Calculate the Output of Linear Time Invariant System Given it Impulse Response [closed]

1. How do you find the output of a linear time-invariant system?
2. What is linear time-invariant system with example?
3. How do you find impulse response given input and output?

How do you find the output of a linear time-invariant 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 linear time-invariant system with example?

Any system that can be modeled as a linear differential equation with constant coefficients is an LTI system. Examples of such systems are electrical circuits made up of resistors, inductors, and capacitors (RLC circuits).

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.