LTI system impulse response output [duplicate]

1. What would happen to the LTI system output when the input or the impulse response is a shifted impulse?
2. What is the impulse response of a LTI system?
3. How do I know if my LTI is causal?
4. How do you find the output of an impulse response?

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.

What is the impulse response of a 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 I know if my LTI is causal?

An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal.

How do you find the output of an impulse response?

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.