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The Fourier transform NMR (nuclear magnetic resonance) spectroscopy is used widely at present as a noninvasive method in the structural analysis of macromolecules in organic chemistry and in the metabolic study of tissue and cells in biochemistry. We believe, however, that the Fourier transform is not adequate in the determination of the density distribution of the nucleus. The NMR signal contains essentially the relaxation (a kind of damping) phenomena, but the Fourier transform does not take this fact into consideration. Consequently, the obtained NNR spectrum is degraded both in intensity and resolution, providing apparent nucleus density distribution which is different from the true value. This paper proposes an estimation of the NNR spectrum, which positively takes the relaxation phenomenon into consideration. The method is derived by extending the Kalman filter to the complex stochastic system and applying the result to the NMR signal represented by the complex stochastic system. The proposed method is applied to the NMR signal of proton (114) obtained from mayonnaise in 2[T] static magnetic field. The result is compared with the NMR spectrum obtained by the Fourier transform, and it is shown that the resolution and the intensity are improved drastically. [ABSTRACT FROM AUTHOR]