In the frequency domain, which variable denotes angular frequency?

In the frequency domain, which variable denotes angular frequency?

• A. s
• B. ω
• C. jω
• D. f

Answer: (C)

In the frequency-domain analysis, the Laplace variable s = σ + jω combines a real part (growth/decay) and an imaginary part (oscillation). For steady-state sinusoidal inputs, we examine the imaginary axis by setting s = jω, so the response is studied as a function of ω, the angular frequency measured in radians per second. The product jω explicitly encodes both the imaginary unit and the angular frequency, which is why transfer functions are written as H(jω) to show how the system behaves across different ω values. For example, turning H(s) into H(jω) reveals the frequency response by substituting s with jω. While ω itself is the angular frequency and f denotes cycles per second, the notation on the frequency axis that captures the oscillatory behavior in the complex plane is jω.