NMR Processing: Convolution

 

Semantics: Although this section is headed convolution, the actual process is a multiplication of the time domain signal, the FID, with an appropriate filter function. One can achieve the same result in the frequency domain, then it is a real convolution, but, as you may have guessed, the process is more convoluted ;-)

Purpose: The objective of a multiplication of the FID with a filter function might be any or all of the following points:

• improvement of the signal-to-noise ratio
• improvement of resolution
• change in lineshape (e.g., from Lorentzian to Gaussian for 2D spectra)
• removal of experimental artefacts (e.g. apodisation)

Exercises: in order to illustrate the effect of the filter functions, I am providing two example data sets for download; they will be used with each of the filter functions:
 

		a synthetic FID without decay to demonstrate the shape of the applied filter function; the untreated FID/spectrum is fid/100.
		an artificially generated synthetic FID to demonstrate the effect of the applied filter function; the spectrum consists of two signals with an integration ratio of 50:50: a 10 Hz broad singlet at 4 ppm and a multiplet (tdd, 7 Hz, 1 Hz, 0.25 Hz) at 6 ppm, broadened by 1 Hz. In addition, 1 % of noise has been added. The untreated FID/spectrum is synth/101. (Without noise, it is actually possible to recover the small 0.25 Hz splitting!)

Filter functions: In TopSpin, the following filter functions have been implemented. Those functions with the "redish" background are those that I have used most often. Click on any of the pictures to obtain more information on this function.

	Exponential decay: EM
	Gauss bell: GM
	Shifted sine bell: SINE, QSINE
	Trapezoidal: TRAP
	Traficante: TRAF, TRAFS
	Sinc: SINC, QSINC