Signal analyzer, dynamic

The power spectra may be directly obtained using dynamic signal analyzers that measure signals as a function of time and perform the fast Fourier transform. The coherence function takes values betweaen 0 and 1 and characterizes statistical validity of the frequency response measurements ... 

Another kind of analyzer has been developed which offers the best features of parallel- and swept-filter spectrum analyzers. So-called dynamic signal analyzers use analog-to-digital conversion followed by frequency-to-time-domain transformation, usually using hard-wired computational machines, to mimic the function of a parallel-filter analyzer with hundreds of filters, and yet are cost-competitive with swept-filter analyzers. In addition, dynamic spectrum analyzers are capable of measuring amplitude and phase accurately these are basically time domain instruments, and their function will be discussed in Section 3.1.4. 

Signals are recorded with a 24 bit- 4 channels dynamic signals analyzer powered by the laptop data acquisition computer s USB port. 

As mentioned in the introductory part of this section, quantum dots exhibit quite complex non-radiative relaxation dynamics. The non-radiative decay is not reproduced by a single exponential function, in contrast to triplet states of fluorescent organic molecules that exhibit monophasic exponential decay. In order to quantitatively analyze fluorescence correlation signals of quantum dots including such complex non-radiative decay, we adopted a fluorescence autocorrelation function including the decay component of a stretched exponential as represented by Eq. (8.11). 

As evidenced from the above discussion, vibrational line shapes provide information mostly about intermolecular structure. Transient hole burning and more recently echo experiments, on the other hand, can provide information about the dynamics of spectral diffusion. The first echo experiments on the HOD/ D2O system involved two excitation pulses, and the signal was detected either by integrating the intensity [20] or by heterodyning [22]. The experiments were analyzed with the standard model assuming Gaussian frequency fluctuations. The data were consistent with a spectral diffusion TCF that was bi-exponential, involving fast and slow times of about 100 fs and 1 ps, respectively. 

The q-space imaging method, which deals with signals only after long diffusion times, discards all information relevant to dynamic aspects of water diffusion and transport, especially the restriction of water transport by membrane and cell wall permeability barriers in cellular tissues. This information is contained in the functional dependence of the pulsed gradient spin echo amplitude S(q,A,x) on the three independent variables q, A, and x (x is the 90-180 degree pulse spacing) [53]. As the tool to explore the q and A dependence of S(q,A,x), generalized diffusion times and their associated fractional populations are introduced and a multiple exponential time series expansion is used to analyze the dependence [53]. 

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