Sinusoidal Interference as Amplitude Modulation

Resolving two closely spaced sinusoids is equivalent to AM demodulation:

$$\cos\left(\omega_c t + \frac{\omega_d}{2} t\right) + \cos\left(\omega_c t - \frac{\omega_d}{2} t\right) = 2\cos\left(\omega_c t\right) \cos\left( \frac{\omega_d}{2} t \right)$$

where $\omega_d$ is the difference frequency in rad/s.

• Intuitively, it makes sense to require two cycles of the difference-frequency $\omega_d$ , since that is one cycle of the equivalent AM modulation (two ``beats'')