Transfer functions error analysis

In addition to the aforementioned slope and variance methods for estimating the dispersion parameter, it is possible to use transfer functions in the analysis of residence time distribution curves. This approach reduces the error in the variance approach that arises from the tails of the concentration versus time curves. These tails contribute significantly to the variance and can be responsible for significant errors in the determination of Q)L. 

Error Analysis and Quantification of Uncertainty. The error associated with paleolimnological inferences must be understood. Two sources of error worthy of special attention are the predictive models (transfer functions) developed to infer chemistry and inferences generated by using those equations with fossil samples in sediment strata. Much of the following discussion is based on the pioneering work reviewed by Sachs et al. (35) and by Birks et al. (17, 22), among others. We emphasize error analysis here because it is not covered in detail in most of the general review articles cited earlier. 

When time-domain errors are additive, Fourier analysis techniques provide statistical properties that are intrinsic to transfer-function measurements. 

Basic functional controls will include those in Table 11.19. Most of the values can be derived from a straightforward transfer function but several, particularly those determining maximum charge current, discharge current, and state-of-charge, will require careful scrutiny of the definition, calculation, and error analysis. 

Here Y z) is the speech, U z) is the source, V z) is the vocal tract and R z) is the radiation. Ideally, the transfer function H z) found by linear prediction analysis would be V(z), the vocal tract transfer function. In the course of doing this, we could then find U(z) and R z). In reality, in general H z) is a close approximation to F(z) but is not exactly the same. The main reason for this is that LP minimisation criterion means that the algorithm attempts to find the lowest error for the whole system, not just the vocal tract component. In fact, H z) is properly expressed as... 

Recall that Equation 13.18 is exactly the same as the linear prediction Equation 12.16, where = fli, 02,..., Op are the predictor coefficients and x[n] is the error signal e n. This shows that the result of linear prediction gives us the same type of transfer function as the serial formant synthesiser, and hence LP can produce exactly the same range of frequency responses as the serial formant S5mthesiser. The significance is of course that we can derive the linear prediction coefficients automatically fi om speech and don t have to make manual or perform potentially errorful automatic formant analysis. This is not however a solution to the formant estimation problem itself reversing the set of Equations 13.14 to 13.18 is not trivial, meaning that while we can accurately estimate the all-pole transfer function for arbitrary speech, we can t necessarily decompose this into individual formants. 

Numerical analysis and simulation of adaptronic systems can be performed in the time or in the frequency domain depending on the representation of the system in the state space or as a matrix of transfer functions. In addition to performance criteria, important goals are stability and robustness of an adaptronic system. In the case of adaptronic structures, performance criteria are often given in terms of allowable static and dynamic errors relating to structural shape if subjected to specified disturbances. Many applications also involve limits in energy consmnption and actuator stroke or force, which must be checked in time-history simulations. A comprehensive introduction on the different aspects and their interaction can be found in [14]. Current research in the field is for instance presented in [15] and [16]. 

The evolution of the fluorescence intensity of CD-St (at 357 nm) as a function of oxazine concentration contains information on the stability constant of the complex and on the energy transfer efficiency. In fact, the latter is directly related to the asymptotic value of the fluorescence intensity (corresponding to full complexation). After correction for the inner filter effect, data analysis provides the value of (2.4 + 0.1) X 10 for the association constant / = [(CD-St)2 oxazine]/[2CD-St] [oxazine]. Moreover, the asymptotic value of the fluorescence intensity is very close to zero within experimental error which means that the energy transfer efficiency is close to 1. However, a full characterization of these photoinduced processes requires time-resolved techniques (see below). 

---