Short-time transformers

Improving the properties of the short-time transform. Another interesting area of research deals with the design of the short-time transform. It is striking to see that while many efforts have been dedicated to the study of advanced suppression rules, little has been done concerning the analysis part of the noise reduction-system. 

The result of the noise suppression rule can always be interpreted as the application of a real gain (1 ip, Qk) to each bin of the short-time transform X(p, Qk) of the noisy signal. Usually, this gain corresponds to an attenuation , ie. lies between 0 and 1. For most suppression rules, G(p,Qk) depends only on the power level of the noisy signal measured at the same bin X (p, Qk) 2 and on an estimate of the power of the noise at the frequency 0, Pv(Qk) = E V(p, Qk) 2 (which does not depend on the time index p because of the noise stationarity). In the following, the ratio Q p, Qk) = X(p, Qk) 2 /Pv(Qf. ) will be referred to as the relative signal level. Note... 

Consequences of the random nature of the attenuation. In the previous section we deliberately left apart a major problem the fact that the attenuation is a random quantity. The randomness of the attenuation comes from the fact that it is (in general) determined as a function of the relative signal level which in turn involves the short-time transform of the noisy signal. This aspect plays a key role in STSA because the relative signal level is estimated by the periodogram (at least in the STFT case) characterized by a very high variance. 

Dembo and Malah, 1988] Dembo, A. and Malah, D. (1988). Signal synthesis from modified discrete short-time transform. IEEE Trans. Acoust., Speech, Signal Processing, ASSP-36(2) 168-181. 

Since the transformer will be in the circuit for only 15 to 20 seconds, the approximate short-time rating of the transformer can be considered to be 10-15% of its continuous rating. The manufacturer of the auto transformer would be a better judge to suggest the most appropriate rating of the transformer, based on the tapping and starting period of the motor. 

Note The above example is only for a general reference. The CDF of the transformer, for the short-time rating, should be increased writh the starting time and the number of starts per hour. Refer to the transformer manufacturer for a more appropriate selection. 

Note With the availability of modern circuit breakers with higher short-time ratings of 65 kA/80 kA/100 kA, it is now possible to use even larger transformers up to 2500 kVA, depending upon their other merits. 

This is not material in voltage transformers, as neither the voltage measuring instruments nor the protective relays will carry any inrush current during a switching operation or a fault. No short-time rating is thus assigned to such transformers. 

Refer to Figures 15.8 and 15.9. These transformers are quite different from a measuring or a protection transformer, particularly in terms of accuracy and short-time VA ratings. They are installed to feed power to the control or the auxiliary devices/components of a... 

Table 15.11 Maximum short-time factors obtainable economically corresponding to rated output, accuracy class, accuracy limit factor and rated short-time for wound primary current transformers...

As discussed in Section 13.4.1(5). these sections are under the cumulative influence of two pow er sources and may be tested for a higher short-time rating, which would be the algebraic sum of the two fault levels, one of the generator and the other of the generator transformer as noted in Table I 3.8. Also refer to Figures 31,1 and 13.18 for more clarity. 

For the tap-offs, connecting a UAT through the main bus section between the generator and the generator transformer, however, as discussed above, the momentary peak current will depend upon the short-time rating of such tap-offs. The likely ratings are noted in Table 13.8. 

Both time-related failure rates and demand-related failure rates can apply to and be reported for many pieces of equipment. Both types of rates are included in some of the data tables in Chapter 5. If a piece of equipment is in continuous service, such as a transformer, the failure rate is dominated by time-related stresses compared to demand-related stresses. Other failure rates may be dominated by demands. Take a piece of wire and repeatedly bend it. With each bend its probability of catastrophic failure increases. In a relatively short time, if the bending is continued, the wire will fail. On the other hand, the same wire could be installed in a manner that would prevent mechanical bending demands. In this case, the occurrence of catastrophic wire breakage would be remote. In the first instance, the failure rate is dominated by demand stresses and in the second by time-related stresses, such as corrosion. 

When dry material or a slurry has been filled, "pickling" is required, which means that the plate is stored in sulfuric acid for a short time. The material is soaked by the acid and transformed, at least partly, into lead sulfate (PbS04), as in the pastemixing process (Section 4.4.2.1). When minium is used, during the "pickling" process lead dioxide is also formed according to Eq. (4). 

Its poles are determined to any order of by expansion of M. However, even in the lowest order in the inverse Laplace transformation, which restores the time kinetics of Kemni, keeps all powers to Jf (t/xj. This is why the theory expounded in the preceding section described the long-time kinetics of the process, while the conventional time-dependent perturbation theory of Dirac [121] holds only in a short time interval after interaction has been switched on. By keeping terms of higher order in i, we describe the whole time evolution to a better accuracy. 

It was demonstrated in Chapter 6 that impact theory is able to describe qualitatively the main features of the drastic transformations of gas-phase spectra into liquid ones for the case of a linear molecule. The corresponding NMR projection of spectral collapse is also reproduced qualitatively. Does this reflect any pronounced physical mechanism of molecular dynamics In particular, can molecular rotation in dense media be thought of as free during short time intervals, interrupted by much shorter collisions ... 

Greatly enhanced sensitivity with very short measuring time is the major advantage of PFT (pulse Fourier transform) experiments. In the CW (continuous wave) experiment, the radiofrequency sweep excites nuclei of different Larmor frequencies, one by one. For example, 500 s may be required for excitation over a 1-KHz range, while in a PFT experiment a single pulse can simultaneously excite the nuclei over 1-KHz range in only 250 jits. The PFT experiment therefore requires much less time than the CW NMR experiment, due to the short time required for acquisition of FID signals. Short-lived unstable molecules can only be studied by PFT NMR. 

Successful combination of a chromatographic procedure for separating and isolating additive components with an on-line method for obtaining the IR spectrum enables detailed compositional and structural information to be obtained in a relatively short time frame, as shown in the case of additives in PP [501], and of a plasticiser (DEHP) and an aromatic phenyl phosphate flame retardant in a PVC fabric [502], RPLC-TSP-FTIR with diffuse reflectance detection has been used for dye analysis [512], The HPLC-separated components were deposited as a series of concentrated spots on a moving tape. HPLC-TSP-FTIR has analysed polystyrene samples [513,514], The LC Transform has also been employed for the identification of a stain in carpet yarn [515] and a contaminant in a multiwire cable [516], HPLC-FTIR can be used to maintain consistency of raw materials or to characterise a performance difference. 

The macroscopic long-time behavior of dense polymer liquids exhibits drastic changes if permanent cross-links are introduced in the system [75-77], Due to the presence of junctions the flow properties are suppressed and the viscoelastic liquid is transformed into a viscoelastic solid. This is contrary to the short-time behavior, which appears very similar in non-cross-linked and crosslinked polymer systems. 

A solid compound X is transformed into Y when it is heated at 75 °C. A sample of X that is quickly heated to 90 °C for a very short time (with no significant decomposition) and then quenched to room temperature is later found to be converted to Y at a rate that is 2.5 times that of a sample that has had no prior heating when both are heated at 75 °C for a long period of time. Explain these observations. 

Milton et al. [1.136] used this methods and refer to it as manometric temperature measurement. They used times of pressure rises of up to 30 s. During this time, the ice temperature will increase, mainly due to continued heat flow. Therefore, an equation has been developed to transform the experimental pressure data, including three other corrections, into the true vapor pressure of the ice. If the valve is closed for only a very short time, < 3 s, and the pressure is measured and documented 60 to 100 times/s, these data can be recorded as shown in Fig. 1.78.1. The automatic pressure rise measurements (1) can then be plotted... 

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