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Due to the discrete nature of the saddle coils for the active feedback control of the plasma instabilities, the emergence of the sideband modes is inevitable. In the Keda Torus eXperiment (KTX), the edge Mirnov coils are unevenly distributed on the inner surface of the vacuum vessel to suppress the sideband modes. These arrays of the Mirnov coils are used for the feedback control system of KTX. They are also used for the magnetohydrodynamics (MHD) mode identification, which is a fundamental and significant method to distinguish and describe the plasma instabilities. A set of suitable MHD mode analysis methods has been utilized to complete the mode detection, including the spatial discrete Fourier transform (SDFT) method, the singular value decomposition (SVD) method and the Lomb periodogram method. These methods can obtain comprehensive mode information of the plasma instabilities and their results can be used as the feedback of the feedback control system. These methods have been successfully applied to detect and characterize an impulsive mode of ($m = 1$ , $n = 0$) and rotating modes of ($m = 2$ , 3, 4, $n = 1$) in the tokamak plasma of KTX, while the matrix decomposition technique is not applicable for KTX. [ABSTRACT FROM AUTHOR]