Bandwidth definition

An alternative definition of the bandwidth is sometimes used. The bandwidth can also be defined as the frequency for which 5( (o) = 0.707 when 5(7(o) crosses 0.707 from below, as shown in Fig. J.13 (Sko-gestad and Postlethwaite, 2005). Fortunately, the two bandwidth definitions typically result in similar numerical values. Furthermore, the values of ix Bw the gain crossover frequency cog are usually very close. 

In spectrophotometric analysis a source of radiation is used that extends into the ultraviolet region of the spectrum. From this, definite wavelengths of radiation are chosen possessing a bandwidth of less than 1 nm. This process necessitates the use of a more complicated and consequently more expensive instrument. The instrument employed for this purpose is a spectrophotometer. 

Precise definition of receiver bandwidth by means of audio filters (improves sensitivity). 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

A chromatographic property of interest is the separation between spots (solutes). The most simple definition is resolution R= z ( - - z 2 H2 (J2 (5 ) with a, the bandwidth of the developed spot. Assuming ai=cj2 and using zJo= NRf [2] N is the plate number) the formula becomes ... 

While for some purposes it may be necessary to have accurate frequency definition, for others good time discrimination is useful. These are opposite requirements. Because of the Fourier relationship between frequency and time, the more precisely the time of a signal is known, the greater bandwidth of frequencies is necessary (there is a close analogy here with Heisenberg s uncertainty principle). Approximately, the time resolution t is the reciprocal of the bandwidth Bw, so that their product Bwr 1. 

Peak Width. Peak width depends on the mass resolution. A resolution of 1 mass unit is sufficient to distinguish ions in most qualitative/quantitative small molecule applications. A typical definition of unit resolution is when the peak width at half-height is about 0.6 to 0.8 mass unit. The profile scan of ions on a typical benchtop LC-MS has a bandwidth of about 1 mass unit (Figure 13.1). 

Before presenting the applications, the theoretical background for the density matrix method should be constructed in molecular terms. For this purpose, a detailed definition of the density matrix of the system should be discussed. Let us consider a molecule at position Ry interacting with an applied laser field of bandwidth 8co and corresponding wave-vector width 8k — 8co/c. Now, it is assumed that the laser beam spot is similar to 8k and a system has only two states described by n> and m ) with respective energies hcontt and ha, within 8co. In this case, the dynamics of the system can be described as... 

A review of current literature reveals a wide variation in the design of photostability cabinets promoted for the testing of pharmaceuticals. Also, the photon source, its intensity, and bandwidth, in addition to the methods used to measure photon intensity, temperature, and time of exposure, vary considerably. This variation is a result of the lack of agreement regarding product exposure and the absence of definitive regulatory guidelines and standards. 

By carefully tuning and matching the probe and the various stages in the transmitter amplifier chain and by allowing for a wide rf bandwidth, it is possible to reduce phase transients (for a definition, see Haeberlen, 1976, Appendix D) to a level where their effect upon the m.p. spectrum becomes insignificant. We therefore confine ourselves here to study by simulations phase errors, nonuniform pulsewidths, and a power droop of the transmitter. 

Figure 2.4. Definitions of fi, ff, and or for to a generic Raman band, ff is the cross section at a particular Raman shift and direction fi is integrated over the bandwidth, and cr,- is integrated over both bandwidth and direction.

This definition takes into account that the interferogram with its noise is multiplied by S(s) before the Fourier transform is carried out, and that the effective noise amplitude is N s) S (s) instead of A s). Furthermore, it is presumed that the bandwidth d/ of the electronics is selected to be appropiate for the maximum wave number 5max- We recall from our considerations in Section 4.6 that the time constant t limiting the bandwidth of the electronic system should have a value close to (cf. Section 4.6)... 

Fig. 2.14 Attenuation analysis by the smoothed spectral ratio method, (a) Definition of a moving window of bandwidth in which the spectral amplitudes are summed, (b) Seven attenuation curves analyzed from the...

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