Frequency domain measurements

Bickel, H.J., Calibrated Frequency Domain Measurements Using the Ubiquitous, Spectrum Analyzer, Federal Scientific Monograph 2, January 1970. 

It is important to note that if a mixture of fluorophores with different fluorescence lifetimes is analyzed, the lifetime computed from the phase is not equivalent to the lifetime computed from the modulation. As a result, the two lifetimes are often referred to as apparent lifetimes and should not be confused with the true lifetime of any particular species in the sample. These equations predict a set of phenomena inherent to the frequency domain measurement. 

This comparison between time and frequency domain measurements is performed at submegahertz frequencies in order to avoid the issue of deconvolution of time domain signals. At megahertz frequencies time domain measurements encounter an additional limitation, these signals must be deconvoluted to isolate the sensor response from the instrument response. The need for deconvolutions adds extra software and computation time, which limits the versatility of time domain techniques for real-time applications. No deconvolutions are necessary in the frequency domain as shown below. 

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... 

Frequency domain measurements require the use of periodic excitation sources. The luminescent molecules respond to the periodic excitation exhibiting the same frequency of modulation. This luminescence exhibits a phase delay and a demodulation with respect to the excitation due to the inability of the sensor molecule to respond to the higher frequencies of the excitation. This inability of the sensor molecules roughly begins at modulation frequencies /modulation of the same order of magnitude or faster than the decay rate... 

I. Gryczynski, J. R. Lakowicz, and R. F. Steiner, Frequency-domain measurements of the rotational dynamics of the tyrosine groups of calmodulin, Biophys. Chem. 30, 49-59 (1988). 

Frequency-domain measurements of fluorescence energy transfer are used to determine the end-to-end distance distribution of donor-acceptor D-A) pairs linked by flexible alkyl chains. The length of the linker is varied from 11 to 2B atoms, and two different D-A pairs are used. In each case the D-A distributions are recovered from global analysis of measurements with different values for the FSrster distance, which are obtained by collislonal quenching of the donors. In all cases essentially the same distance distribution Is recovered from the frequency-domain data for each value of tha Ffirster distance. The experimentally recovered distance distributions are compared with those calculated from the RIS model. The experimentally recovered distance distributions for the largest chain molecules are In agreement with the predictions of the RIS model. However, the experimental and RIS distributions are distinct for the shorter D-A pairs. 

In general, the quantities being determined by microwave measurements are complex reflection and transmission coefficients or complex impedances normalized to the impedances of the transmission lines connecting a network analyser and the device-under-test (dut). In addition to linear frequency domain measurements by means of a network analyser the determination of possible non-linear device (and thus material) properties requires more advanced measure-... 

Metelko D, Jamnik J, Pejovnik S (1992) Comparison between the impedance spectra of Li/SOCl2 batteries obtained using the time and the frequency domain measurement techniques. J Appl Electrochem 22 638 13... 

As an alternative to methods that use an applied sinusoidal voltage, called frequency-domain measurements, a step change in voltage across a specimen may be made and the ensuing current transient observed. Such time-domain measurements may be translated into frequency-domain terms by Fourierj integral transformations. 

Fig. 4.100. Argand diagrams of a completely dissociated electrolyte and its pure solvent. Full circles experimental data from frequency domain measurements on aqueous potassium chloride solutions at 25 °C. Curve 1 Argand diagram of pure water. Curve 2 Argand diagram, ff = f(E ), of an 0.8 Waqueous KCI solution, Curve 3 Argand diagram, e"=f(e )r obtained from curve 2. (Reprinted from P. Turq, J. Barthel, and M. Chemla, in Transport, Relaxation and Kinetic Processes in Electrolyte Solutions, Springer-Verlag, Berlin, 1992, p. 78).

The high-frequency precision of t.d.s. methods has been tested by making measurements on water itself. The data for water at 278 K are shown on Figure 12, together with a r resentative sample of frequency domain measurements. On the basis of most of the previous dielectric S. K. Garg and C. P. Smyth, J. Phys. Chem., 1965,69, 1254. 

We have performed optically heterodyne-detected optical Kerr effect measurement for transparent liquids with ultrashort light pulses. In addition, the depolarized low-frequency light scattering measurement has been performed by means of a double monochromator and a high-resolution Sandercock-type tandem Fabry-Perot interferometer. The frequency response functions obtained from the both data have been directly compared. They agree perfectly for a wide frequency range. This result is the first experimental evidence for the equivalence between the time- and frequency-domain measurements. 

Frequency-domain measurements provide an attractive alternative to transient techniques involving steps in potential or current because their capability to make repeated measurements at a single frequency improves the signal-to-noise ratio and extends the range of characteristic frequencies sampled. These measurements are a type of transient measurement in which the input signal is cyclic. 

The methods described in this chapter and this book apply to electrochemical impedance spectroscopy. Impedance spectroscopy should be viewed as being a specialized case of a transfer-function analysis. The principles apply to a wide variety of frequency-domain measurements, including non-electrochemical measurements. The application to generalized transfer-function methods is described briefly with an introduction to other sections of the text where these methods are described in greater detail. Local impedance spectroscopy, a relatively new and powerful electrochemical approach, is described in detail. 

This part provides a conceptual understanding of stochastic, bias, and fitting errors m frequency-domain measurements. A major advantage of frequency-domain measurements is that real and imaginary parts of the response must be internally consistent. The expression of this consistency takes different forms that are known collectively as the Kramers-Kronig relations. The Kramers-Kronig relations and their application to spectroscopy measurements are described. Measurement models, used to assess the error structure, are described and compared with process models used to extract physical properties. 

Impedance spectroscopy is, of course, not a religion, but an application of a frequency-domain measurement to a complex system that cannot be easily visu-... 

HRV assesses the modulation of autonomic tone on the sinus node, or simply put, the irregularity of sinus rhythm. Methods of measuring HRV fall under broad categories of being either time domain or frequency domain analyses. Time domain measurements involve statistical analyses of the variability in the R-R interval, while frequency domain measurements use spectral analysis of a series of R-R intervals to classify HRV into ultra-low frequency, very low frequency, low frequency, high frequency, and total power. One method is not better than another as there is no gold standard (65). 

Phase shift fluorimetry, the other important method for measuring fluorescent lifetimes, also continues to be developed and improved. The effects of Inaccurate reference lifetimes on the interpretation of frequency domain fluorescence data can be removed or minimized by a least squares analysis method.The direct collection of multi-frequency data for obtaining fluorescence lifetimes can be achieved by the use of digital parallel acquisition in frequency domain fluorimetry. Frequency domain lifetime measurement has been used for on-line fluorescence lifetime detection of eluents in chromatography. An unusual use of frequency domain measurement which has been reported is for the examination of photon migration in living tissue. Photons in the... 

Typical frequency-domain data for two proteins are shown in Fig. 17. The data consist of the phase angles and modulation, each measured over the widest possible range of frequencies. This requirement illustrates the transform relationship between the time and the frequency-domain measurements. In the time-domain, the most desirable excitation profile is the shortest obtainable pulse. The Fourier transform of a 5-function consists of all frequencies. Hence, the experimental requirements are similar, short pulses or wide range frequencies. For each protein (Fig. 17) the phase angle increases and the modulation decreases as the frequency increases. The data are analyzed in a manner analogous to the time-domain data. That is, a decay law is assumed and the parameters varied until the best possible match is obtained... 

OVERVIEW OF TIME-DOMAIN AND FREQUENCY-DOMAIN MEASUREMENTS... 

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