Difference Equations, why M<=N for causality?

1. What is the significance of difference equations?
2. How do you determine the causality of a system?
3. What are the conditions for stability and causality of an LTI system?
4. Is the system y n ]= 2x n ]+ 2 linear?

What is the significance of difference equations?

As stated briefly in the definition above, a difference equation is a very useful tool in describing and calculating the output of the system described by the formula for a given sample n. The key property of the difference equation is its ability to help easily find the transform, H(z), of a system.

How do you determine the causality of a system?

A system is said to be causal if it does not respond before the input is applied. In other words, in a causal system, the output at any time depends only on the values of the input signal up to and including that time and does not depend on the future values of the input.

What are the conditions for stability and causality of an LTI system?

LTI System Properties

An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal.

Is the system y n ]= 2x n ]+ 2 linear?

8. Is the system y[n]=2x[n]+2 linear? ∴ The system does not satisfy superposition principle ⇒ The system is not linear.