Impulse response of a linear time-variant system

1. What is the impulse response of a linear time invariant system?
2. What is impulse response of a linear system?
3. Can a linear time varying system be described by its impulse response?
4. Is it possible for a time variant system to be linear?

What is the impulse response of a linear time invariant system?

The impulse response for an LTI system is the output, y ( t ) y(t) y(t), when the input is the unit impulse signal, σ ( t ) \sigma(t) σ(t). In other words, when x ( t ) = σ ( t ) , h ( t ) = y ( t ) .

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.

Can a linear time varying system be described by its impulse response?

A LTV system can be viewed as a system with impulse response that is time dependent, i.e. the output of the system to an impulse input δ(t−s) depends on both t and s. where, t is time, and s is the time instant at which the impulse is applied.

Is it possible for a time variant system to be linear?

Linear-time variant (LTV) systems are the ones whose parameters vary with time according to previously specified laws. Mathematically, there is a well defined dependence of the system over time and over the input parameters that change over time.