Choice of Fourier
Window

The properties of the windowed Fourier transform are determined by the window g, or rather its Fourier transform, whose energy should be concentrated around 0. Three important parameters evaluate this energy spread:

• the root mean square bandwidth Dw defined by
  

  If Dw is small, the energy of the window is well concentrated around 0.

• the maximal amplitude A of its first side lobes, measured in decibels:
  

  These side lobes can create "shadows" on each side of the frequency center.

• The polynomial exponent which describes the decay of the window's Fourier transform at high frequencies
  

  It sums up the behavior of the Fourier transform beyond the first side lobes.

The following table gives the values of these parameters for classical windows, normalized so that g(0) = 1.