# A Characterization for Windowed Fourier Orthonormal Basis by Liu Y.M.

By Liu Y.M.

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**Extra resources for A Characterization for Windowed Fourier Orthonormal Basis with Compact Support**

**Example text**

R;- {R;, = V400 - '{4 = 18. Thus for the scintillation counter and for the proportional counter V 1, 600 - '{40 = 33. 7 therefore the scintillation counter is the better option. B Since T= T,. + Tb substitution for Tb in terms of T,. /Rb will give an expression for Tp in terms of VR,! Rb and T. 158 1 100 . C Fmallye%=Vl48· 33 . 245% 29 QUESTION 12 Count rate differences with Geiger and proportional counters A silicon specimen is being examined using nickel filtered Cu Ka radia- · tion. The intensities of two reflections are measured with a Geiger-MUller counter and the following counting rates obtained: Geiger-MUller counter Peak A PeakB 1,400 c/s 200 c/s However, when the measurements are checked with a xenon filled sealed proportional counter the count rates now obtained are: Peak A proportional counter 2, 110 c/ s PeakB 210 c/ s Which of the measurements is most likely to yield the correct line intensity ratio of A : B.

If the background is ignored, however, the counting error is calculated simply from: E% = 100 fN (10) where N is the total number of counts collected at the peak position. Prepare a calibration curve which shows the error introduced by ignoring the background, for the following experimental conditions: total analysis time 120 s peak counting rate 100 c/s The curve should cover the range of 2 - 25 in terms of peak to background ratio. 48 ANSWER 18 If the background were ignored all of the 120 seconds would be used in collecting counts on the peak (R,).

How many maxima will be seen in the pulse amplitude distribution from the flow counter. Plot out roughly the pulse amplitude distribution obtained* at the setting of the Na Ka line, where the peak to background ratio is about 1. 6, assuming a detector resolution of 38% for Na Ka. Bear in mind that a potassium K escape peak will occur with an intensity roughly 10% of that of the photopeak. Use the given detector resolution for Na Ka to calculate the resolution (R) for other energies (It) which occur, using the expression: k R=- "fE (7) where k is a constant.