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.

Multiplication

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 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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This entry was posted on Friday, April 21st, 2006 at 11:02 pm and is filed under DSP Lessons. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.