When can the impulse response become zero?

1. Can impulse response be zero?
2. What does the impulse response tell us?
3. Why does the impulse response of LTI system take form of zero input response?
4. How do you calculate impulse response?

Can impulse response be zero?

so the output is the impulse response (the derivative of the unit step response). It is important to keep in mind that the impulse response of a system is a zero state response (i.e., all initial conditions equal to zero at t=0^-).

What does the impulse response tell us?

An impulse is a signal with amplitude of 1 at t = 0 and zero everywhere else. Using an impulse to excite a system provides “infinite” frequency content, i.e. the impulse response tells us how the system will behave for inputs at all frequencies.

Why does the impulse response of LTI system take form of zero input response?

The zero-input response, which is what the system does with no input at all. This is due to initial conditions, such as energy stored in capacitors and inductors.

How do you calculate 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.