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Several approaches are considered, including a Riemann summation using left endpoints, the use of random wave numbers to sample a the spectrum in proportion to the energy it contains, and a combination of the two.
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SI06 tested various types of spectra; in this paper I discuss the results of the power spectra in proportion to 1/ν, where ν is frequency.
A likely source of error in the intensities is the assumption that only structures I, J, K, and L contribute to the experimental spectra in proportions governed by their relative energies and the synthesis temperature.
All of the spectra were taken with the same instrument settings and protein concentration, and therefore the areas under the spectra are in proportion to the quantum yields of the proteins.
This power law range seems to be a bridge between a very low frequency range where horizontal spectra scale in proportion to the square of the mean velocity and frequencies a decade below the low frequency end of the inertial subrange.
The left axis is actually amplitude in volts from the amplifier but the spectra have been offset in proportion to the temperature at which they were collected and the axis is labeled in Kelvin.
Segments of the low-temperature spectra are shown in Figure 3, stacked in proportion to the temperatures at which they were collected.
Figure 10 contains segments of spectra from the high-temperature instrument, stacked in proportion to the temperature at which they were collected.
To obtain the total excitation spectra, we sum up the individual contributions weighted in proportion to the number of corner, edge, and terrace sites in the powder.
For each mass spectrum we calculated the intensity of each peptide peak in proportion to the alytesin external standard.
The measured spectra showed that the number of excited carriers seems in proportion with the accelerating voltage.
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