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In damage detection, an important aspect is the accurate frequency evaluation which permits observing the modal parameter changes at the earliest stage. The frequency resolution improvement, achieved by extending the time interval of the analysis, is in the case of standard frequency estimation the key to increasing the accuracy of the study. This is not always possible due to the rapid decay of higher-order modes. Many methods to improve frequency readability are nowadays available in the literature, such as those increasing the spectral lines density or those based on several-point interpolation. We debate herein the limitations of the actual methods and introduce an advanced algorithm that uses for interpolation three peaks from three different spectra, achieved from the acquired signal that is stepwise cropped. Processing the signal in this way allows identifying minor natural frequency changes, thus allowing for the observation of damage occurrence in the earliest stage. The algorithm was successfully tested against generated and real signals.