In this study, we revisited nuclear magnetic relaxation of (1)H in water at very low Larmor frequencies that has been studied intensively in earlier years. We make use of the recently developed superconducting quantum interference device based ultra-low field NMR technique, which enables much easier access to the longitudinal spin-lattice relaxation time T(1) and the transversal spin-spin relaxation time T(2) below several kHz than traditional field cycling methods. Our data reproduce and complement the earlier results, in that they corroborate the finding of an exchange process with a correlation time of about 0.34 ms at room temperature which can be attributed to the migration of hydronium and hydroxyl ions in neutral water via hydrogen bridges. The corresponding relaxation process is driven by the interaction of the protons with (17)O and contributes to the T(1) and the T(2) relaxation rate by about 0.12 s(-1). In addition, we found evidence of a very slow exchange process at about 100 Hz that has hitherto not been reported.
Cosine-sum windows with minimum sidelobes (minimum sidelobe windows) have good properties in terms of peak sidelobe level (PSL) and equivalent noise bandwidth (ENBW). But neighboring windows (the number of coefficients differ by one) have quite large PSL differences. If, for a special data analysis, the PSL of the window should not exceed a given value, then often windows with a much lower PSL than specified have to be used. Due to increasing ENBW in the case of decreasing PSL, this leads, amongst others, to more uncertainty in the determination of signal amplitudes.This article describes how to design modified minimum sidelobe windows which have similar properties to minimum sidelobe windows for a given PSL. Their ENBW were, however, traded off against PSL. Using such a design, windows can be created exactly for a given value of PSL at small ENBW. The adjustment of the asymptotic decay of the sidelobes and the determination of the window coefficients will be done without solving linear systems of equations to avoid known numerical problems. By using the proposed algorithm, more than 6000 windows with PSL values greater than -350 dB were created. The parameters and coefficients of selected windows will be given in the article.
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