The preceding figures suggest that, for a rectangular window of length , two sinusoids can be most reliably resolved when they are separated in frequency by a full main-lobe width:
This implies there must be at least two full cycles of the difference-frequency under the window. (We'll see later that this is an overly conservative requirement--a more careful study reveals that cycles is sufficient for the rectangular window.)
Resolving two closely spaced sinusoids is equivalent to AM demodulation:
where is the difference frequency in rad/s.
In principle, arbitrarily small frequency separations can be resolved if
The rectangular window provides an abrupt transition at its edge. We will soon look at some other windows which have a more gradual transition. This is usually done to reduce the height of the side lobes.