Noise inverse frequency

The primary sources of noise in this region are classified as thermal or Johnson noise together with shot noise due to the particulate nature of photons and electrons. Additionally there is non-equilibrium or inverse frequency noise, often termed pink noise to distinguish it from the other two that have a uniform white noise frequency distribution. 

Inverse frequency noise has a power spectrum corresponding to the formula ... 

Crowell discovered a variety of effects numerically, including modified Rabi flopping, which has an inverse frequency dependence similar to that observed in the solid state in reciprocal noise [73]. The latter is also explained by Crowell [17] using a non-Abelian model. A variety of other effects of RFR on the quantum electrodynamical level was also reported numerically [17]. The overall result is that the occurrence, classically, of the B V> field means that there is a quantum electrodynamical Hamiltonian generated by the classical term proportional to 3 2. This induces transitional behavior because it contributes to the dynamics of probability amplitudes [17]. The Hamiltonian is a quartic potential where the value of determines the value of the potential. The latter has two minima one where B = 0 and the other for a finite value of the B i) field, corresponding to states that are invariants of the Lagrangian but not of the vacuum. 

Figure 4 Combining smoothing and differentiating in the frequency domain (a) the truncation filter to remove high frequency, noise sigruds and provide the first derivative (b) the transform of the spectrum form Figure 3(a) after application of the filter (c) the resultingfirst derivative spectrum from the inverse transform...

FIGURE 5-12 Digilal filtering with the Fourier transform (a) noisy spectral peak, (b) ihe frequency-domain spectrum of part (a) resulting from the Fourier transformation, (c) (ow-pass digital-filter function, (d) product of part fb) and part (c). (e) the inverse Fourier transform of part (d) with most of the high-frequency noise removed. 

The noise (ripple) is a kind of a jitter of Eq which throws around and destroys some ions otherwise passing the gap. This effectively constrains the gap, so in curved FAIMS increasing the noise sharpens the peaks, improving the resolving power R (Figure 4.21a and b). As more ions are destroyed, the sensitivity drops. Like with oscillations due to E(t) by Equation 3.43, the magnitude of wobble due to Ec perturbation is proportional to its amplitude and inverse frequency. Hence greater... 

Weighting can be imposed on noise readings, which corresponds to the inverse of the equal-loudness contours. If this weighting is used, all readings that are numerically equal will sound equally loud, regardless of frequency. 

Instrumental transmission (convolution by the PSF) is always a smoothing process whereas noise is usually non-negligible at high frequencies, the noise amplification problem therefore always arises in deconvolution. This is termed as ill-conditioning in inverse problem theory. 

Figure 2b and Eq. (10) show that the Wiener inverse-filter is close to the direct inverse-hlter for frequencies of high signal-to-noise ratio (SNR), but is strongly attenuated where the SNR is poor ... 

Ideally, any procedure for signal enhancement should be preceded by a characterization of the noise and the deterministic part of the signal. Spectrum (a) in Fig. 40.18 is the power spectrum of white noise which contains all frequencies with approximately the same power. Examples of white noise are shot noise in photomultiplier tubes and thermal noise occurring in resistors. In spectrum (b), the power (and thus the magnitude of the Fourier coefficients) is inversely proportional to the frequency (amplitude 1/v). This type of noise is often called 1//... 

The SIN defined by Equation 7.6 for a given NMR resonance is proportional to the square of the nuclear precession frequency (mo, rad/s), the magnitude of the transverse magnetic field (Bi) induced in the RE coil per unit current (/), the number of spins per unit volume (Ns), the sample volume (Vs), and a scaling constant that accounts for magnetic field inhomogeneities. The SIN is inversely proportional to the noise generated in the RE receiver and by the sample (Vnoise) as defined by the Nyquist theorem,... 

Let us not forget, at this point, that well-designed bandpass filtering can only prevent the appearance of solution frequencies totally rejected by z(eo). Noise in the frequency range that we wish to restore cannot be thus rejected, however. In the limit of simple inverse filtering we find that... 

The second constraint restricted the Fourier spectrum. This was an ad hoc filter that was applied to the entire inverse-filtered spectrum to bring the magnitudes of the high-frequency values of the spectrum (which were mostly noise) to values much closer to the correctly restored ones. This procedure resulted in observable improvement over the inverse-filtered estimate for infrared lines obtained from grating spectroscopy (Howard, 1982). 

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