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As a method to estimate the frequency spectrum, the discrete Fourier transform is employed widely, since a high-speed algorithm is available. However, the discrete Fourier transform has the following problems. The presence of noise is not considered, and the resolution of the frequency spectrum is determined uniquely by the sample duration. Other problems are that the sampling inter- val must be kept constant and the decay of the signal is not considered. This paper proposes a high-resolution frequency spectrum estimation where the complex Kalman filter is applied to the observed signal represented by the complex stochastic system, effectively utilizing the a priori knowledge of the signal source. The method is applied to the measured data and to the simulation, and it is demonstrated that a high-resolution frequency spectrum is obtained by suppressing the effect of the discrete approximation of the frequency component, and, when the frequency spectrum is concentrated, the resolution can be improved approximately by a factor of two, without iterating the measurement. It is shown also that the sampling interval can be set arbitrarily in the proposed method, and the noise and the decay can be considered. A theoretical discussion is made on the relation between the special case of the proposed method and the discrete Fourier transform. [ABSTRACT FROM AUTHOR]