## 1 Introduction
In 2005, the British scholar [PERSON] proposed the LMD on the basis of EMD to deal with non-stationary signals in a self-adaptive way [7]. LMD uses an iterative approach to decompose a signal into a set of product functions (PFs). Each of the PF is the product of an envelope signal and a pure frequency-modulation signal. LMD has a capacity of time-frequency analysis and demodulation analysis for non-stationary signals. Compared with EMD, LMD solved the problem of over-envelope and under-envelope and suppresses the end effect to a certain extent. Scholars have already proved the superiority in LMD [11] and improved the algorithm. LMD has been applied widely to the fault diagnosis of rolling bearing. Through spectrum analysis, various frequency components contained in the vibration signal can be clearly viewed. However, when performing Fourier transform of signals on computers, which can only process discrete data, it is unavoidable to suffer spectrum leakage and barrier effect [12; 13] because of time domain truncation and limited samples. This will lead to errors in frequency, amplitude, and phase, and eventually, affect the extraction accuracy [14]. The frequency resolution \(\Delta w\) of a signal has relations to the sampling number \(N\) and the sampling frequency \(F_{s}\), based on the formula \(\Delta w=F_{s}/N\). Therefore, the longer the signal length is, the better the frequency resolution can be reached. However, this leads to an increase in the cost and time of computer calculation. It is always needed to analyze signals as fast as possible and reduce the calculating time under the premise of ensuring calculation accuracy, especially in online real-time monitoring application. Therefore, it is considered to correct the spectrum based on less sampling number of raw data. This method can make the spectrum close to the true value to the maximum extent in the case of ensuring the extraction accuracy of fault frequency. Accurate frequency estimation is one of the most basic problems in the field of signal processing. The amplitude of frequency reflects the strength of signal energy and its accurate estimation is of great value. Since the 1970s, some scholars have devoted themselves to the research of discrete spectrum correction theory and proposed a number of methods to correct the error of spectrum analysis. The task of spectrum correction is to calculate the frequency, amplitude and phase accurately using the information provided by discrete spectrum analysis. In order to get the exact position of the frequency, the most direct method is to interpolate values between the amplitude of the main line and several neighboring lines and then calculate the precise frequency position according to an interpolation formula. Such kind of method is called the interpolation spectrum correction methods, such as the ratio method [15; 16], the energy center method [17; 18; 19], the Candan method [20] and its improved version [21], the Macloed method [22], and the Jacobsen method [23]. These methods are based on the traditional spectrum analysis of fast Fourier transformation (FFT). Therefore, the inherent spectrum leakage will affect the accuracy of spectrum correction. In addition, the accuracy of spectrum correction also suffers from errors of the inter-spectral interference and noise. Spectrum leakage and barrier effect cause the interaction of the various frequencies and then produces errors. Windowing can reduce the spectral interference from each frequency and improve the correction accuracy. Another important impact factor of interpolation spectrum correction methods is the interference from the noise. When there is no noise in the signal, the interpolation spectrum correction methods are accurate, which can correct the frequency, amplitude and phase accurately. However, the correction accuracy decreases when there is a noise, especially when the signal-to-noise ratio (SNR) is small. The spectrum of the noise is always broadband, and the spectrum of the signal is usually narrowband.