The method of separating harmonic signals from multiplicative and additive noises

This paper focuses on the extraction of a harmonic signal from multiplicative and additive noises. A method is proposed in two stages: (1) to square the original discrete time series, which includes both signals and noises, and form a new time series. By this means, the multiplicative noise is converted to additive noise; and (2) to filter out the noise by using existing noise removal schemes. With a large amount of simulation, experimental results demonstrated the efficiency and effectiveness of this newly developed method in terms of Signal-to-Noise Ratio (SNR) and other criteria. From the experiment, it is also found that: the two kinds of noises affect the SNR differently. In general, the SNR is not influenced by multiplicative Gaussian noise regardless of its variance. However, if both kinds of noise exist, the SNR decreases with the incensement of the Variance of Additive Noise to Multiplicative Noise Ratio (VAMNR). This analysis is also supported by simulation work.