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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.


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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