Spectral Window Weightings

Abstract

A spectral widow weight is a function applied to the time domain data that changes the frequency domain representation in a controllable way. Nearly always, a spectral window function is a symmetrical bell-shaped curve that de-emphasizes the ends of the intervals of the time data. Its effect is observed by the DFT response to a sine wave of variable frequency and phase. Without a window weight function, the output of an FFT follows the familiar sine of x over x shape except when the frequency of the tone is exactly positioned at the center of a frequency bin. In a plot of amplitude in decibels versus frequency, this is the familiar Christmas-tree shape. With a spectral window, the main lobe is broadened slightly, while the sidelobes are lowered, particularly the near-in sidelobes.