Discrete analysis of stochastic NMR. I

Three dimensional nuclear magnetic resonance spectroscopic imaging of sodium ions using stochastic excitation and oscillating gradients

“…There is also systematic noise in the reconstruction, which arises from the random nature of the excitation [34].…”

“…The sign of the phase along each axis is selected by a bit output from a separate MLS generator. This modulation scheme was examined in detail by Wong [14], and found to be quite effective for stochastic NMR. MLS's are attractive because they are very easily generated in simple hardware using a shift register, or in software using bit manipulation operations.…”

Discrete analysis of stochastic NMR.II

“…This implies that they have zero mean values. For the case of non-zero mean excitation see reference (19). The second condition is that ax(n) and ay(n) are white: a2 (a;(n) a;(m)) = 2 bnm where j = x or y, a 2 = (a(n)T a(n)) is the average excitation power and bnm is.…”

“…As in conventional FT-NMR, Eq. [19] shows that the measurement noise tepn is inversely proportional to the number of data points, N, used in the reconstruction. It will be shown in the next section that the systematic noise power is also inversely proportional to N, so that increasing N does not change the relative amount of the systematic and measurement noise power.…”

“…[1][2][3][4][5]) for a specific excitation sequence. The results cannot be expressed in simple closed forms, but can be calculated numerically (19). The numerical calculation has been done for random flip angle excitation using Gaussian white noise and random quadrature excitation using random binary sequences.…”