0 Chen, J Shaka, AJ Mandelshtam, VA 2000 J. Magn. Reson 147 129?137 A new numerical expression, called the regularized resolvent transform (RRT), is presented. RRT is a direct transformation of the truncated time-domain data into a frequency-domain spectrum and is suitable for high-resolution spectral estimation of multidimensional time signals. One of its forms, under the condition that the signal consists only of a finite sum of damped sinusoids, turns out to be equivalent to the exact infinite time discrete Fourier transformation. RRT naturally emerges from the filter diagonalization method, although no diagonalization is required. In RRT the spectrum at each frequency s is expressed in terms of the resolvent R(s)