What is a linear system?

A discrete system is nothing more than an algorithm, where input is transformed into output. The output is transformed by operator L(), which describes the discrete system.
Let’s see the few most common operators of discrete systems.


This means that output queue is delayed by on sample.


This operator takes each sample of input queue and multiplies by constant a.

Sum operator

Takes two or more sample queues and adds them in the output.

Assuming we can say, that the system is linear if input sum reaction is equal to sum of inputs reactions:

The system has stable parameters if:
y(n-k)=L(x(n-k)), this means that output delay should be the same as the input.
It is obvious that delay, multiply, and sum operators are linear and have stable parameters. We will need them for further lessons.

Leave a Reply