Impulse response of an LTI system given the input and output signals

1. How do you find impulse response given input and output?
2. How to find impulse response of LTI system from given input and output?
3. How do you calculate response of LTI system?
4. What would happen to the LTI system output when the input or the impulse response is a shifted impulse?

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 given 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 ) .

How do you calculate response of LTI system?

A linear time-invariant (LTI) system can be represented by its impulse response (Figure 10.6). More specifically, if X(t) is the input signal to the system, the output, Y(t), can be written as Y(t)=∫∞−∞h(α)X(t−α)dα=∫∞−∞X(α)h(t−α)dα.

What would happen to the LTI system output when the input or the impulse response is a shifted impulse?

In general, however, any relationship which is linear and time-invariant, with unit impulse as input qualifies as a valid impulse response for an LTI system. Because such systems are time-invariant, if the impulse is shifted to a new location, the output is simply a shifted version of the impulse response.