Bandwidth intervals

The second part of ISO 17497 specifies a method of measuring the directional diffusion coefficient of surfaces in a free field (ISO, 17497-2, 2012). The diffusion coefficient characterizes the sound reflected from a surface in terms of the uniformity of the reflected polar distribution. The directional diffusion coefficient is a frequency dependent value derived from the polar distribution of the scattered sound (Cox and D Antonio, 2009). First the scattering from a surface is measured in terms of a polar distribution. Then the diffusion coefficient is evaluated at 1/3 octave bandwidth intervals, which has the advantage of smoothing out some of the local variations in the polar responses. 

The rms noise is measured in a noise bandwidth, The D is called D star lambda when the spectral band is limited to a given interval, and D blackbody when the total blackbody incident power density is used in the calculation. 

The resolution of a monochromator is the smallest frequency interval the instrument can separate. The limiting resolution is the bandwidth measured at half height when scanning across an infinitely narrow intense source 22). As already mentioned, the broader excitation line width of Ar+ lasers (0.15 to 0.25 cm-1) compared to that of the He-Ne lasers (0.05 cm-1) means a lower resolution limit when the Ar+ laser is used as a Raman source. 

It should be noted that when we compare the brightness of a LGS to a NGS, the result depends on the spectral bandwidth, because the LGS is a line source, whereas the NGS is a continuum one. The magnitude scale is a logarithmic measure of flux per spectral interval (see Ch. 15). This means that a (flat) continuum source has a fixed magnitude, no matter how wide the filter is. In contrast, the magnitude of a line source is smaller for narrower bandpasses. It is therefore advisable to use the equivalent magnitude only for qualitative arguments. The photon flux should be used in careful system analyses. 

Figure 2 illustrates typical Fourier space sampling as provided by monostatic SAR. As shown, the samples in the radial dimension straddle a term proportional to the carrier frequency and have an extent proportional to the signal bandwidth. Samples in the angular dimension correspond to pulse numbers in the coherent processing interval. In... 

The Bandwidth is essentially a normalized half confidence band. The confidence interval bandwidths for 9 data sets using inverse transformed data are given in Table X. The bandwidths are approximately the vertical widths of response from the line to either band. The best band was found for chlorpyrifos, 1.5%, at the minimum width (located at the mean value of the response) and 4.9% at the minimum or lowest point on the graph. Values for fenvalerate and chlorothalonil were slightly higher, 2.1-2.2% at the mean level. The width at the lowest amount for the former was smaller due to a lower scatter of its points. The same reason explains the difference between fenvalerate and Dataset B. Similarly, the lack of points in Dataset A produced a band that was twice as wide when compared to Dataset B. Dataset C gave a much wider band when compared to Dataset B. 

Table X. Confidence Interval Bandwidths from the Regression of Transformed Data Sets. Inverse Transformed Data.

The bandwidths for this data are found in Table XIV. Typical estimated amount intervals are found in the analysis for fenvalerate. At 4 ng this compound gave a range of 3.5 to 4.5 ng at the confidence level described. This range was similar in the analysis for fenvalerate in Dataset E, chlorothalonil, and chlorpyrifos due to tight control of standards. These ranges amounted to bandwidth percentages of from 10 to 14%. In more... 

Table XIV. Estimated Amount Interval Bandwidth from Inverse...

Mitchell s computer program first applied the method to a linear model and then calculated the amount values corresponding to response values of unknowns and the accompanying estimated amount interval calculated as a bandwidth. Bandwidth was defined as the percentage of half the difference of the upper and lower values of the estimated amount interval divided by thex corresponding amount. The standards data was then shortened at the ends, always in such a way to maintain unknowns within the range, and the bandwidth recalculated. Narrower bandwidths were often found in this way. The method also allowed a further recalculation using a second order function model. 

Estimated Amount Interval and Bandwidth Data. The bandwidths for each of the points compared were calculated from Wegscheider s data. They were markedly smaller than those calculated by either of the other two workers. His bandwidths ranged from 4.9 to 16.0% for all of the three data sets. Refer to Table III. 

When I calculated the estimated amount interval from only the response dispersion for the data using Kurtz methods, there was a substantial reduction in the amount bandwidth from the total bandwidth. This calculation was done by intersecting the bounds of the response dispersion with the linear regressed line and projecting these points to the amount axis. This reduction, however, was not nearly enough to account for differences from Wegscheider s calculation to the others. In Table IV the data is... 

Similar results were obtained by De Shazer using a different detection technique, where laser oscillations in the sample were forced to develop from the narrow-band radiation, injected from a second small aperture laser into the sample laser cavity. The interionic transfer allowed the feeding of this narrow-band radiation by ions having frequencies outside this interval. The effeciency of energy extraction within the narrow bandwidth and the degree of depolarization of the laser oscillations parametrize the cross relaxation effects. 

The absolute values of the absorption cross sections of HCHO have been somewhat controversial. This appears to be due to a lack of sufficient resolution in some studies as discussed in Chapter 3.B.2, if the spectral resolution is too low relative to the bandwidth, nonlinear Beer-Lambert plots result. The strongly banded structure means that calculations of the photolysis rate constant require actinic flux data that have much finer resolution than the 2- to 5-nm intervals for which these flux data are given in Chapter 3 or, alternatively, that the measured absorption cross sections must be appropriately averaged. One significant advantage of the highly structured absorption of HCHO is that it can be used to measure low concentrations of this important aldehyde in the atmosphere by UV absorption (see Sections A.ld and A.4f in Chapter 11.). 

Photometric accuracy is determined by comparing the difference between the measured absorbance of the reference standard materials and the established standard value. Many solid and liquid standards are commonly used to verify the photometric accuracy of a spectrophotometer. An optically neutral material with little wavelength dependency for its transmittance/absorbance is desirable because it eliminates the spectral bandwidth dependency of measurements. The advantages and disadvantages of various commonly used photometric accuracy standards are summarized in Table 10.6. Even for a relatively stable reference standard, the intrinsic optical properties may change over time. Recertification at regular intervals is required to ensure that the certified values of the standards are meaningful and accurate for the intended use. 

The luminescence emission spectrum of a specimen is a plot of luminescence intensity, measured in relative numbers of quanta per unit frequency interval, against frequency. When the luminescence monochromator is scanned at constant slit width and constant amplifier sensitivity, the curve obtained is the apparent emission spectrum. To determine the true spectrum the apparent curve has to be corrected for changes of the sensitivity of the photomultiplier, the bandwidth of the monochromator, and the transmission of the monochromator with fre-... 

Under the effect of temperature, each atomic transition leads to emission or absorption spread over a narrow interval of wavelengths. This uncertainty around the theoretical value constitutes the natural bandwidth of the line and leads to enlargement of the image of the line seen by a monochromator. The natural bandwidth ranges from 1CT5 nm under ideal conditions to about 0.002 nm at 3 000 K. 

Several parameters, for example focal length, determine linear dispersion, which is expressed in millimetres per nanometre (or its inverse, which is called reciprocal dispersion). Linear dispersion represents the spread, in the focal plane, of two wavelengths differing by l nm. Bandwidth, which must not be confused with the width of the slit, is the interval of the spectrum that corresponds to the width in picometres exiting the slit. This width is generally greater than the natural width of the line being transmitted. 

The time-bandwidth product, constraining the minimum analysis filter bandwidth to be inversely proportional to the observation time interval, must also be confronted. 

It is true that in the case of a broadband photoelectric detector, there will be more electrons released per micron interval if the excitation source is tailored so as to provide a constant amount of energy per micron interval. However, this does not have any effect on the coefficient of absorption the effect is on the number of quanta actually passing through the system. In this respect, the output signal is a function of the number of quanta absorbed per unit spectral bandwidth. Most plots of this signal output should employ a stimulus containing equal number of photons per spectral interval. 

The study that we describe below was inspired by our work on fitting the dynamic susceptibilities measurements for real assemblies of fine particles. Those data typically describe polydisperse systems in the low-frequency bandwidth a>/2% = 1 — 103 Hz. As To 10 s or smaller, then, using formula (4.132) for estimations, one concludes that the frequency interval mentioned becomes a dispersion range for the interwell (superparamagnetic) mode at coto< ct > 1, that is, a > 10. For temperatures up to 300 K, this condition holds for quite a number of nanomagnetic systems. 

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