Time-domain information

Remade F and Levine R D 1993 Time domain information from resonant Raman excitation profiles a direct inversion by maximum entropy J. Chem. Phys. 99 4908-25... 

Figures 40.3 and 40.4 are two representations of the same signal, each providing specific information. In the time domain information is available on the overall...

Klimant I, Huber C, Liebsch G, Neurauter G, Stangelmayer A, Wolfbeis OS (2001) Dual lifetime referencing (DLR) - a new scheme for converting fluorescence intensity into a frequency-domain or time-domain information. In Valeur B, Brochon JC (eds) Springer Ser Fluoresc 1 257-274... 

Time resolved coherent anti-Stokes Raman spectroscopy of condensed matter has been recently extended to the femtosecond domain allowing direct and detailed studies of the fast relaxation processes of molecular vibrations in liquids. The vibrational phase relaxation (dephasing) is a fundamental physical process of molecular dynamics and has attracted considerable attention. Both experimental and theoretical studies have been performed to understand microscopic processes of vibrational dephasing. Developments in ultrafast coherent spectroscopy enables one now to obtain direct time-domain information on molecular vibrational dynamics. Femtosecond time-resolved coherent anti-Stokes Raman scattering measuring systems have been constructed (see Sec. 3.6.2.2.3) with an overall time resolution of less than 100 fs (10 s). Pioneering work has been per-... 

Figure 5.12 Diagrammatic representation of general FT 2D NMR experiments involving multiple 90° pulses with signal observation and acquisition in time domain <2 prior to fourier series transformation of time domain information SpiDCti, t2) into frequency domain (spectral intensity) information, 2)-...

Integration of frequency and time domain information [69] by assuming that some of the frequency points are equal to zero. 

In the time domain, information is obtained on the total amplitude, but not on the frequencies of the signal. The frequency domain contains information on the frequencies and... 

The drawback to this approach is relating the time domain information to a chemical species or physical phenomena. Many broadline systems are used in an empirical fashion in which the results are correlated with a process control parameter or measured physical property. However, this approach alone does not indicate which chemical species is being measured. The signals could be due to water or fat content, bound water versus free water in a slurry or different phases of a polymer, crystalline, amorphous or interfacial regions. To ensure that these correlations are due to specific chemical species broadline NMR data must be related to some other primary analytical technique such as high resolution NMR. 

Although the discrete cosine Fourier transform yields N calculated frequency-domain values for N measured time-domain data points, the second half of the cosine F.T. data is a mirror image of the first half, and thus gives no new information. The other half of the time-domain information is contained in the first N/2 frequency-domain values of the sine Fourier transform. [It is possible to put all the information into the cosine transform by first adding N... 

Figure 3 A nonstationary signal (solid line) is fitted with an FT basis function (dashed line). The basis function is fitted well against a single signal peak, but outside of the immediate region of the peak, the signal approximation suffers. It illustrates the ability of a Fourier basis function to isolate frequency information but not time-domain information.

Translating time-domain information into the frequency domain yields an amplitude-frequency spectrum or, as it is commonly called, simply a spectrum. Figure 1.108(a) shows the spectrum of the waveform in Fig. 1.104 and Fig. 1.106, in which the height of each line represents the ampHtude of that particular component and the position of the fine along the frequency axis identifies its frequency. This kind of display is a line spectrum because there are sound components at only certain specific frequencies. The phase information is shown in Fig. 1.108(b), where the difference between the two waveforms is revealed in the different phase-frequency spectra. 

Although it is taken for granted now that the components of a sound spectrum vary substantially during the sound emission, these variations were not considered relevant enough to be represented until recently. In his paper, Gabor proposed the basis for a representation method which combines frequency-domain and time-domain information. His point of departure was to acknowledge the fact that the ear has a time threshold for discerning... 

Another option for performing time-resolved nonlinear Raman spectroscopy is to use a fast detector such as a streak camera. By combining short picosecond or femtosecond pulses with longer nanosecond pulses, a generated signal can be produced that evolves over time. This approach can be used to obtain simultaneously both frequency and time domain information. 

This process creates L blocks of new free induction decays. These free induction decays contain the time-domain information from the evolution period. Figure 6 shows the transposed data blocks corresponding to the finequency-domain data in Fig. 5. 

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