Theory of stochastic NMR spectroscopy. Application of the ITÔ and Stratonovich calculus

Discrete analysis of stochastic NMR. I

“…The analysis in a later section of this work will show that this type of excitation causes undesirable spectral distortions as the RF excitation power is increased. This result will be used to explain discrepancies and artifacts in earlier results (9,17). A subsequent paper (Part II (18)) will analyze two new types of random RF excitations that do not exhibit such artifacts.…”

Multi-dimensional spectroscopy

“…table 1) [8,9]. Spectra a and b exhibit-a phase twisted 2D lineshape which is well known in standard 2D FT N.M.R.…”

“…From equations (1), (2) and (3) we thus obtain the following spectra The stochastic method has been applied by several authors for calculation of //1 [5][6][7][8][9] and only recently for the calculation of multi-dimensional spectra [2]. There are, in general, two different ways of arriving at nD spectra [1 ; 2 b, d].…”

Discrete analysis of stochastic NMR.II

“…[14] and [16] by solving the stochastic difference equation (Eq. [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).…”

“…In all previous stochastic NMR studies (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16), the RF excitation vector was assumed to lie along one axis in the rotating frame with the flip angle being a Gaussian white noise or a random binary sequence. The theoretical and experimental results presented in Part I {17) show that fixing the phase of the RF vector causes a notch artifact, a shift in the resonance offset and a non-uniform response across the spectrum.…”