Hadamard NMR spectroscopy

Maximum length binary sequences (MLBSs) of length N = 2l-l, where I is a positive integer, have a perfectly flat power spectrum [77]. The deconvolution in Eq. (61) can be computed very efficiently by means of a fast Hadamard transform, and they have, for example, been employed for Hadamard NMR spectroscopy [78]. 

In a mixture containing a number of complexes at the same time, for example, a catalyst along the reaction pathway, HMBC spectra offer an easy way for signal assignment in ID spectra of sufficiently sensitive nuclei. However, as conventional HMBC experiments take up to 2h, fast reactions are not observable by this technique. Hadamard NMR spectroscopy was described to allow such experiments in the minute scale [15], when chemical shifts in the indirect dimension (e.g., Pt) are identified from preliminary experiments. 

Hadamard NMR spectroscopy [3] is based on the Hadamard Transform rather than the more conventional Fourier Transform. The NMR frequencies are encoded using the Hadamard matrices and multiply-selective frequency encoding pulses. Only the frequencies of interest are used at the encoding stage. Thus vast spectral regions that contain no interesting information can be excluded and the correlation spectra can be recorded much faster. Some prior knowledge about the peak positions in the indirectly detected dimensions is required for these experiments. 

Stochastic excitation with m sequences and the use of the Hadamard transformation have been investigated in NMR spectroscopy [Kail, Zie2] as well as in NMR imaging [Chal]. Processing of the nonlinear response to m sequences by Hadamard and Fourier transformation results in signal distortions reminiscent of noise, which are caused by the nonlinear parts of the response [B1U2]. 

Kaiser, R., Application of the Hadamard Transform to NMR Spectroscopy with Pseudonoise Excitation , J. Magn. Reson. 1974,15, 44—63. 

Structure determination of soluble proteins of moderate size (up to 30 kDa) by multinuclear multidimensional NMR spectroscopy is now fairly standard with well-established protocols. In the chapter NMR with Multiple Receivers, an acquisition scheme employing multiple receivers is described which allows for faster structure determination in small molecules. Further, recently employed fast acquisition schemes such as Hadamard spectroscopy, projection-reconstruction techniques, and reduced dimensionality experiments are explained. 

Time reduction in homonuclear spectra using Hadamard spectroscopy Time reduction in heteronuclear spectra using Hadamard spectroscopy GFT NMR experiments for resonance assignments... 

Keywords Hadamard spectroscopy Multidimensional NMR Multiple Parallel acquisition NMR Projection reconstruction... 

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