Hypercomplex Fourier transform

The signals S+ and S are now amplitude-modulated as a function of tp, therefore, a double hypercomplex Fourier transformation of these data, following for instance the States-Haberkom-Ruben procedure, yields a pure-absorption 2D spectrum with sign discrimination in the 12 j dimension [169]. 

Note that these expressions are the same as those in Eq. 10.11, without the —1 factor from the change in detector phase. The signals may be processed by a very useful method, introduced as the hypercomplex Fourier transform method and popularized as the States method (or SHR method, as described by States, Haberkorn, and Ruben107). The two signals in Eq. 10.14 (with relaxation terms restored) are separately Fourier transformed with respect to t2 to give... 

Figure 7.3.1.7 A 13C-decoupled HMQC spectrum of 54 mM chloroquine diphosphate in D2O acquired with an inverse detection microcoil probe. The 740-nl F0bs contained 40 nmol (13 jig) of chloroquine. The data, 32 transients per slice, 1024 x 128 (x2, hypercomplex) points, were acquired in 3.6h. The data were zero-filled to 256 points in the 13C dimension. A 40° shifted sinebell function was applied, followed by Gaussian multiplication prior to Fourier transformation...

NOESY was performed at 32 °C on a VXR-500 spectrometer operating at a proton frequency of 500 MHz. The protein was dissolved in 20 mM sodium phosphate, pH 7.5 (direct pH meter reading), 100 mM NaCl, 5 mM DTT in D2O. The protein concentration was 2 mM. The data was acquired in the hypercomplex mode with a mixing time of 150 ms (Jeener et al., 1979 Macura Ernst,1980). The spectral width was 7200 Hz in both dimensions. 2048 complex points in the t2 dimension and 256 complex points in the tl dimension were acquired. 96 transients were collected for each FID. Data processing was performed on a Sun Sparc 10 station using VNMR software from Varian. The time domain data were zero-filled once and multiplied by shifted sinebell or Gaussian functions before Fourier transformation in both dimensions. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d4. 

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