reader can have both a feed forward path with coefficients b0 until bM1 and feedback path with coefficients a1 until aN1. From the figure it follows that we can describe such a basic LTI system with the following Difference Equation (DE): (1)y[n]=k=0M1bkx[nk]+k=1N1aky[nk]