By Frank Fahy, John Walker
Complex purposes in Noise and Vibration provides remedies of acoustic and vibration phenomena including summaries of the most recent wisdom, research and strategies at the moment on hand for facing useful difficulties.
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Extra resources for Advanced Applications in Acoustics, Noise and Vibration
A common approach is to regard x n as having arisen from appropriate operations on white noise u n (defined by E u n u k = 0, n = k and E u n 2 = 2 . We shall restrict our discussions to linear operations and stationary time series. 53) k=− When expressed in this form, it is perhaps not apparent that u n is an ‘input’ and x n an ‘output’. The reason for choosing this structure for the model is that we are trying to find some linear relationship between past, present and future values of the time series x n which reduces it to white noise.
In practice, the eigenvectors uk are calculated from an estimate of correlation matrix Ryy , so that only approximate orthogonality is attained due to the finite data length, leading to peaks, rather than singularities, appearing in the MUSIC spectrum. The MUSIC spectrum peaks at frequencies where there are likely to be sinusoidal components and is not a measure of power within a filter band. So it is inappropriate to regard it as a true spectral estimate, but rather as a method for identifying frequencies of sinusoids in noise.
It should be noted that this cross-term lies midway between the two auto-terms and it oscillates. The magnitude of the cross-term is twice that of the auto-terms (assuming A1 = A2 . The cross-term oscillates more rapidly, further apart the auto-terms. These properties of cross-terms are not exclusive to this example; they apply to a much wider class of signals. Much research effort in the field of time–frequency analysis has centred on the problem of reducing the cross-terms introduced by the WVD (Cohen 1989; Hlawatsch and Boudreaux-Bartels 1992).
Advanced Applications in Acoustics, Noise and Vibration by Frank Fahy, John Walker