Frequency domain noise analysis

The results of both experiments showed that the analysis in the frequency domain provides new technological possibilities of testing characteristics of austenitic steels. Using known phase-frequency characteristics of structural noises it is possible to construct algorithms for separation of useful signal from the defect, even through amplitude values of noise and signal are close in value. 

Research on the hearing process carried out by many people (see [Scharf, 1970]) led to a frequency analysis model of the human auditory system. The scale that the ear appears to use is called the critical band scale. The critical bands can be defined in various ways that lead to subdivisions of the frequency domain similar to the one shown in table 2.1. A critical band corresponds to both a constant distance on the cochlea and the bandwidth within which signal intensities are added to decide whether the combined signal exceeds a masked threshold or not. The frequency scale that is derived by mapping frequencies to critical band numbers is called the Bark scale. The critical band model is most useful for steady-state tones and noise. 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

Figure 9. FFT analysis of the sum of sine wave perturbation left side, no optimization right side, optimization of phases, (a) Perturbation voltage in the time domain, (b) Perturbation voltage in the frequency domain, (c) Complex plane plots of simulated impedance spectra with 5% noise added to the current response. Solid lines show response without noise.

Clearly, the final MDS diagram is partially dependent on the parameters of the noise imposed on the system. It is possible that frequency domain approaches to time series analysis [10] may help in a study of the role of frequency transfer functions in the control of chemical networks. We have assumed that all species involved in the mechanism may be identified and measured. For systems with many species this may be difficult. When there are missing species, CMC may still be performed on the measurable subset of species. The effects of the other species are subsumed into the correlations among the known species, and a consistent diagram can be constructed. The MDS diagram, then, may not be an obvious representation of the underlying mechanism. In fact, due... 

FTs are especially suitable if different frequency parts are present in the original signal, or if, for example, the ac mains frequency has to be removed. From spectral analysis in the frequency domain, important information about the type of noise can be derived, and as a consequence, the signal-to-noise ratio can be systematically improved. Shot noise is recognized by a uniform frequency spectrum. This is typical for thermal... 

To check vdiether the system is operating at a dose level at vdiich quantum noise is the largest component, the response function can be used to translate typical pixel values (in the unprocessed image) to a detector dose level. It is also possible to evaluate the noise components in the frequency domain using the Noise Power Spectra. However, these results are more difficult to interpret and for QC purposes the analysis in the spatial domain is sufficient (Ravaglia et al. 2009). 

In order to test the instrument and the data analysis procedures we made a number of experiments on dummy cells, for example the one shown in Fig.6. Here we made use of the possibility of time-domain averaging, the ac excitation was repeated 8 times and the data were averaged. The dummy cell was enclosed in a Faraday cage and the noise level was quite low, reducing the need for frequency-domain averaging, i.e., averaging of admittance data, after Fourier transformation and calculation of the admittance. 

Shaver JM, McGown LB (1996) Maximum entropy method for frequency domain fluorescence lifetime analysis. 1. Effects of frequency range and random noise. Anal Chem... 

Ramezanzadeh, B., Arman, S.Y., Mehdipour, M., et al., 2014. Analysis of electrochemical noise (ECN) data in time and frequency domain for comparison corrosion inhibition of some azole compounds on Cu in 1.0 M H2SO4 solution. Appl. Surf. Sci. 289, 129—140. 

The methods used for expressing the data fall into two categories, time domain techniques and frequency domain techniques. The two methods are related because frequency and time are the reciprocals of each other. The analysis technique influences the data requirements. Reference 9 provides a brief overview of the various mathematical methods and a multitude of additional references. Specialized transforms (Fourier) can be used to transfer information between the two domains. Time domain measures include the normal statistical measures such as mean, variance, third moment, skewness, fourth moment, kurto-sis, standard deviation, coefficient of variance, and root mean squEire eis well as an additional parameter, the ratio of the standard deviation to the root mean square vtJue of the current (when measuring current noise) used in place of the coefficient of variance because the mean could be zero. An additional time domain measure that can describe the degree of randonmess is the autocorrelation function of the voltage or current signal. The main frequency domain... 

This analysis demonstrates elearly that two-stage frequency conversion enables us to increase the seleetivity of our apparatus. It also makes it possible for us to reduce the and noise with the help of a very selective filter e.g., a ceramic filter centered at 10.7 MHz) inserted in between the two mixers. Figure 19 shows the distribution of different frequencies available in the frequency domain at the inputs and outputs of a double-mixer circuit. In order that the intervals do not overlap each other, an operating range of frequencies 500 kHz to 9 MHz has been chosen here. 

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