Identification of nuclear magnetic resonance (NMR) spin systems by non-linear adaptive filtering

Presents two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. In the first method, the nonlinear relationship between excitation (input) and system response (output) is described by truncated discrete Volterra series. First-, second- and third-order kernels of this series are calculated by employing the least mean square (LMS) algorithm with variable adaptive gains. Three parallel filters then model the NMR spin system so that the system output is no more than simple convolution products between filters, coefficients and combinations of the input signal. In the second method, the nonlinear input-output relationship is governed by a recursive nonlinear difference equation with constant coefficients. The variable-gain LMS algorithm is used again to calculate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analysed and compared. It is shown that our methods permit a simple identification of NMR spin systems and that they may be useful for the real implementation of optimum NMR signal detection and processing systems, as well as for accurate NMR signal spectral analysis