Question

For an LTI system with the above impulse response, calculate the frequency response function H, and the Laplace transform H(s). How do these two functions compare?

Answer 1

The frequency response function H is obtained by taking the Fourier Transform of the impulse response of an LTI system. The Laplace Transform H(s) incorporates the complex variable s and represents the system's response to different frequencies and its transient and steady-state behavior.

Step-by-step explanation:

The frequency response function H of an LTI (Linear Time-Invariant) system is obtained by taking the Fourier Transform of its impulse response. The frequency response describes how the system responds to sinusoidal inputs of different frequencies.

To calculate H, we take the Fourier Transform of the given impulse response. The Laplace Transform H(s) is the Fourier Transform of H with the frequency variable s, where s = jw. Comparing H and H(s), we can see that they both represent the system's response to different frequencies, but H(s) incorporates the complex variable s to account for the system's transient and steady-state behavior.