Determining whether a system is linear or not having the impulse response

1. How do you identify if a system is linear or non linear?
2. How do you determine impulse response of a system?
3. What is impulse response of a linear system?

How do you identify if a system is linear or non linear?

To determine if a system is linear, we need to answer the following question: When an input signal is applied to the system, does the output response exhibit homogeneity and additivity? If a system is both homogeneous and additive, it is a linear system.

How do you determine impulse response of a system?

Given the system equation, you can find the impulse response just by feeding x[n] = δ[n] into the system. If the system is linear and time-invariant (terms we'll define later), then you can use the impulse response to find the output for any input, using a method called convolution that we'll learn in two weeks.

What is impulse response of a linear system?

The impulse response of a linear transformation is the image of Dirac's delta function under the transformation, analogous to the fundamental solution of a partial differential operator. It is usually easier to analyze systems using transfer functions as opposed to impulse responses.