Properties:

• Zero crossings at integer multiples of
  $$\Omega_M \isdef \frac{2\pi}{M} = \hbox{frequency sampling interval for a length $M$\ DFT.}$$

• Main lobe width is $2 \Omega_M = \frac{4\pi}{M}$.
• As $M$ increases, the main lobe narrows (better frequency resolution).
• $M$ has no effect on the height of the side lobes (same as the ``Gibbs phenomenon'' for truncated Fourier series expansions).
• First side lobe only 13 dB down from the main-lobe peak.
• Side lobes roll off at approximately 6dB per octave.
• A phase term arises when we shift the window to make it causal, while the window transform is real in the zero-phase case (i.e., centered about time 0).