Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 42

As shown in section 1.5.4 and Equation (1.164) the expected value of the Fourier transform of an ensemble of signals of infinite duration is given by:

It is helpful to convert this into an expression for a finite number of signals of finite duration. Usually, there is one signal of time length T available that is separated into M partitions of length T_w. So the estimate would be:

(1.167)

In Bendat and Piersol (1980) it is shown that the relative error is given by:

(1.168)

So for a given time length T the more we average, the more precise is the spectral estimate, but we sacrifice spectral resolution against statistical precision.

Figure 1.23 Sketch of a single-input–single-output system. Source: Alexander Peiffer.