Filter Gauss

As we have commented in Section 4.1, for wavelengths close to the central value, the filter response is very similar to the Gauss filter for wavelengths far from the central value, the filter response is similar to a 3 order Bessel filter with less out band attenuation. Both of them have a linear phase characteristic, which means a constant group delay. These simulations are in agreement with experimental measurements shown in (Parker et al.., 1998). 

Figure 4, Triplet EPR spectra of ZnTCP ( -10 ) in Cn Cl-CII OH recorded at 10 K before (solid line) and after (dotted line) addition of KCl ( S x 10 ). Microwave power 0.5 mW, field modulation 20 gauss (100 kHz), excitation with square wave modulated (13 Hz) light from an Xe high pressure arc (1000 W) passed through a CuSO heat filter.

Fig. 4. Two-dimensional (2D) spectra of cyclo(Pro-Gly), 10 mM in 70/30 volume/volume DMSO/H2O mixture at CLio/27r = 500 MHz and T = 263 K. (A) TCX SY, t = 55 ms. (B) NOESY, Tm = 300 ms. (C) ROESY, = 300 ms, B, = 5 kHz. (D) T-ROESY, Tin = 300 ms, Bi = 10 kHz. Contours are plotted in the exponential mode with the increment of 1.41. Thus, a peak doubles its intensity every two contours. All spectra are recorded with 1024 data points, 8 scans per ti increment, 512 fi increments repetition time was 1.3 s and 90 = 8 ps 512x512 time domain data set was zero filled up to 1024 x 1024 data points, filtered by Lorentz to Gauss transformation in u>2 domain (GB = 0.03 LB = -3) and 80° skewed sin" in u), yielding a 2D Fourier transformation 1024 x 1024 data points real spectrum. (Continued on subsequent pages)...

SlMl.dat Section 1.4 Five data sets of 200 points each generated by SIM-GAUSS the deterministic time series sine wave, saw tooth, base line, GC-peak, and step function have stochastic (normally distributed) noise superimposed use with SMOOTH to test different filter functions (filer type, window). A comparison between the (residual) standard deviations obtained using SMOOTH respectively HISTO (or MSD) demonstrates that the straight application of the Mean/SD concept to a fundamentally unstable signal gives the wrong impression. 

The aim of the signal analysis in the MErKoFer project was to determine significant deviations of the various signals (i.e., process and other recorded values) from their stable state. Of course, care had to be taken of noise, oscillations, and similar issues. Several methods where therefore applied and evaluated. Partially, Gauss or median filters were used for preprocessing. 

Fig. 8. Wavelength dependence of radical formation in polypropylene. Irradiations were carried out at —196° C in nitrogen atmosphere by applying a series of color glass filters a UV-35 filter (>325mg), for 29min b UV-33 filter (>300mg), for 21min cUV-31 filter (> 275 mg), for 20 min d UV-29 filter (>255 mg), for 18 min e UV-27 filter (>227 mg), for 18 min f UV-25 filter (>205 mg), for 22 min and g no filter, for 18 min. The separation between two Mn++ peaks is 86.7 gauss. The arrow mark shows a signal due to color centers induced in the quartz sample tube by irradiation. [J. Polymer Sci B 10, 139 (1972), Fig. 1]...

Figure 6. ESR spectra for sample containing 20 mole % acetonitrile in methyltetrahydro-furan after y-irradiation for 28 minutes at a dose rate of 2.9 X 1017 e.v. gram 1 min. 1. Sample at 77°K. during and after irradiation. A After gamma irradiation. B Immediately after bleaching with 1 kwatt W lamp using Corning filter No. 2030. Arrow represents time when lamp was turned on. Scan rate was 100 gauss per minute, response time 0.3 sec. C Spectrum 27 minutes after start of photobleach-ing. Microwave power is 0.01 mwatt in each case...

Figure II. ESR spectra of y-irradiated sample containing 1.4 mole % (CHS)S CBr and 15 mole % CHSCN in MTHF (dose 8.9 X 101 e.v. gram 1). A after y-irradiation. B after photobleaching with 1-kwatt W lamp using Corning Filter No. 2030 ( >640 n.m.). Vertical line (left) represents point at which the lamp was turned on. Scan rate 100 gauss per minute, y-lrradiation and subsequent ESR measurements at 77° K. Microwave power 0.01 mwatt...

Resolution of overlapping electrochem. peaks with Kalman filtering TITFIT, a comprehensive program, Newton-Gauss-Marquardt method Calcn. using [H+] as independent and [B4] as dependent variable using pocket calculators... 

Last but not least, digital filter functions (e. g., of Butterworth, Chebychew or Gauss) have sometimes been used for derivative algorithms [120]. In this connection, it must be signalized that it is also possible, of course, to differentiate a sum of approximating polynomials, as was performed in the previous chapter (see Sec. 2.3.4). 

Arasaratnam I et al (2007) Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proc IEEE 95 953-977... 

Jia B et al (2011) Sparse Gauss-Hermite quadrature filter with application to spacecraft attitude estimation. J Guidance Control Dyn 34 367-379... 

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