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The paper is aimed at improving the efficiency of signal processing for intermode fiber-optic interferometers. To do so, we propose to use the MUSIC algorithm. It is shown that the use of traditional methods for estimating the number of signal components leads to poor operation of the MUSIC algorithm when applied to intermode interference signals. The possibility of using machine learning to estimate the number of signal components was investigated. The advantage of the proposed signal processing for demodulating the signals of an intermode interferometer over the Fourier transform has been experimentally demonstrated on the examples of simultaneous strain and curvature measurement, as well as pulse-wave sensing. The results can be also applied for processing signals of other optical-fiber sensors and multi-component signals of a different nature, for example, optical coherence tomography and radar signals.