Multi-sine

Impedance transfer functions may be determined through use of an input signal containing more than a single frequency. Such signals may be a tailored multi-sine... 

The third approach is to use experimental methods to assess the error structure. Independent identification of error structure is the preferred approach, but even minor nonstationarity between repeated measurements introduces a significant bias error in the estimation of the stocheistic variance. Dygas emd Breiter report on the use of intermediate results from a frequency-response analyzer to estimate the variance of real and imaginary components of the impedance. Their approach allows assessment of the variance of the stochastic component without the need for replicate experiments. The drawback is that their approach cannot be used to assess bias errors and is specific to a particular commercial impedance instrumentation. Van Gheem et have proposed a structured multi-sine... 

Fokker Bond Tester. An ultrasonic inspection technique commonly used for aircraft structures is based on ultrasonic spectroscopy [2]. Commercially available instruments (bond testers) used for this test operate on the principle of mechanical resonance in a multi-layer structure. A piezoelectric probe shown in Figure 3b, excited by a variable frequency sine signal is placed on the surface of the inspected structure. A frequency spectrum in the range of some tens of kHz to several MHz is acquired by the instrument, see Figure 3a. 

The use of multi-funetional teams also enables eoneurrent engineering, sinee all the team members are aware of the effeet of their funetional input to the projeet on other areas, as diseussed earlier. The team are able to plan aetivities that may be earried out in parallel. While sometimes obtaining reasonable results, this approaeh often faees a number of obstaeles (Towner, 1994) ... 

Data analysis in phase fluorometry requires knowledge of the sine and cosine of the Fourier transforms of the b-pulse response. This of course is not a problem for the most common case of multi-exponential decays (see above), but in some cases the Fourier transforms may not have analytical expressions, and numerical calculations of the relevant integrals are then necessary. 

The method of strueture analysis developed by the Soviet group was based on the kinematieal approximation that ED intensity is directly related (proportional) to the square of structure factor amplitudes. The same method had also been applied by Cowley in Melbourne for solving a few structures. In 1957 Cowley and Moodie introdueed the -beam dynamical diffraction theory to the seattering of eleetrons by atoms and crystals. This theory provided the basis of multi-sliee ealeulations whieh enabled the simulation of dynamieal intensities of eleetron diffraetion patterns, and later electron microscope images. The theory showed that if dynamical scattering is signifieant, intensities of eleetron diffraetion are usually not related to strueture faetors in a simple way. Sinee that day, the fear of dynamical effects has hampered efforts to analyze struetures by eleetron diffraction. 

Sinusoid Pure periodic sine and cosine inputs seldom occur in real chemical engineering systems. However, the response of systems to this kind of forcing function (called thefrequency response of the system) is of great practical importance, as we show in our Chinese lessons (Part Three) and in multi-variable processes (Part Four). 

Reboiler pump - Centrifugal sine le or multi-stage pump ... 

Stolwijk s model [19] has made mueh advaneement compared to previous multi-node models as it is not only eapable of ealeulating the spatial temperature distribution for eaeh node, but also has improved the representation of the human s circulatory system sinee the blood circulation is the most important function of human body. This model has been validated with the good agreements between the experimental and predicted results of most cases. The limitation of this model is that it cannot be used for die highly non-uniform environmental situations caused from the negligence of spatial tissue temperature gradients. 

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