Checking linearity/time-invariance etc. for recursive system

1. How do you know if a system is linear or time invariant?
2. What is time invariance of a system?
3. What is time invariance in DSP?

How do you know if a system is linear or time invariant?

One test to verify time invariance/variance property of a system is to shift the response of the system to an input signal and apply a shifted input, to the same system and compare the two waveforms, so obtained. If the system is time invariant, the two waveforms will match when the input and output shifts match.

What is time invariance of a system?

Mathematically speaking, "time-invariance" of a system is the following property: Given a system with a time-dependent output function , and a time-dependent input function , the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function.

What is time invariance in DSP?

For a time-invariant system, the output and input should be delayed by some time unit. Any delay provided in the input must be reflected in the output for a time invariant system.