LTI system output given input and frequency response

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

How do you calculate the output of an LTI system?

The output of any LTI system can be calculated using the input and the impulse function for that system. Convolution has many important properties: Commutativity: x ( t ) ∗ h ( t ) = h ( t ) ∗ x ( t ) x(t) \ast h(t) = h(t) \ast x(t) x(t)∗h(t)=h(t)∗x(t)

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.

How do you find the frequency response of a LTI system?

−jΩm = C(Ω) − jS(Ω) = H(Ω) . , where H(Ω) is the frequency response of the LTI system. The system therefore produces an output signal that is the “3-point weighted moving average” of the input.

What is meant by the frequency response of an LTI system?

=frequency response function. The response of an LTI system to a sinusoidal or complex exponential input is a sinusoid or complex exponential output at the same frequency as the input. LTI systems cannot change frequencies.