As the penetration of renewable energy increases to a large scale and power electronic devices become widespread, power systems are becoming prone to synchronous oscillations (SO). This event has a major impact on the stability of the power grid. The recent research has been mainly concentrated on identifying the parameters of sub-synchronous oscillation. Sub/Super synchronous oscillations (Sub/Sup-SO) simultaneously occur, increasing the difficulty in accurately identify the parameters of SO. This work presents a novel method for parameter identification that effectively handles the Sub/Sup-SO components by utilizing the Rife-Vincent window and discrete Fourier transform (DFT) simultaneously. To mitigate the impact of spectral leakage and the fence effect of DFT, we integrate the tri-spectral interpolation algorithm with the Rife–Vincent window. We use the instantaneous data of the phasor measurement unit (PMU) to identify Sub/Sup-SO-related parameters (Sub/Sup-SO damping ratio, frequency, amplitude and phase). First, the spectrum of the Sub/Sup-SO signals is analyzed after incorporating the Rife-Vincent window, and the characteristics of the Sub/Sup-SO signal are determined. Then, the signal spectrum is identified using a three-point interpolation algorithm, and the damping ratio, amplitude, frequency, and phase of the Sub/Sup-SO signals are obtained. In addition, we consider the identification accuracy of the algorithm under various complex conditions, such as the effect of Sub/Sup-SO parameter variations on parameter identification in the presence of a non-nominal frequency and noise. The proposed algorithm accurately identifies the parameters of multiple Sub/Sup-SO components and two Sub-SO components that are in close proximity. Testing with synthetic and real data demonstrates that the proposed algorithm outperforms existing methods in terms of identification accuracy, identification bandwidth, and adaptability. •Sub/Sup-SO parameter identification is proposed via tri-spectral line interpolation.•This method obtains wide identification band range and high measurement accuracy.•Parameter identification is proposed for parameters containing Sub-SO and Sup-SO frequencies.•The deviation of parameter identification was less than 1 % in most cases.