Noise excitation

For signals represented approximately by the output of a linear system driven by periodic pulse or noise excitations (e.g., human speech or woodwind instruments), the sine-wave model of the previous section can be refined by imposing a source/filter representation on the sine waves components. Within this framework, the notion of phase coherence [Quatieri and McAulay, 1989] is introduced, becoming the basis... 

Terms of this equation are defined similarly to those for the LSAR interpolator of section 4.3.3, with subscript V referring to the autoregressive process for the noise pulses. Av is a diagonal matrix whose mth diagonal element Xy m is the variance of the with noise excitation component, i.e. 

Poirot et al., 1988] Poirot, G., Rodet, X., and Depalle, P. (1988). Diphone sound synthesis based on spectral envelopes and harmonic/noise excitation functions. Proc. of International Computer Music Conference, Koln. 

Impulse-response and transfer functions can be measured not only by pulse excitation, but also by excitation with monochromatic, continuous waves (CW), and with continuous noise or stochastic excitation. In general, the transformation executed by the system can be described by an expansion of the acquiired response signal in a series of convolutions of the impulse-response functions with different powers of the excitation [Marl, Schl]. Given the excitation and response functions, the impulse-response functions can be retrieved by deconvolution of the signals. For white noise excitation, deconvolution is equivalent to cross-correlation [Leel]. 

Therefore, for measurements with noise excitation, the linear transfer function K (co) (cf. Fig. 4,1.1 (a)) is obtained after cross-correlation of excitation and response and subsequent Fourier transformation of the cross-correlation function Ci (tr) (cf. Fig. 4.1.1 (c)). 

Nonlinear cross-correlation of the system response y(t) (4.2.4) with different powers of a white-noise excitation x(t) yields multi-dimensional impulse-response functions hn (tTl,. . . , CTn),... 

They differ from the kernels it (ti, ..., r ) of the Volterra series only by a faster signal decay with increasing time arguments [Bliil]. For coinciding time arguments the crosscorrelation function is the sum of the n-dimensional impulse-response function h with the impulse-response functions hm of lower orders m < n. The stochastic impulse-response functions h are the kernels of an expansion of the system response y(t) similar to the Volterra series (4.2.4) but with functionals orthogonalized for white-noise excitation x t) [Bliil, Marl, Leel, Schl], This expansion is known by the name Wiener series, and the h are referred to as Wiener kernels. 

Fig. 6.4.1 [Blul] In imaging with noise excitation the spin density convolved by a localization function can be retrieved by linear cross-correlation of the system response with a function of the space coordinate r = (x, y, z ) and the time delay

Fig. 6.4.2 (a) Timing diagram for imaging with noise excitation and oscillating gradients. The... 

A single-degree-of-freedom (SDOF) system is subjected to zero-mean stationary white noise excitation with spectral intensity Spo = 0.0048 s. The mass, damping coefficient and stiffness are taken to be Af = 1.0 kg, C = 0.4ar N s/m, and K = (4 r) N/m so that the natural frequency and damping ratio of the system are 2.0 Hz and 5.0%, respectively. Its velocity is sampled at a rate of 100 Hz for 10 s. To generate the time history of the velocity measurement, 10% of the rms noise is superimposed onto the velocity time history, i.e., the root-mean-square (rms) of the measurement noise is equal to 10% of the rms value of the noise-free velocity of... 

The second example uses a ten-story shear-building model. It has equal floor mass and interstory stiffness distributed over all stories. The building is subjected to base acceleration adequately modeled by stationary Gaussian white noise excitation with spectral intensity... 

Although the above formulation was presented for displacement time history, it can be easily modified for velocity or acceleration measurements. In this case the right hand side of Equations (3.4) or (3.17) can be modified with the corresponding expressions for velocity or acceleration. Of course, the case of relative acceleration with white noise excitation is not realistic since the response variance is infinity. However, the absolute acceleration measurements can be considered for ground excitation. Another choice is to utilize a band-limited excitation model. 

Proppe, C. Exact stationary probability density functions fo" nonlinear systems under Poisson white noise excitation, bitemational Journal of NrmlinearMechanics 38(4) (2003), 557-564. 

Liao, M.-Y. Zax, D.B. Analysis of signal-to-noise ratios for noise excitation of quadmpolar nuclear spins in zero field. J. Phys. Chem. 1996, 100. 1483-1487. 

MFCC synthesis is a technique which attempts to S3mthesise from a representation that we use because of its statistical modelling properties. A completely accurate S3mthesis from this is not possible, but it is possible to perform fairly accurate vocal tract filter reconstruction. Basic techniques use an impulse/noise excitation method, while more advanced techniques attempt a complex parameterisation of the source. 

The testing procedure comprises two types of tests. The first raie is a low level white noise test to obtain the main dynamic characteristics of the wall (natural modes and frequencies, damping ratio). This test lasts about 3 min, to reach a stationary vibration state. A random white noise excitation with frequency content between 1 and 100 Hz and at Root-Mean-Square (RMS) level of about 0.1 g is generated using an Advantest R9211C Spectmm Analyser. 

Detailed evaluation of the load transfer mechanism and of the contact length was also presented. The identification of the natural vibration modes under low level white noise excitation raises the question of the accuracy of the values of the shear modulus usually suggested in the main reference documents, this modulus seeming to be significantly overestimated for the studied type of masonry. 

Based on the method illustrated in Figure 5, resonance frequencies calculated for seven White Noise excitations are shown in Figure 6. Firstly, it can been seen that, the resonance frequency of soft rock model (1 model) is smaller than that of hard rock model (2 model). Then another observation is that, as test goes on (along with the increasing excitation intensity), the resonance frequency of two model slopes decreases. The sharp drop begins in White 5 excitation, which indicates a sudden change of the internal structure of the model slope, when the excitation intensity increases up to 0.5 g. 

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