Filter width

Box-Car) averaging with a box width (filter width, window) in the range 1 < W < iV W = 1 just connects the points, while W = N calculates the overall Xmean- The mean for each box will be displayed as a horizontal line. 

As a rule of thumb, Otto [8] suggested three main guidelines to select the most appropriate filter (i) around 95% of the noise is filtered in just one application, so single smoothing is often sufficient, (ii) the filter width should correspond to the full width at half-maximum of a peak and (iii) the filter width should be small if the height rather than the area is used. 

Figure 2 - Left IF analysis, using a 100 cm 1 Gaussian filter (solid) (other filter widths gave similar results). The sliding window FFT results are shown for comparison (squares). The inset illustrates the exponential decay of the v7 mode. Right FFT of the IF showing a large peak near 50 cm 1. The resolution of this plot is fundamentally limited by the decay of the v7 mode.

To obtain an accurate absorption spectrum, and preserve the true shape of the spectrum, a filter width of less than 5.0 nm is recommended. This filter width is easily obtained with modem spectrophotometers. 

The filter is moved along the time series or spectrum, each datapoint being replaced successively by the corresponding filtered datapoint. The optimal filter depends on the noise distribution and signal width. It is best to experiment with a number of different filter widths. 

A solution of 18.5 mg (0.08 mmol) of (3a, 8a7 ,9a7 )-3a,4,6,7,8,8a,9.9a-octahydro-9,8-dimethyl-3-methylene-naphtho[2,3-h]furan-2(3.ff)-one and 2 mg of methylene blue in 10 mL of ethanol is photooxygenated for 8h at 22 + 2 °C. using a constant oxygen flow and a medium-pressure 400-W mercury lamp with a 1-cm filter width and filtering through a 2% aq sodium nitrite solution. The solvent is then evaporated in vacuo and the residue chromatographed (silica gel, hexane/EtOAc 4 1) to give an oil yield 12 mg (57%) [[Pg.444]

Error in the determination of the position of a simulated, asymmetrical reflection (without noise) at 29 = 20° and with 0.17° half width (W). Top With minimum of 2nd derivative calculated with a polynomial of 2nd/3rd order. Middle With zero of the 1st derivative calculated with a polynomial of 3rd/4th. order (best result as long as the filter width does not appreciably surpass the half width) Bottom With zero of 1st derivative with a polynomial of lst/2nd order. (After Huang, 1988, or Huang and Parrish, 1984. )... 

There are also differing viewpoints on the role of the numerical stress in LES. The simplest view is that the LES equations should be solved accurately. That is, for a given filter width, A, the grid spacing h should be chosen to be sufficiently small so that the numerical stress, a , is negligible... 

For finite difference and finite volume discretizations using the box filter, the filter width, A, yields ... 

These stresses are similar to the classical Reynolds stresses that result from time or ensemble averaging of the advection fluxes, but differ in that they are consequences of a spatial averaging and go to zero if the filter width A goes to zero. 

Figure 3.13. The effect of analogue filters on signal-to-noise. Spectrum (a) was recorded with the correct filter width (1.25 times the spectral width), and (b) and (c) with it increased 10- and 100-fold respectively.

Note set filter width to a smaller value for a smoother curve with... 

Figure 3.1 Moving-average filter for computing the first and last aver-a filter width of 2m +1 = 3, that is, age. Original signal value, o fil-m = 1. Note that for the extreme tered signal value, points, no filtered data can be calculated, since they are needed for...

After applying the moving-average filter, the data contain less noise. In the case of structured data, the filter width has to be chosen such that the structure of the data, for example, of a peak, is not distorted. 

Figure 3.2 demonstrates the filtering of raw data by using a 5-point moving-average filter (curve 1). In this example, the filter width of 5 points leads already to the distortion of peaks. This effect is enhanced if the filter width is further increased as demonstrated here for an 11-point filter (Figure 3.2, curve 2). The appropriate choice of the filter width is discussed as follows. 

Too large a filter width decreases the original height of a peak and leads simultaneously to its broadening. 

After deciding on the filter width, the filtered value for the Ath data point is calculated by... 

The filter coefficients Cj are tabulated in Table 3.1 for different filter widths. Figure 3.2, curve 3, demonstrates the effect of a Savitzky-Golay filter with a filter width of 5 points applied to the raw data. Compared to the 5-point moving-average filter, the obviously better fit can be seen. 

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