information for NMR spin systems from a set of N complex excitation-response data pairs is presented. The spin system is excited
with RF pulses, the flip angles and phases of which are represented by a discrete stochastic process. The relation between complex excitation and complex response is analyzed by perturbation the-The n-dimensional time functions k n (t 1 , . . . , t n ) are called ory and is shown to be a special functional series. The 1D spectrum kernels and describe the system characteristics.
is obtained by Fourier transformation of the complex cross correla-
The Volterra series is of limited practical value since there tion between response and excitation time functions in first order.
is no general way to estimate the Volterra kernels from a A 2D spectrum of the E. COSY type is derived with a new algogiven excitation-response data set. If, however, the excitarithm which performs the complex cross correlation of response tion x(t) is Gaussian white noise of zero mean, the sumwith excitation in third order, the 3D Fourier transformation, and the selection of the 2D diagonal spectral plane ( v 1 , v 2 , v 3 ร
0v 2 ) mands of the Volterra series can be orthogonalized. The in an integrated, rapid manner. It is shown that the complex result is the Wiener series which up to the third order reads approach yields 2D quadrature detection. The validity of this new as approach is demonstrated with simulation calculations.