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== Correlation spectrometer ==
The problem of computing pairwise correlation as a function of frequency can be solved by two mathematically equivalent but distinct ways. By using [[Discrete Fourier Transform]] (DFT) it is possible to analyze signals in the time ___domain as well as in the spectral ___domain. The first The first approach is "XF" correlation because it first cross-correlates antennas (the "X" operation) using a time-___domain "lag" convolution, and then computes the spectrum (the "F" operation) for each resulting baseline. The second approach "FX" takes advantage of the fact that convolution is equivalent to multiplication in Fourier ___domain. It first computes the spectrum for each individual antenna (the F operation), and then multiplies pairwise all antennas for each spectral channel (the X operation). A FX correlator has an advantage over a XF correlators in that the computational complexity is [[Big O notation|O]](N<sup>2</sup>). Therefore, FX correlators are more efficient for larger arrays.<ref>{{cite journal▼
▲two mathematically equivalent but distinct ways. By using [[Discrete Fourier Transform]] (DFT) it is possible to analyze signals in the time ___domain as well as in the spectral ___domain. The first The first approach is "XF" correlation because it first cross-correlates antennas (the "X" operation) using a time-___domain "lag" convolution, and then computes the spectrum (the "F" operation) for each resulting baseline. The second approach "FX" takes advantage of the fact
| last1=Parsons |first1=Aaron |last2=Backer |first2=Donald |last3=Siemion |first3=Andrew |authorlink3=Andrew Siemion
| date = September 12, 2008
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