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Audio Filters

Audio Filters

Audio filters serve to exclude signals at frequencies greater than the spectral width.  The ideal filter would have no effect on signals within the spectral window (the “pass-band”), and would eliminate all frequencies outside it (the “stop-band”).  A sharp cut-off minimizes the amount of noise that folds back into the spectrum, maximizing the signal to noise ratio.  Real filters fall short of this ideal, and can be the source of phase, amplitude and baseline distortions.

The two most common types of filters used in NMR spectrometers are Bessel and Butterworth.  A Butterworth filter yields the flattest amplitude response in the pass-band with a sharp cut-off when entering the stop-band.  This gives the best integration, but its slower pulse response time leads to distortions of the first few points in the FID, causing baseline distortions.

A Bessel filter has more amplitude roll-off in the pass-band than a Butterworth filter, meaning that peaks near the edges of the spectral window are attenuated, resulting in inaccurate integration.  However, the better pulse response time of the Bessel filter causes less distortion of the early points in the FID and gives flatter baselines. 

In addition to the amplitude response in the pass-band and the response time, filters also distort the phase in the pass-band.  Bessel and Butterworth filters have typically been used in NMR because these distortions are of low order, and can be corrected with zero- and first-order phase correction.  Residual distortions can be observed as slightly out-of-phase peaks near the filter pass-band cut-off (near the ends of the spectrum), usually avoided by widening the spectral width so these distortions do not interfere with peaks of interest.  This type of phase distortion can have significant detrimental effects on NOESY spectra – see illustration.

In the course of providing technical support to NUTS customers, we receive sample data sets whose origins run the gamut of spectrometer models and manufacturers.   We have observed spectra with much more severe phase distortions than described above.  After phasing with the normal zero- and first-order correction, the remaining out-of-phase peaks are not observed merely at the extreme ends of the spectrum, but well into the spectral window.

In the spectrum of ethylbenzene below, note that the aromatic and methyl peaks are correctly phased, but TMS and methylene peaks have phase distortions of opposite sign. (The spectrum is shown with increased vertical scale so the phase irregularities are clearly visible).  It is not possible to phase all peaks simultaneously using zero- and first-order correction.  The distortion in this case is approximately 7 degrees, and is clearly sufficient to interfere with integration.  Note that both ends of the displayed integral are flat, meaning that the commonly employed “drift and tilt” integral adjustment cannot compensate.

Plots created by processing on the spectrometers often appear correctly phased, leading us to surmise that the spectrometer software is doing something in addition to “traditionalphase correction.  The obvious first attempt at resolving this is addition of a second-order term to the phase correction.

The spectrum above resulted from zero- and first-order phase correction of –121 and 37 degrees, respectively.  The pivot point is the downfield edge of the spectrum.

The same spectrum is shown below after phase correction using zero-, first- and second-order values of –155, 185 and –130 degrees, respectively.  It appears that addition of one more term is sufficient to yield an acceptable spectrum.

It appears that in the search for ever-increasing signal-to-noise, sharper cut-off filters, which cause undesired phase shifts in the pass-band, are being used.  As with many other aspects of NMR hardware, this is a trade-off, and each spectroscopist needs to be aware of the choices being made. 

Last updated: 01/22/2003