2001 digital signal processing techniques 1 5 to

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Unformatted text preview: ate forms of random excitation focus on eliminating the source of leakage by customizing the random signal to match the requirements of fast Fourier transform (FFT) that is used in converting from the time to frequency domain. The FFT requires that the time domain signal must either be totally observed in the observation period (T) or be periodic in the observation period (T). For leakage free FRF measurements, all of the input and output signals must match one of these two requirements. Burst random excitation is an attempt to match the first requirement; pseudo and periodic random excitations are attempts to match the second requirement. 5.3.1 Excitation Assumptions The primary assumption concerning the excitation of a linear structure is that the excitation is observable. Whenever the excitation is measured, this assumption simply implies that the measured characteristic properly describes the actual input characteristics. For the case of multiple inputs, the different inputs must often be uncorrelated for the computational procedures (5-38) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + to yield a solution. In most cases this means only that the multiple inputs must not be perfectly correlated at any frequency. As long as the excitation is measured, the validity of these limited assumptions can be evaluated. Currently, there are a number of techniques that can be used to estimate modal characteristics from response measurements with no measurement of the excitation. If this approach is used, the excitation assumptions are much more imposing. Obviously, if the excitation is not measured, estimates of modal scaling (modal mass, modal A, residues, etc.) cannot be generated. Even under the assumption that the estimation of these parameters is not required, all of these techniques have one further restriction: an assumption has to be made concerning the characteristics of the excitation of the system. Usually, one assumes that the autospectrum of the excitation signal is sufficiently smooth over the frequency interval of interest. In particular, the following assumptions about the excitation signal can be used: • The excitation is impulsive. The autospectrum of a short pulse (time duration much smaller than the period of the greatest frequency of interest) is nearly uniform, or constant in amplitude, and largely independent of the shape of the pulse. The excitation is white noise. White noise has an autospectrum that is uniform over the bandwidth of the signal. The excitation signal is a step. A step signal has an autospectrum that decreases in amplitude in proportion to the reciprocal of frequency. The step signal can be viewed as the integral of an impulsive signal. There is no excitation. This is called the free response or free decay situation. The structure is excited to a condition of nonzero displacement, or nonzero velocity, or both. Then the excitation is removed, and the response is measured during free decay. This kind of resp...
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