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

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)

The main idea is that H(jω) is the system’s transfer function in the frequency domain. It tells you how each frequency component of the input is scaled and shifted by the system. For a linear time-invariant system, the output spectrum is the product of the input spectrum and the frequency response: Y(jω) = H(jω) X(jω). H(jω) is complex, so it has a magnitude |H(jω)| and a phase ∠H(jω). The magnitude shows how much each frequency is amplified or attenuated, while the phase shows the corresponding shift (delay) introduced to that frequency component.

It’s not the time-domain impulse response itself (that would be h(t)); its Fourier transform is H(jω). It’s also not the energy of the output, which relates to integrals of |y(t)|^2 in time. Bandwidth is a property you derive from the shape of |H(jω)|, describing the range of frequencies that pass with little attenuation, but H(jω) is the full frequency response, not a single bandwidth value. For example, a simple RC low-pass filter has H(jω) = 1/(1 + jωRC), which shows how gain and phase vary with frequency: magnitude decreases with ω and the phase lag increases with ω.