What is a linear system?

Discrete system is nothing more than algorithm, where input is transformed to output. The output is transformed by operator L() which describes discrete system.
Lets see few most common operators of discrete systems.

Delay

This means that output queue is delayed by on sample.

delay.jpg

Multiplication

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

multiply.jpg

Sum operator

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

sum.jpg

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

linear.jpg

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

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