By Frank Fahy, John Walker
Complicated purposes in Noise and Vibration provides remedies of acoustic and vibration phenomena including summaries of the newest wisdom, research and strategies at present to be had for facing functional difficulties.
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Extra resources for Advanced Applications in Acoustics, Noise and Vibration
In each frame, the spectrum of the filtered noise is shown as a dotted curve and the frequencies of the sinusoidal components are indicated by vertical dotted lines. 14a,b shows the results obtained from segment averaging. 14a) results in a heavily smoothed spectral estimate in which the two closely spaced sinusoids are not resolved and the heights and the depths of the resonance and anti-resonance are underestimated. The result of using a longer window in segment averaging is to improve the resolution (the closely spaced sinusoids are resolved) but there is a significant loss of smoothness.
This decomposition leads to a spectral estimate that is sharply peaked at the sinusoidal component frequencies. A widely used method is the so-called MUSIC (multiple signal classification) algorithm briefly described in this section following Vaseghi (1996). 86) Suppose N values of y n are known and the column vector yn contains the previous L > p samples of the sequence. 88) L−1 fP The P -dimensional vector space defined by the columns of S is referred to as the signal subspace. Any noise-free measurements xn span this subspace, which means that xn is formed as linear combination of the columns of S.
The estimates of the autocovariance function contain the effects of additive noise and data truncation. The first problem was considered by Ables (1974) who suggested the modification that the autocorrelation be constrained to pass close to measured values. The problem of data truncation amounts to a violation of the basic principle of data reduction. R. K. 66) we note that knowledge of R0 R p gives enough information to obtain the ai . 66) but note that the coefficient matrix is symmetrical and has a diagonal symmetry of the coefficients (elements on leading diagonals are equal).
Advanced Applications in Acoustics, Noise and Vibration by Frank Fahy, John Walker