COSY Spectrum 
 
Correlation spectroscopy (COSY) was among the first two-dimensional (2D) nuclear magnetic resonance (NMR) experiments to be developed. In COSY–type experiments, cross peaks arise in a 2D map at the intersections of two chemical shifts if a resolved spin-coupling interaction exists between the nuclei characterized by the two shifts. The cross peaks have considerable fine structure, consisting of positive and negative signals if the lines of the spectrum are sufficiently narrow.
The appearance of the cross peaks in a COSY–type experiment relates to a quantum-mechanical phenomenon known as coherence transfer. In NMR, a coherence is characterized by a specific Larmor precessional frequency that is essentially defined by the magnetic field of the spectrometer and the chemical shifts of the spins involved in the creation of the coherence. A cross peak in COSY–type experiments develops because magnetization that was initially characterized by one precessional frequency is converted at some point to a coherence that precesses at a different frequency, defined by another chemical shift. The COSY 2D experiment in effect measures the precessional frequency of the coherence during both parts of the experiment. Coherence transfer occurs only if spins are J-coupled to each other. In peptide and protein systems, the appearance of a cross peak in proton-proton COSY experiments generally identifies sets of protons that are adjacent to each other in the covalent structure. With sufficiently narrow lines, it is possible to analyze the structure of COSY cross peaks to obtain values for the spin-spin coupling constant involved in the coupling interaction signaled by the cross peak.
 Many variations on the basic ideas of the COSY experiment are now available, including DQFCOSY (double quantum filtered COSY). The advantages of the DQFCOSY experiment include a much narrower set of diagonal peaks (so that cross peaks close to the diagonal can be detected more readily) and drastic reduction of the intensities of singlets. Such singlets tend to be very intense and can cause noise and various artifacts in a 2D spectrum.
 Note the requirement that a resolved spin-coupling interaction be present for optimum detection of a COSY–type cross peak. With greater molecular weights of samples, proton NMR spectral lines increase in width. Under these conditions, the positive and negative components of COSY cross peaks can begin to cancel one another, with the detection of the cross peak relative to noise becoming more difficult. Thus, although the presence of a cross peak in a COSY–type spectrum indicates mutual spin coupling between (probably) adjacent groups of protons, the absence of a cross peak in a COSY–type spectrum cannot be taken as evidence that two nuclei are not coupled to each other.
References
D. L. Turner (1985) Prog. NMR Spectrosc. 17, 281–358. 
D. E. Wemmer (1988) In Recent Advances in Organic NMR Spectroscopy (J. B. Lambert and R. Rittner, eds.), Norell Press, Landisville, New Jersey.