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Purpose - The purpose of this paper is to present a symmetrical method to extract smooth signal from linear mixtures in the frequency domain; with experimentations, the method is thereafter evaluated. Design/methodology/approach - The Second-order Frequency Identification (SOFI) algorithm has been presented to retrieve baseband signals which have inactive bands and different bandwidths in the frequency domain. However, the SOFI method will bring about accumulative error, therefore an improved method is proposed in this paper by using symmetric extraction mode. In contrast to the SOFI algorithm, the ISOFI method can extract simultaneously the signal with the highest degree of smoothness and the signal with the lowest degree of smoothness. This means that the signals are not extracted one by one; instead, they are extracted in parallel. Experimental results in both noise-free and noisy scenarios verified that the proposed method has a significant improvement compared with the SOFI algorithm. Findings - An improved SOFI (ISOFI) method is proposed to reduce the accumulated error encountered in the SOFI algorithm. In the proposed method, the symmetric mode is utilized to extract in parallel the signals with different smooth degrees. Experimental results demonstrated that the ISOFI has a higher accuracy and lower accumulated error compared to the original algorithm. Originality/value - The paper demonstrates use of the symmetric extraction mode to overcome the disadvantage of accumulated errors existing in the SOFI algorithm. [ABSTRACT FROM AUTHOR]