Spectral Bin Numbers

Since the $k$th spectral sample $X(\omega_k)$ is properly regarded as a measure of spectral amplitude over a range of frequencies, nominally $k-1/2$ to $k+1/2$, this range is sometimes called a frequency bin (as in a ``storage bin'' for spectral energy). The frequency index $k$ is called the bin number, and $\left\vert X(\omega_k)\right\vert^2$ can be regarded as the total energy in the $k$th bin (see §7.4.9). Similar remarks apply to samples of any bandlimited function; however, the term ``bin'' is only used in the frequency domain, even though it could be assigned exactly the same meaning mathematically in the time domain.