Response of LTI system to a Random Input Signal

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

What is response of an LTI 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 ) .

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 is frequency response of LTI system?

The frequency response of the system, from the definition in Equation (12.11), is thus. −jΩ −j2Ω H(Ω) = h[0] + h[1]e + h[2]e .

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.