Fourier analysis with Probe

Since we have already spent a good deal of simulation time and we are already in Probe, we can use Probe to view the frequency components of a signal. We will first view the components of the input Delete the trace V(OUTl so that only the input voltage trace is displayed  

The input should be a sine wave with only one frequency, 1 kHz. To view the frequencies contained in this waveform we need to select the Fourier Processing option. Select Plot and then Axis Settings from the Probe menus. The X AxtS tab is automatically selected  

Click on this square to select the Fourier option. 

Click the LEFT mouse button on the square D next to the text FOUller. The square will fill with a checkmark, 13, indicating that the option is selected  

When we select the FOUller option, the x-axis scale changes to frequency. Click the OK button to accept the setting  

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Fourier analysis of neutron diffraction data (time-of-flight method) was also employed by Etherington et al. (1984b) to probe the structure of the barium dizirconate glass and the combination of the X-ray and neutron methods allowed an assignment of the different peaks in the total correlation function with a good degree of... 

From the above examples, the generalization of the procedure to cases including arbitrary nonlinear processes of any order is straightforward. In Ref. 110 the case of four-wave mixing experiments with three incident laser fields has been discussed. To calculate the contributions of the polarization in N directions, one has to perform N calculations of the overall polarization P 4>) with different phases 4>, and solve the resulting linear system of equations for the P in (62). Beyond the RWA, however, one needs to generalize the ansatz (62) and tag both the interactions with the pmnp and the probe fields with phases = kix and = k2X, respectively, thus performing a two-dimensional Fourier analysis of the overall polarization. 

Silverans et studied interference effects between ground (or metastable) and excited states in a setup that is analogous to Ramsey s separated microwave field method. In comparison with other optical experiments, the interference conditions are easy to establish with fast ion beams, and the observed fringes are consistent with a Fourier analysis of the evolution in time of the laser frequency probed by the ions. ... 

The frequency components involved in the real-time spectra were extracted by a Fourier analysis of the normalized pump probe data (see Fig. 3.22a for excitation with A = 620 nm, and Fig. 3.22b for 642 nm). Both Fourier spectra are dominated by a band of frequencies centered around 107.8 cm" and 111.3 cm" for the respective wavelengths. This main frequency band contains the frequencies of the energy spacings of neighboring vibronic levels (i.e. Av — 1), simultaneously excited by the spectrally broad femtosecond laser pulse. An additional frequency group with lower amplitude appears for both experiments, around 214 cm" in Fig. 3.22 a and around 222 cm" in Fig. 3.22b. This contribution appears to be due to the fact that... 

The molecular specificity of Fourier transform infrared (FTIR) lends itself quite well to applications in pharmaceutical development labs, as pointed out in a review article with some historical perspective.10 One of the more common applications of mid-IR in development is a real-time assessment of reaction completion when used in conjunction with standard multivariate statistical tools, such as partial least squares (PLS) and principal component analysis (PCA).18,19 Another clever use of FTIR is illustrated in Figure 9.1, where the real-time response of a probe-based spectroscopic analyzer afforded critical control in the charge of an activating agent (trifluoroacetic anhydride) to activate lactol. Due to stability and reactivity concerns, the in situ spectroscopic approach was... 

A major reason why XAFS spectroscopy has become a critically useful probe of catalyst structure is the fact that it is easily adapted to characterization of samples in reactive atmospheres. The X-ray photons are sufficiently penetrating that absorption by the reaction medium is minimal. Moreover, the use of X-ray- transparent windows on the catalytic reaction cell allows the structure of the catalyst to be probed at reaction temperature and pressure. For example, the catalyst may be in a reaction cell, with feed flowing over it, and normal online analytical tools (gas chromatography, residual gas analysis, Fourier transform (FT) infrared spectroscopy, or others) can be used to monitor the products while at the same time the interaction of the X-rays with the catalyst can be used to determine critical information about the electronic and geometric structure of the catalyst. 

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