Resolving Sinusoidal Components Robustly

We cannot normally assume a sum of precisely two sinusoids with no noise, and so we choose our window length to resolve them robustly:

• FFT window length $M$ spans at least two periods of the difference frequency under a rectangular window (and longer for other windows)
• $\Longleftrightarrow$ Window transform (asinc) separated by a full main-lobe width at the minimum supported peak-frequency separation
• Any narrower peak spacing is then treated as amplitude modulation that plays out over time as spectral-frame amplitude modulation

We are still assuming that sinusoidal signal components are present, at least over the window duration, but this is commonly a good assumption.