Solving for impulse response h[n] given input-output pairs

1. How do you find impulse response given input and output?
2. How to find impulse response of LTI system from input and output?
3. What is the impulse response H n of this system?
4. How do you find the impulse response of a signal?

How do you find impulse response given input and output?

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.

How to find impulse response of LTI system from input and output?

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 the impulse response H n of this system?

The function h[n] is called the impulse response of the system. It is the output (response) of the system when the input is a delta function (impulse).

How do you find the impulse response of a signal?

Key Concept: The impulse response of a system is given by the transfer function. If the transfer function of a system is given by H(s), then the impulse response of a system is given by h(t) where h(t) is the inverse Laplace Transform of H(s).