Friday, 22 February 2008

Why aren’t Bruker FIDs time corrected?

Most of NMR has finally gone totally digital and is now routinely resorting to high-frequency ADC sampling at rates of several tens of MHz, with a tendency to ever higher sampling frequencies. Such a drastic oversampling has clear advantages in simplifying the front-end electronics. It has also many side benefits due to the fact that the subsequent down-conversion to low frequency range is done digitally and therefore theoretically artefact free. This includes perfect, calibration-free quadrature detection and drastic reduction of quantization noise. By the way, such techniques are routine in other areas of electronics (military, astronomy, audio, …); NMR is just a latecomer to this world.

High-frequency (HF) oversampling, however, has also some problems of its own. The digital decimation from the HF range to the audio range and the contextual digital filtering (a combination of CIC and FIR filters) need to be properly implemented in the hardware in order to be completely transparent to the User.

However, in the case of Bruker spectra a death time or group delay can be observed in the FID: it starts with very small values and then, after some points (usually between 60-80 points) the normal FID starts.

If a plain FT is applied to this FID, we will get a spectrum with a lot of wiggles in the baseline analogous to the convolution with a sinc function centred in the middle of the spectral window. This can be explained by recalling the time shift theorem of the Fourier Transform which says that if the time domain signal is shifted by n points, the frequency domain spectrum corresponds to the standard spectrum (when the FID has not been shifted) multiplied by exp(-i2*pi*w*n). In other words, we have introduced a very large first order phase correction in the spectrum. For example, if the FID is right shifted by 60 points (death time = 60 points), f-spectrum will exhibit a first order phase distortion of 60 * 360 = 21600 degrees.

In order to work around this problem, most NMR software packages read the decimation factor (and the DSP firmware version) from Bruker files and calculate the required phase correction. So far, so good.
However, the fact remains that Bruker FID’s are not time corrected. Evidently, Varian also uses oversampling and digital filtering and their FIDs are time corrected, that is, they start at time = 0. If the digital filter is known in advance, which is always the case, the group delay should be compensated in the spectrometer, therefore, in my opinion, this death time or group delay is a bug in the spectrometer. For this reason, and going back to the title of this article, any input given as to why Bruker FID’s are not time corrected, would be greatly appreciated.