Demodulation

In order to facilitate the way of notation, it is useful to represent the virtual voltage sources by SF = [SF] cos (2coLf) and Sc = [Sc] cos (2col ). Again, the Laplace transform method is most useful for solving 

Tedious, but straightforward, algebra leads to the explicit expressions for x and y and, after substitution into eqn. (79), to the explicit expression for AE2 = — AEm [27]. The result is conveniently written as 

This notation is deliberately used because it facilitates the deduction of a useful relationship [27] 

combination of demodulation results with unprocessed admittance results enables the important quantity [SF] to be determined. 

Also in the demodulation method, controlled-current perturbation is applied, which means that here, too, eqn. (84) is to be used to substitute El by a term containing the squared amplitude of the current density,.  

---

Very good integration one DSP can demodulate up to 4 frequencies at 5kHz. 

The biggest innovation of this new instrument is the fully digital demodulator. The prineiple of a traditionnal demodulator is reealled on figure 3 ... 

The instrument uses a sinusoidal driver. The spectrum is very clean as we use a 14 bits signal generator. The probe signal is modulated in amplitude and phase by a defect signal. The demodulation is intended to extract the cartesian values X and Y of this modulation. 

To carry out digital demodulation, it is necessary to digitize the signal. As ET signals require a great dynamic range, the standard in new instruments is 16 bits. 

On the other hand, one current upper limit of the frequency range of instruments is 4 MHz So, it is theoretically impossible to digitally demodulate a 4 MHz ET signal. 

To demodulate the signal, it is then necessary to multiply the carrier by itself. Of eourse, the carrier of the driver must be exactly the same as the demodulator one. But, as it is modified to be demodulated, we nevertheless need a common frequency reference for the driver and for the DSP. This reference is delivered by a quartz oscillator. 

Then, when the digitizer samples the signal, the phase to be used for signal demodulation is known exactly. The FIFO memory is added because the output sample rate of the digitizer is between 8 and 64 kHz (depending on the bandwidth) and the output sample rate of the DSP (of the demodulator) is 5 kHz maximum. So, during one demodulation cycle, many points are written in the FIFO by the digitizer. The DSP reads them and the demodulation is carried out. 

The demodulation algorithm is very simple the DSP multiplies the received signal by each carrier, and then filters the result using a FIR filter. This kind of digital filter is phase linear, (constant group delay important for the EC combinations). Other filters may be programmed, other demodulation algorithms may be used. 

All vibration equipment shall eonform to API 670. The probes shall be properly loeked to prevent movement during operation. Conneetions from oseillator/demodulators to the Purehaser s wiring shall terminate at suitable terminal bloeks loeated within junetion boxes mounted at the edge of the unit or baseplate. The probes shall be externally removable and adjustable without unit shutdown. 

For most applications, the modulator/demodulator is calibrated to a scale of 200 millivolts per mil. This means that for each one mil of gap change, there will be a corresponding 200 millivolt change. Five mils nt gap change will produce a one volt change in output of the modulator/ demodulator,... 

If the observed surface is moving, the modulator/demodulator output varies in direct proportion to the peak-to-peak movement of the observed surface. Having a flat frequency response from DC to 10,000 Hz, the transducer is able to accurately follow motion at frequencies in excess uf those typically encountered. 

There are several types of information available from each probe and modulator/demodulator. Average gap, or position, data are available from the DC output. Thus, the system can be used for measurement of average position, eccentricity, concentricity, thickness, etc. 

The AC component of the modulator/demodulator output is an indica tion of dynamic motion, or vibration. This signal provides data relating to the peak-to-peak amplitude, frequency, and form of the dynamic action of the observed surface. 

Using amplitude demodulation,180,181 the Ea=0 for pc-Cd/aqueous NaF and Na2S04 solutions has been found to be very close to that measured by impedance.10,74,637-644 A slight variation of Egsa with cc) has... 

Mishuk et a/.675,676 have applied the modified amplitude demodulation method to electrochemically polished pc-Bi in aqueous NaF solution. The curves of the real component of the nonlinear impedance Z" as a function of the electrode potential, unlike pc-Cd and pc-Pb, intersect for various cNaF at E - -0.62 V (SCE),674 i.e., at Ea=0 for pc-Bi, as obtained by impedance.666-672 The different behavior of pc-Bi from pc-Cd and pc-Pb at a > 0 has been explained by the semimetallic nature of pc-Bi electrodes. A comparison of inner-layer nonlinear parameter values for Hg, Cd, and Bi electrodes at a < 0 shows that the electrical double-layer structure at negative charges is independent of the metal.675,676... 

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). 

For single exponential fluorescence decay, as is expected for a sample containing just one fluorophore, either the phase shift or the demodulation can be used to calculate the fluorescence lifetime t. When the excitation light is modulated at an angular frequency (o = 2itv, the phase angle f, by which the emission modulation is shifted from the excitation modulation, is related to the fluorescence lifetime by ... 

Luminescence lifetimes are measured by analyzing the rate of emission decay after pulsed excitation or by analyzing the phase shift and demodulation of emission from chromophores excited by an amplitude-modulated light source. Improvements in this type of instrumentation now allow luminescence lifetimes to be routinely measured accurately to nanosecond resolution, and there are increasing reports of picosecond resolution. In addition, several individual lifetimes can be resolved from a mixture of chromophores, allowing identification of different components that might have almost identical absorption and emission features. 

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. 

The quantity of interest is the precession of the components perpendicular to B0 that are measured in the experiment by induced voltage in the coil, which is subsequently amplified and demodulated. We can write them either as individual components Mx, M, or by a vector M+, which combines both of them. In the static field, the precession about B0 occurs with the Larmor frequency w0 = /B0. If we neglect those processes which dampen the amplitude of the rotating transverse magnetization as precession proceeds, this already describes the frequency that we pick up with our receiver coil, and it is the third and perhaps the most important of our three fundamental equations of NMR ... 

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 analyze frequency domain FLIM data, first the phase shift and demodulation of the fluorescence light with respect to the excitation light are estimated. In the case of single frequency data, this reduces the FLIM data to only three parameters phase shift, demodulation, and total intensity. This step can be done in various ways as described in the following sections. From these parameters, the lifetimes can be estimated either by Eqs. (2.6 and 2.7), or by more elaborate approaches as described below. 

---