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I use the term spectral correlator for a radio astronomy interferometry correlator that produces a spectral energy distribution (SED) over its band of interest. (This term has been used with this meaning but there doesn't seem to be a consensus term; also, the ability to produce some spectral information is fairly common in radio-astronomy correlators and often presumed.) Such correlators are of obvious interest in interferometry, including very-long-baseline interferometry (VLBI), but are more complex than those used merely to pinpoint the source and measure its strength. Often the signal is digitized and a discrete Fourier transform (DFT) is used, the latter to act as a filter, producing signals at different frequencies.
Designs include FX (i.e., FX correlator or FX spectrometer) and XF (XF correlator or XF spectrometer), depending upon whether correlation is performed before or after the Fourier transform. More complex designs/configurations are also used.