Gaussian-shaped waveform

By giving a set of arbitrary values for two parameters P and W, we can expre.ss a variety of light fields with incoherent and/or coherent modulation for computer simulation. Figure 5 shows the intensity waveforms of typical four kinds of light fields with the "same" power spectrum of Gaussian shape,... 

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

The following Check its will use the Bloch simulator module of NMR-SIM to study and analyse a number of different shaped pulses. Time Evolution, the Excitation Profile and the Rf field profile simulation are illustrated using a 90° Gaussian pulse while an adiabatic CHIRP pulse is used for the Waveform analysis. 

A common definition of Q (t,tmax) is a squared sine wave, time scaled and shifted to fit its first halfperiod into the systolic time interval, and zeroed elsewhere, for example, see Martin et al. [ 1986]. Another common definition uses the first half-period of a sine wave, time-scaled and shifted to fit into the systolic interval. It is sometimes clipped and sometimes modified with a second harmonic to skew the waveform, for example, see Rideout [1991]. Still others have approximated a (t,tniax) as a square wave [Warner, 1959], a triangle wave [McLeod, 1966 Katona et al, 1967], a sum of charging and discharging exponentials [Sun and Chiaramida, 1992], and even as a sum of gaussian (bell-shaped) exponentials [Chung et al., 1994]. 

FIGURE 18.8 Cross-correlation-based method to detect the presence of spikes or action potentials in multiunit activity. The continuous waveform with the action potentials is shown in (b). The shapes of the action potentials to be detected are known a priori (deteiministic signal). Using a cross-correlation of the known signal [templates (c) and (d)] with the measured signal, the presence of action potentials is indicated by a vertical line in (a). This approach is optimal in the presence of white Gaussian noise. 

TA = Tf — T + Tf- For semi-Gaussian pulse outputs, the factors listed in Table 4.6 (Chapter 4) can be used to calculate peaking time, Tp, and the overall peak processing time, from the shaping time. However, these are defined differently for different types of pulse processor. The various relevant waveforms are shown in Figure 14.15. 

Figure 3.13a-c shows the output pulse waveform from GI POFs with microscopic heterogeneities, with microbending, and without any perturbations, calculated for different fiber lengths. The temporal pulse shape of the incident light is Gaussian with a full width at half-maximum of 83 ps. Owing to intermodal... 

---