Instantaneous impulse response in a linear time-varying system

1. What is impulse response of a linear system?
2. What is the impulse response of a discrete time system?
3. What is a time varying response?

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.

What is the impulse response of a discrete time system?

Impulse response h[n] of a discrete-time system. The impulse response of a discrete-time system is defined as the response of a discrete-time system when the input is a delta pulse, thus x[n]=δ[n] x [ n ] = δ [ n ] .

What is a time varying response?

A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior.