Resolving Spectral Peaks

Recall from Lecture 1 the spectral magnitude overlay of two windowed sinusoids:

For this much main-lobe separation, we need $B_w \le \Delta$ , where

$$\begin{eqnarray*} \Delta &=& \mbox{minimum sinusoidal frequency separation}\\ B_w &=& K\Omega_M = \mbox{main-lobe width}\\ \Omega_M &=& 2\pi/M \mbox{ (rectangular-window sidelobe width)}\\ K &=& \mbox{main-lobe width as a multiple of $\Omega_M$}\\ M &=& \mbox{window length} \end{eqnarray*}$$