SWT based separation method for periodic signal with non-stationary noise and its application in EMF

Periodic signal superimposed with strong non-stationary noise that follows an approximate 1/f distribution cannot be easily separated with traditional signal processing methods. Using the stationary wavelet transform, the noisy signal is decomposed into wavelet coefficients including both the detail and approximate coefficients. According to its periodic feature, detail coefficients on each scale are extracted to form the same-phase sequences which consist of coefficients with the same phase values in each cycle. The amplitude probability distribution functions of same-phase sequences follow approximate Gaussian distribution. Therefore, noise in the same-phase sequences can be removed with the non-linear median filter and moving average filter. Since non-stationary noise follows approximate 1/f distribution, the approximate coefficients on the lowest frequency level have strong non-stationary property. Due to spectrum leakage of different frequency sections, the leakage signal components are superimposed on the approximate coefficients. Three different filtering methods are proposed to process the approximate coefficients in order to extract the useful signal components and to reconstruct the periodic signal accurately. Finally the proposed method is used to process the output signal of electromagnetic flowmeter during slurry flow measurement under different slurry concentrations and different flow rates. Results show that the proposed method is effective in the separation of periodic signal and strong non-stationary noise which follows the approximate 1/f distribution.