バイスペクトル分析による雑音に埋もれた周期信号の分離

抄録

A method is proposed for separating a desired periodic signal, i.e., for detecting its direction and estimating its Fourier components, from other periodic signals scattered in a field contaminated with Gaussian random noise.
The auto-bispectrum of a signal composed of a periodic signal plus Gaussian random noise preserves the information about both relative amplitudes and relative phases of the components of the periodic signal, while it cancels out the over-all phase shift caused by the time delay of the signal.
The cross-bispectrum of the two waveforms observed at two different points, on the other hand, preserves information about the inter-regional phase shift of each component.
These characteristics are clarified and used as the basis, of the method. The direction of the desired signal is measured by means of the auto- and cross-bispectra of the observed waveforms. The Fourier components of the desired signal are estimated by using the auto-bispectrum, and the desired signal can be reconstructed by means of Fourier synthesis.
An example of reconstruction is shown, and the estimation errors of the program used are discussed. The estimated value varies because of finite averaging, and the distribution of the deviation from the true value can be regarded as almost normal. The relative error diminishes almost linearly as the signal/noise ratio increases when the signal/noise ratio is larger than 1.0.