Polynomial analysis

Table I Comparison of Results Between the Guinier Analysis and the Polynomial Analysis... 

Gulnler vs. Polynomial Analysis. The values obtained from... 

Namely, the polynomial analysis has higher valued COD S, where a value of 1 means a perfect fit, and all the data from the slice are used. For example, In the case of the sample molded at 285 C and air quenched, the Gulnler Is 1.43 pm, with a COD of 0.861 from 50 data points. In contrast the polynomial analysis yields an of 1.66 pro, with a COD of 0.991 using 129 data points. In fact a key advantage of this method Is that little. If any, data must be disregarded to yield meaningful results. 

POLYMATH polynomial analysis. The second, third, fourth, and fifth columns of the processed data in Table E5-I.3 are plotted in Figure E5-1.3 to determine the reaction order and specific reaction rate. 

Section 10.4 fully described the relationship between the time domain difference equations and the z-domain transfer function of a LTI filter. For first order filters, the coefficients are directly interpretable, for example as the rate of decay in an exponential. For higher order filters this becomes more difficult, and while the coefficients a/ and bk fully describe the filter, they are somewhat hard to interpret (for example, it was not obvious how the coefficients produced the waveforms in Figure 10.15). We can however use polynomial analysis to produce a more easily interpretable form of the transfer function. 

We will now show how polynomial analysis can be applied to the transfer function. A polynomial defined in terms the complex variable z takes on just the same form as when defined... 

We will now show how polynomial analysis can be applied to the transfer function. A polynomial defined in terms of the complex variable z takes on just the same form as when defined in terms ofx. The z form is actually less misleading, because in general the roots will be complex (e.g. /(z) = z + z - 0.5 has roots 0.5 + 0.5J and 0.5 - 0.5J.). The transfer function is defined in terms of negative powers of z - we can convert a normal polynomial into one in negative powers by multiplying ly z. So a second-order polynomial is... 

Despite the tricky polynomial analysis, we need to make some key observations here. First, it is important to notice that the r coordinate is scaled according to Z and n as, so even though the... 

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