The frequency response of a linear time-invariant system is obtained from which of the following?

The frequency response of a linear time-invariant system is obtained from which of the following?

• A. The impulse response
• B. The unit step response
• C. The input signal
• D. The output signal

Answer: (A)

In a linear time-invariant system, the frequency response describes how each frequency component is scaled and shifted in phase. The whole frequency behavior is captured by the impulse response h(t); the frequency response is its Fourier transform H(jω) = F{h(t)}. Because sinusoids are eigenfunctions of LTI systems, the system’s response to any input can be built from these frequency components, with each component scaled by H(jω) and shifted in phase accordingly. The unit step response is related to the impulse response but does not directly give the full frequency response, and the input or output signals alone don’t determine the system’s intrinsic frequency characteristics without knowing the system itself. Therefore, the impulse response provides the correct route to the frequency response.