http://link.springer.com/content/pdf/10.1007/978-3-642-61351-7_3.pdf

Mathematical Analysis of Random Noise-Conclusion

Spectral Theory of Random Actions on Dynamic Systems

Expressions for the Dual Input Describing Functions (DIDF's) of a two-state relay with hysteresis have been obtained by using an equivalent function generator for the non-linearity. These DIDF's were then applied to analyse the effects of sinusoidal input signals on the stability of a feedback system which includes the hysteretic relay. These results, as substantiated by simulator data, indicate that, besides the stabilizing effects, the presence of sinusoidal signals at the input of the particular system studied may produce dual mode operation over a. range of input amplitudes.

On the Stability of a Hysteretic System under Sinusoidal Excitation

A method of calculating the effects of interfacial roughness on the grazing-incidence reflectivity and transmissivity of a synthetic multilayer x-ray reflector (SMR) is developed; this method makes it possible to investigate the dependence of an SMR’s performance on the spatial-frequency content of the roughness profile. The roughness is modeled by a superposition of volume diffraction gratings that are described mathematically by using a coupled-wave approach. The coupled-wave equations for both the electric and magnetic fields are derived without invoking the usual slowly varying envelope approximation, and exact analytical solutions are obtained for unslanted gratings. The effects of individual gratings with different spatial periods are investigated for 1.5-keV x rays, and it is found that the performance of the SMR is affected most strongly by short-period gratings, whereas gratings with longer periods have relatively little effect. At higher energies, guided wave resonances occur for gratings with short periods, giving rise to singular behavior of the equations describing the system; this behavior is discussed in some detail. The theory of random functions provides methods for constructing the superposition of many gratings, each with a different spatial frequency, so that a randomly rough surface is modeled. The reflectances and transmittances of typical SMR’s designed for x rays of 1.5, 8, and 17 keV are calculated for rough interfaces with different power spectra, and the results are compared with those of similar calculations for an ideal SMR. It is shown that the resonance effects are inconsequential for power spectra that characterize the interfacial roughness that is expected to occur in the fabrication of a typical SMR. The effects on SMR performance of interpenetration of the multilayer constituents at the layer interfaces are also calculated by using a simple averaging model, and it is shown that for these energies such effects are dominant in comparison with those of boundary roughness.

Effects of interfacial defects on the performance of grazing-incidence synthetic multilayer reflectors for medium- and low-energy x rays

CHAPTER 6 – Analysis of Membrane Noise at Synaptic Junctions

Factors in the design of a transformer to be inserted between the thermocouple of an infra-red spectrometer and the input stage of an a.c. electronic amplifier are discussed. The principles evolved lead to a construction in which the effects of external interference are negligible, and the signal-to-noise ratio closely approaches a maximum.

http://iopscience.iop.org/article/10.1088/0950-7671/30/4/119/pdf

Mathematical Analysis of Random Noise-Conclusion

Citations

Spectral Theory of Random Actions on Dynamic Systems

On the Stability of a Hysteretic System under Sinusoidal Excitation

Effects of interfacial defects on the performance of grazing-incidence synthetic multilayer reflectors for medium- and low-energy x rays

CHAPTER 6 – Analysis of Membrane Noise at Synaptic Junctions

The design of thermocouple transformers for infra-red chopped beam systems

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