NMR Processing: Convolution: Shifted Sine Bell - SINE, QSINE

Function:
 

 
The figure shows the continuous example FID after sinm with SSB = 1, SSB = 2, and SSB = 8; these are datasets fid/104, fid/105, and fid/106 in the download package.
 
Sine-bell multiplication multiplies the FID with a sinusoidal function with a period twice the acqusition time. The value of SSB determines the phase of the sinusoidal function and results in the following filter functions:

SSB	Result
0, 1	sine
2	cosine
>2	increasingly sine

Examples/Exercises:
 

	Click on the figure to see how sinm with SSB = 0 or SSB = 1 (sine) applied to the synthetic dataset synth/112 in the download package affects the spectrum. Note the resolution enhancement and apodisation at the expense of signal-to-noise ratio. Also, note the negative contributions.
	Click on the figure to see how sinm with SSB = 2 (cosine) applied to the synthetic dataset synth/113 in the download package affects the spectrum. Note the apodisation and slight increase of signal-to-noise ratio without significant loss in resolution.
	The apodization effect is also visible in this second example: A truncated FID shows after zero-filling and FT excessive "wiggles" in the spectrum (black, left). Application of a cosine filter results in apodization without significant broadening (red, right).
	SSB > 2: weighted mixture of both objectives.

Properties/Purpose:

• the resolution enhancement is only modest
• may result in negative wings of the peaks -> integration is hampered
• primarily used for 2D spectra, especially if the acquisition time is short and the FIDs truncated
• also used for 2D spectra to convert Lorentzian line shapes into something with less excessive wings; to that end, the squared sine bell version might be more useful

Literature:

• Hoffman, Levy, Progr. NMR Spectrosc. 1991, 23, 211; doi:10.1016/0079-6565(91)80005-M
• Lindon, Ferrige, Progr. NMR Spectrosc. 1980, 14, 27; doi:10.1016/0079-6565(80)80002-1
• Gassner, Jardetzky, Conover, J. Magn. Reson. 1978, 30, 141; doi:10.1016/0022-2364(78)90234-2
• Guéron, J. Magn. Reson. 1978, 30, 515; doi:10.1016/0022-2364(78)90277-9