Noise power, mean

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

Noise is characterized by the time dependence of noise amplitude A. The measured value of A (the instantaneous value of potential or current) depends to some extent on the time resolution of the measuring device (its frequency bandwidth A/). Since noise always is a signal of alternating sign, its intensity is characterized in terms of the mean square of amplitude, A, over the frequency range A/, and is called (somewhat unfortunately) noise power. The Fourier transform of the experimental time dependence of noise intensity leads to the frequency dependence of noise intensity. In the literature these curves became known as PSD (power spectral density) plots. 

We run Monte Carlo simulations to examine the performance of the sensor selection algorithm based on the maximization of mutual information for the distributed data fusion architecture. We examine two scenarios first is the sparser one, which consists of 50 sensors which are randomly deployed in the 200 m x 200 m area. The second is a denser scenario in which 100 sensors are deployed in the same area. All data points in the graphs represent the means of ten runs. A target moves in the area according to the process model described in Section 4. We utilize the Neyman-Pearson detector [20, 30] with a = 0.05, L = 100, r) = 2, 2-dB antenna gain, -30-dB sensor transmission power and -6-dB noise power. 

There are several ways of detecting peaks in such noisy signals. The Wiener-Hopf filter minimizes the expectation value of the noise power spectrum and may be used to optimally smooth the original noisy profile [19]. An alternative approach described by Hindeleh and Johnson employs knowledge of the peak shape. It synthesizes a simulated diffraction profile from peaks of known width and shape, for all possible peak amplitudes and positions, and selects that combination of peaks that minimizes the mean square error between the synthesized and measured profiles [20], This procedure is illustrated... 

Fig. 9.96 (a) Mach-Zehnder interferometer with variable phase delay (p realized by an optical wedge, (b) Detected mean intensity (I) measured at / = 0, and phase-independent photon noise power density, measured at / = 10 MHz with and without input intensity Iq... 

If the incident laser beam in Fig. 9.96a is blocked, the mean intensity (/) becomes zero. However, the measured noise power density Pn(/) does not go to zero but approaches a lower limit po that is attributed to the zero-point fluctuations of the vacuum field, which is also present in a dark room. The interferometer in Fig. 9.96a has two inputs the coherent light field and a second field, which, for a dark input part, is the vacuum field. Because the fluctuations of these two inputs are uncorrelated, their noise powers add. Increasing the input intensity Iq will increase the signal-to-noise-ratio... 

If the frequency spectrum 1(f) of the detector signals is measured with a spectrum analyzer at sufficiently high frequencies /, where the technical noise is negligible, one obtains a noise power spectrum Pn(/), which is essentially independent of the phase 0 (Fig. 14.62b), but depends only on the number of photons entering the interferometer. It is proportional to /N. It is surprising that the noise power density Pn(f) of each detector is independent of the phase 0. This can be understood as follows the intensity fluctuations, because of the statistical emission of photons, are uncorrelated in the two partial beams. Although the mean intensities I ) and I2) depend on 0, their fluctuations do not The detected noise power pn oc Va shows the same noise level pn oc for the minimum of 7(0) as for the maximum (Fig. 14.62b). 

Figure 7-9 Linear plots of measured noise power against PVC mass flow at specified values of mean transport velocity (King, 1973). Reproduced with permission of BHRA Fluid Engr.

A drawback of ZF is that nulling out the interference without considering the noise can boost up the noise power significantly, which in turn results in performance degradation. To solve this, MMSE minimizes the mean squared-error, i.e. /(W) = E (x-a ) (x-a), with respect to W [13], [14],... 

The first far-infrared LMR spectra were recorded by using Golay cells. These have the advantage of room temperature operation and are easy to use, but their response is slow and hence only low modulation frequencies (approximately 10-100 Hz) can be used. A further gain in sensitivity was realized by use of a helium-cooled Ge bolometer the much faster response of the bolometer allows much higher modulation frequencies ( 1 kHz), and this, together with the lower noise equivalent power, means that the sensitivity is limited mainly by inherent noise in the laser source. By far the most commonly encountered far-infrared detectors are helium-cooled photoresistors (Ge B, Ge In, Ge Ga, Ge As, nIn Sb, etc.) modulation frequencies of up to hundreds of kHz can be used. 

The output from gravitational wave detectors is generally time series data that provide a direct measure of the strain on the detector. Extraction of the gravitational wave signal is frustrated by noise which limits the sensitivity of the instrument. If the calibrated strain signal from a given detector is h(t), the detector sensitivity can be expressed in terms of the mean square instrumental noise per unit frequency. Specifically, the noise power spectral density of the instrumental strain noise is... 

When measuring the noise level, i.e. the limiting mean sound power level in dB for airborne noise emitted by a machine, reference may be made to the following lEC and ISO publications ... 

Each fan has a unique set of characteristics which are normally defined by means of a fan curve produced by the manufacturer which specifies the relationship between airflow, pressure generation, power input, efficiency and noise level (see Figure 28.1). For geometrically similar fans, the performance can be predicted for other sizes, speeds, gas densities, etc. from one fan curve using the fan laws set out below. 

Except for the impulse at the origin representing d.c. power and arising from the fact that the vacuum tube current has a nonzero mean value. We shall neglect this mean value m the following discussion, and concentrate only on the time-varying part of the noise. 

The phase spectrum 0(n) is defined as 0(n) = arctan(A(n)/B(n)). One can prove that for a symmetrical peak the ratio of the real and imaginary coefficients is constant, which means that all cosine and sine functions are in phase. It is important to note that the Fourier coefficients A(n) and B(n) can be regenerated from the power spectrum P(n) using the phase information. Phase information can be applied to distinguish frequencies corresponding to the signal and noise, because the phases of the noise frequencies randomly oscillate. 

---