Time domain definitions for finite bandwidth white noise, and filtered white noise, are detailed and are of pedagogical value. The associated power spectral density and autocorrelation functions are given. The potential Gaussianity of white noise is noted.
Articles you may be interested inDevice reliability study of high gate electric field effects in AlGaN/GaN high electron mobility transistors using low frequency noise spectroscopy An ultralow noise transimpedance amplifier with a gain of 10 10 , a bandwidth greater than 10 kHz, and an input equivalent noise power spectral density of 1.7ϫ10 Ϫ30 A 2 /Hz ͑single sided͒ for frequencies less than 10 Hz and a level of 5ϫ10 Ϫ30 A 2 /Hz at 1 kHz is described. This level of performance is achieved with standard electronic devices, rather than batteries, powering the amplifier. Very good agreement between theoretical and experimental noise measurements is achieved due to careful measurement and modeling of the significant noise sources. It is shown that the noise level of the 10 10 ⍀ feedback resistor increases with frequency and contributes a significant level of noise for frequencies in the kHz frequency range. The usefulness of the amplifier is demonstrated through measurement of the noise of a HgCdTe planar photovoltaic 3-5 m mid-wavelength infrared detector cooled to 80 and 120 K.
In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series approximation. It is shown that a spline based series approximation to an integral yields, in general, a higher accuracy for a set order of approximation than a dual Taylor series, a Taylor series and an antiderivative series. A spline based series for an integral has many applications and indicative examples are detailed. These include a series for the exponential function, which coincides with a Padé series, new series for the logarithm function as well as new series for integral defined functions such as the Fresnel Sine integral function. It is shown that these series are more accurate and have larger regions of convergence than corresponding Taylor series. The spline based series for an integral can be used to define algorithms for highly accurate approximations for the logarithm function, the exponential function, rational numbers to a fractional power and the inverse sine, inverse cosine and inverse tangent functions. These algorithms are used to establish highly accurate approximations for π and Catalan’s constant. The use of sub-intervals allows the region of convergence for an integral approximation to be extended.
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