In frequency domain, what does H(jω) represent?

• A. The time-domain impulse response.
• B. The ratio of output to input in the frequency domain, including magnitude and phase.
• C. The energy of the output signal.
• D. The bandwidth of the system.

Answer: (D)

H(jω) is the system’s frequency response. For a linear time-invariant system, the output spectrum is the input spectrum scaled by H(jω): Y(jω) = H(jω) X(jω). This means each frequency component is multiplied by a complex factor that has a magnitude |H(jω)| (how much it’s amplified or attenuated) and a phase ∠H(jω) (the phase shift it undergoes). Equivalently, H(jω) is the Fourier transform of the impulse response h(t), linking the time-domain behavior to the frequency domain. It does not directly represent the energy of the output, which is about the total power across all frequencies, nor is it the bandwidth itself—bandwidth is a property you derive from the magnitude response by identifying where |H(jω)| remains significant.