Signal, frequency-modulated

The reduction of zinc ions at d.m.e. has widely been studied and the reaction has been reported to be quasi-reversible.94 Van Der Pol and co-workers54 studied this reaction by the faradaic rectification polarographic technique using high-frequency modulated signals. The kinetic parameters have been evaluated by the... 

Dividing V(t) by this decay function leaves the frequency modulated signal btOintra (Fig 16.2B) of the wanted intramolecular interaction (Eq. (16.2)). 

Fig. 4 Frequency modulation signals from oxygen absorption. The peak-to-peak amplitude of each spectra is proportional to oxygen concentration (noted to the right of each scan). (From Ref ", p. 41. Copyright 2002 Advan-star Communications Inc.)...

Automatic tuning can be substituted for manual firequency variation. Instruments employing such frequency modulated signals have been in use for many years for measuring thickness by ultrasonic resonance. This resonance electric equipment usually does not provide a linear amplitude vs frequency readout and is therefore only suitable for the detection of resonance peaks in spectra. 

Discriminator A device or circuit whose output amplitude and polarity vary according to how much the input signal varies from a standard or from another signal. A discriminator can be used to recover the modulating waveform in a frequency modulated signal. 

Another type of level measurement makes use of radar or microwave signals. In this case the sensor is located at the top of the vessel in which the Uquid height should be measured. A sensor outputs a frequency-modulated signal from 0-200 Hz. The signal that is reflected by the liquid surface is delayed in proportion to the distance between the level and the surface. 

This scheme also employs a complex signal to modulate a carrier oscillator. In this case, however, the modulating signal is a frequency modulated signal (Figure 2.19). The sideband frequencies are calculated using the same method used above for parallel modulators, but the calculation of the amplitude scaling factors is different. The order of the outermost modulator is used to scale the modulation index of the next modulator ... 

DDS - Direct Digital Synthesizer produces a synthesized chirp (compound frequency modulated) signal ... 

The pyrolysis of CR NH (<1 mbar) was perfomied at 1.3 atm in Ar, spectroscopically monitoring the concentration of NH2 radicals behind the reflected shock wave as a fiinction of time. The interesting aspect of this experiment was the combination of a shock-tube experiment with the particularly sensitive detection of the NH2 radicals by frequency-modulated, laser-absorption spectroscopy [ ]. Compared with conventional narrow-bandwidth laser-absorption detection the signal-to-noise ratio could be increased by a factor of 20, with correspondingly more accurate values for the rate constant k T). 

When accelerated sufficiently, amplitude-frequency modulation in the absence of dephasing results in signal monochromatization, just like in the case of pure frequency modulation. Before the spectrum collapses, exchange between branches causes their broadening, but after collapse it provides their coalescence into a single line at frequency... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

Equations (33) and (34) demonstrate that the motion quantities 5 (displacement) and v (velocity) are encoded in phase and frequency modulation of the detector output signal, purely referenced to the laser wavelength A. Tobeableto recover the time histories s(t) and v t) from the modulated detector signal, adequate phase and frequency demodulation techniques, or both, are utilized in the signal decoder blocks of a laser vibrometer. 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

To improve the S/N ratio, the modulation signal is processed by amplification with a tuned amplifier using phase-sensitive detection. This means that the detected signal must not only be at the modulation frequency, but must also be in phase with the modulation. Since the amplifier itself can introduce a bit of phase shift, there is a phase control which, in principle, should be adjusted to maximize the signal amplitude. In practice, this control needs to be adjusted only rarely and in most cases the best approach is to leave it alone. 

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