Filters/filtering noise

PCA can be used to filter noise from data sets. 

Audibility of the noise at the output. In the case where the signal component is not cancelled, the processed signal exhibits a band of filtered noise located around the sinusoidal component. It is clear that this phenomenon, if audible, is an important drawback of the method because it makes the remaining nuisance noise correlated with the signal, which was not the case for the original broad-band noise. 

Principal component regression and partial least squares are two widely used methods in the factor analysis category. PCR decomposes the matrix of calibration spectra into orthogonal principal components that best capture the variance in the data. These new variables eliminate redundant information and, by using a subset of these principal components, filter noise from the original data. With this compacted and simplified form of the data, equation (12.7) may be inverted to arrive at b. 

Phosphorus was monitored at 214.9nm (second order). The analog signal was taken out through the profile mode of a computer program. In order to filter noise, a 50k 2 resistor and 20 gF condenser were installed before the recording, giving an approximate time constant of Is. 

Figure 8 Dissociation of (a) glow discharge generated copper dimer ions using a filtered noise field results in (b) bare copper product ions.

DE Goeringer, KG Asamo, SA McLuckey, D Hoekman, SW Stiller. Filtered noise field signals for mass-selective accumulation of externally-formed ions in a quadrupole ion trap. Anal Chem 66 313—318, 1994. 

Informed by the technique of sines plus noise spectral modeling, we can now improve our sinusoidal additive synthesis model significantly by simply adding a filtered noise source as shown in Figure 6.13. 

Figure 6.13. Sinusoidal additive model with filtered noise added for spectral modeling synthesis.

The instrument used in these analyses was a modified version of the Finnigan ion trap mass spectrometer (ITMS) running ICMS software and coupled with a Teledyne HST-1000 filtered noise field system. The end caps of the IT were modified with larger apertures (5 mm) that were covered with spot-welded 90% pass grids. The instrument was operated in the negative-ion mode. 

Ion isolation was achieved using a filtered noise field applied to the end caps to achieve capture of a mass range of approximately 10 u centered on the ion of interest. The voltage of the field was adjusted such that unwanted ions were ejected, without unduly compromising the intensity of the ions of interest. 

The basic biopotential amplifier described above, along with the specific design considerations for each biopotential, can yield a signal acquisition of acceptable quality in most laboratory settings. In practice, however, further enhancements are always necessary to achieve acceptable clinical performance in novel applications. These enhancements include circuits for reducing electric interference, filtering noise, reduction of artifacts, electrical isolation of the amplifier, and electrical protection of the circuit against defibrillation shocks [9]. 

Filtered noise White noise that has been passed through a hlter. The power spectral density of hltered white noise has the same shape as the transfer function of the hlter. 

Equations (4) and (5) are not evaluated explicitly in the minimization program, but are fit using a combination of spline [17] methods, which provide stability, the ability to filter noise easily, and the flexibility to describe an arbitrarily shaped potential curve. Moreover, the final functional form is inexpensive to evaluate, making it amenable to global minimization. The initial step in our methodology is to fit the statistical pair data for each amino acid and for the density profile to Bezier splines [17]. In contrast to local representations such as cubic splines, the Bezier spline imposes global as well as local smoothness and hence effectively eliminates the random oscillatory behavior observed in our data. 

Filter noise - removing the points placed in imdesirable regions due to measurement errors, this can be done automatically ... 

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