Quadrature signal

Response (FIR) filters have been implemented in the FPGA. Finally, the in-phase and quadrature signal pair is stored in a memory, also built inside the FPGA, according to the acquisition phase indicated by the pulse programmer. 

Bayesian probability theory157 can also be applied to the problem of NMR parameter estimation this approach incorporates prior knowledge of the NMR parameters and is particularly useful at short aquisition times158 and when the FID contains few data points.159 Bayesian analysis gives more precise estimates of the NMR parameters than do methods based on the discrete Fourier transform (DFT).160 The amplitudes can be estimated independently of the phase, frequency and decay constants of the resonances.161 For the usual method of quadrature detection, it is appropriate to apply this technique to the two quadrature signals in the time domain.162-164... 

I is necessary if one is seeking to obtain the very high resolution spectra I which can, in principle, be obtained from this particular sample. I. Quadrature detection was used, with sequential acquisition of the two I quadrature signals ( 1.4.2). Eight transients were collected using 7t/4 I pulses and a 5 s relaxation delay. In this sample, the spin-lattice relaxation is very slow and long recycle times (15 s) are necessary to avoid errors in signal intensities ( 1.4.7). 

FIGURE 3.3 Depiction of the quadrature signal in Eq. 3.8 for (a) reference frequency bjd < a> (b) (o,( = or, (c) etyf > to. The inward spiral results from transverse relaxation at rate 1/T2. From Chen and Hoult,37 Biomedical Magnetic Resonance Technology by C.-N. Chen and D. I. Hoult. Copyright 1989 IOP Publishing Limited. Reproduced with permission. 

In practice, additional phase cycling is needed in order to generate quadrature signals that can be processed as discussed in Section 10.3 to produce properly phased line shapes. Because of the DQC precession frequency, phase increments of tt/4 are needed to provide the same sort of data usually obtained with tt/2 phase shifts. Hence, a second set of phase-cycled repetitions is needed, with data stored in a separate location. Overall, the following phase cycling can be... 

For H NMR spectra, the number of scans should be a multiple of 4, since this is the length of the CYCLOPS phase cycle used to minimize imperfections associated with quadrature signal detection (Section 5-8). Anywhere from 4 to 128 scans are usually sufficient to obtain a good spectrum with a relatively flat baseline. This number, however, depends heavily on the concentration of the sample. Nevertheless, accumulation times of over 1 hour are relatively rare. 

Monitor quadrature signal throughout temperature scan for capacitive effects and report results. 

The synchronous demodulator (4) eliminates the quadrature signal. This demodulator multiplies the input signal with a reference signal, which is generated by the sensor drive velocity. The signal conditioner (7) corrects any time delay and phase shift, because the reference signal has to relate in the phase exactly to the velocity of the sensor drive. 

Manufacturing tolerances of the sensor element often require a mechanical alignment, by laser trimming of the element for example, in order to minimize the quadrature signal. 

Inherent frequency limited by increasing quadrature signal. 

Another method to correct imperfect phases and amplitudes of the two supposedly quadrature signals is to do it mathematically. The basic idea is to construct a linear combination of the two signals to create a third which is truly in quadrature with one of the original signals (Stejskal and Schaefer, 1974b Parks and Johanneson 1976). 

After a first paper in 1988, " Bretthorst paved the way for the application of Bayesian probability theory (BPT) in a series of three papers.- The first presents the connection between the theory and the case of NMR phenomena and discusses parameter estimation and detection of quadrature signals. The second " shows the ability of Bayesian methods to measure the quality of a model. The third " provides examples of applications to experimental data where decaying sinusoids are assumed. A fourth paper, produced during the following two years, discusses computer time requirements and noise, and it is shown to be important to include knowledge in the analysis," " while a fifth publication is devoted to amplitude estimations for multiplets of well-separated resonances. 

The low-pass filtered result is a DC voltage proportional to the cosine of the phase difference between the signals quadrature signals (

peak amplitude of the 2. harmonic component is half the fundamental and independent of the phase. 

Using a dual-phase lock-in amplifier, the in-phase and quadrature signals become ... 

Hemsing, W.F. Visar Interferometer Quadrature Signal Recording by Electronic Streak Camera, Proc. 8th Symposium (Intemational) on Detonation, NSWC MP 86-194, Albuquerque, NM, 1985, pp. 468-473. 

Lo Y L, In-fiber Bragg grating sensors using interferometric interrogations for passive quadrature signal processing , IEEE Photon. Technol. Lett, 1998,10(7), 1003-5. 

Fig. 1.22 Heterodyne-detected -Riiiiii fifth-order Raman response of CS2 measured using the crossed-beam geometry and 100 p.m pathlength. Two phase settings are shown solid line is the in-phase signal (A0 = 0), dotted line is the in-quadrature signal (A0 = 7t/2), The signal scans are,/rom top to bottom, probe delay (T4), pump delay (T2), and diagonal scan (t2 = T4) [23], Reused with permission from [23], Copyright 2002, American Institute of Physics...

---