Sensing frequency-domain

Figure 1.2. Intensity, time-domain, and frequency-domain sensing, as applied in the laboratory, a cuvette, and blood sample in a clinical setting,...

As mentioned earlier, we acquire data in the time domain but to make sense of it, we need to view it in the frequency domain. This is where the Fourier transformation comes in. There is not too much to do here - there are no parameters to change, ft is a necessary step but the automatic routines will perform this for you with no input. 

Esposito, A., Gerritsen, H. C. and Wouters, F. S. (2007a). Optimizing frequency-domain fluorescence lifetime sensing for high-throughput applications photon economy and acquisition speed. J. Opt. Soc. Am. 24, 3261-73. 

Topics discussed above are some basic principles and techniques in voltammetry. Voltammetry in the frequency domain where i-E response is obtained at different frequencies from a single experiment known as AC voltammetry or impedance spectroscopy is well established. The use of ultramicroelectrodes in scanning electrochemical microscopy to scan surface redox sites is becoming useful in nanoresearch. There have been extensive efforts made to modify electrodes with enzymes for biosensor development. Wherever an analyte undergoes a redox reaction, voltammetry can be used as the primary sensing technique. Microsensor design and development has recently received... 

In order to implement frequency domain based sensing systems capable of monitoring the temporal luminescence of sensors, in few seconds, data must be collected at multiple frequencies simultaneously. Single-frequency techniques have been used to make frequency domain measurements of luminescent decays. 14, 23 28) This approach is unsuitable for real-time applications since data must be acquired at several frequencies in order to precisely and accurately determine the temporal variables of luminescent systems. 1 Each frequency requires a separate measurement, which makes the single frequency approach too slow to monitor the evolution... 

J. R. Alcala, C. Yu, and G. J. Yeh Digital phosphorimeter with frequency domain signal processing application to real time fiber optic oxygen sensing, Rev. Sci. Instrum. 64, 1554-1560 (1993). 

Answer The spectrum was produced by the misapplication of a trick commonly used in solid-state NMR spectroscopy ( 8.4 and 9.6). If the early data points in the FID are distorted by the recovery time of the probe and/or receiver, one can often improve the appearance of the baseline by left-shifting the data file and adding a zero to the righthand end for each left-shift. If quadrature detection is in use, it is essential that an even number of left-shifts be performed. In this example, a single left-shift was applied and the frequency sense of the spectrum has been reversed the signals have been flipped from left to right in the frequency domain because we have, in effect, reversed the x and y axes in the experiment ( 1.3.2). 

The term 2D NMR, which stands for two-dimensional NMR, is something of a misnomer. All the NMR spectra we have discussed so far in this book are two dimensional in the sense that they are plots of signal intensity versus frequency (or its Fourier equivalent, signal intensity versus time). By contrast, 2D NMR refers to spectroscopic data that are collected as a function of two time scales, tx (evolution and mixing) and t2 (detection). The resulting data set is then subjected to separate Fourier transformations of each time domain to give a frequency-domain 2D NMR spectrum of signal intensity versus two frequencies, Fx (the Fourier transform of the t time domain) and F2 (the Fourier transform of the t2 time domain). Thus, a 2D NMR spectrum is actually a three-dimensional data set ... 

In a general sense, the frequency-domain error structure is determined by the nature of errors in the time-domain signals and by the method used to process the time-domain data into the frequency domain. The ceU impedance influences the frequency-dependence of the variance of the measurements, but the cell impedance does not influence whether the variances of real and imaginary components are equal or whether errors in the real and imaginary components are uncorrelated. 

The fimdamental constraints are that the system be stable, in the sense that perturbations to the system do not grow, that the system responds linearly to a perturbation, and that the system be causal in the sense that a response to a perturbation cannot precede the perturbation. The Kramers-Kronig relationships were foimd to be entirely general with application to all frequency-domain measiuements that could satisfy the above constraints. Bode extended the concept to electrical impedance and tabulated various extremely useful forms of the Kramers-Kronig relations. ... 

The divergence of all the global characteristic times for anomalous diffusion—as defined in their conventional sense (which is a natural consequence of the underlying Levy distribution), rendering them useless as a measure of the relaxation behavior—signifies the importance of characteristic times for such processes in terms of the frequency-domain representation of... 

All of this information about vibrational frequencies and transition intensities is observable directly in the frequency domain absorption spectrum, A"= o(w) The autocorrelation function picture is an alternative way of deriving a ball-and-spring physical picture (or dynamical mechanism) from the raw experimental data. Although there is a simple Fourier transform relationship between Ivn (to) and ( f (f)l F(O)), profoundly different intuitive pictures are used to make sense of experimental results and to guide the design of new experiments. 

In the optical frequency domain, superradiance in the Dieke and Bonifacio sense (Dieke 1954, Bonifacio and Lugiato 1975), i.e. with strong radiation damping, seems to have been observed in solids up to now only in photon-echo experiments, as already mentioned. The difficulty lies in the preparation of the macro-dipole in a volume smaller than ). However the recent interest in restrained geometry, e.g. the so called 2D, ID... 

The method of determining T via amplitude modulation of Hi relies on variation of the modulation frequency, denoted by QJIti, until it exceeds T), at which point the magnetization cannot respond to the power variation and there is a loss in the detected EPR signal amplitude (Herve Pescia, 1960a). In a sense, this Ti measurement is analogous to that used to analyze the impedance of a nonlinear system, sueh as a passive filter. The precept is that the response of a system y t) to some perturbation x t) is determined by some differential equation of order n. In the case of a linear system and perturbation x(t)=A sin((oO, one observes a response y(t)=B sin(co -l-(t)) and one defines a transfer function as the ratio of output to input (in the frequency domain) H(j( i)= H(( i) wherey((o) and x(co)... 

Figure 5.12 shows the impedance spectra of the Nation 115 membrane, obtained by the two-point probe method with different distances between voltage sensing probes (Pt strips), at room temperature and under fully hydrated conditions [60]. Each impedance spectmm shows a semicircle in the high-frequency domain and a straight line with an angle of 45° in the lower-frequency domain. The membrane resistance is extracted from the lower-frequency intercept of the semicircle at the Zreai axis. It can be seen from Fig. 5.12 that at low frequency, the behavior of the Pt/Nafion interface is blocked by the 45° line, indicating that interface impedance has very little impact on the results of membrane conductivity. 

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