Pulse rectangular

Comparing inputs of delta function pulse 0.5 ms wide rectangular pulse 1.0 ms wide rectangular pulse... 

Figure 1.15 Time domain representation of a hard rectangular pulse and its frequency domain excitation function. The excitation profile of a hard pulse displays almost the same amplitude over the entire spectral range.

This experiment requires a well-separated proton resonance for excitation rectangular pulses are used for the soft excitation. 

Rather high charging currents cross the electrode when a variable potential component is applied. Therefore, to reduce the influence of these currents in the case of rectangular pulses, the measurements are made at a specific time after the potential change, when the charging current has decreased drastically. In the case of sinusoidal superimposed currents, one uses another device based on the fact that the... 

The rectangular pulse can be generated by subtracting a step function with dead time T from a step function. We can derive the Laplace transform using the formal definition... 

This is a prelude to the important impulse function. We can define a rectangular pulse such that the area is unity. The Laplace transform follows that of a rectangular pulse function... 

In this example, we have a stirred-tank with a volume Vj of 4 m3 being operated with an inlet flow rate Q of 0.02 m3/s and which contains an inert species at a concentration Cm of 1 gmol/m3. To test the mixing behavior, we purposely turn the knob which doses in the tracer and jack up its concentration to 6 gmol/m3 (without increasing the total flow rate) for a duration of 10 s. The effect is a rectangular pulse input (Fig. 2.7). 

Figure 2.7. A rectangular pulse in real and deviation variables.

Hence the rectangular pulse is really a perturbation in the inlet concentration ... 

We now want to use an impulse input of equivalent "strength," /.e.. same amount of inert tracer added. The amount of additional tracer in the rectangular pulse is... 

With the rectangular pulse to the first vessel, we use the response in Eq. (2-40) and substitute... 

We also see another common definition—bounded input bounded output (BIBO) stability A system is BIBO stable if the output response is bounded for any bounded input. One illustration of this definition is to consider a hypothetical situation with a closed-loop pole at the origin. In such a case, we know that if we apply an impulse input or a rectangular pulse input, the response remains bounded. However, if we apply a step input, which is bounded, the response is a ramp, which has no upper bound. For this reason, we cannot accept any control system that has closed-loop poles lying on the imaginary axis. They must be in the LHP. 1... 

For useful applications, lsimo is what we need to simulate response to, say, a rectangular pulse. This is one simple example using the same transfer function and time vector that we have just defined ... 

Henderson SR, Baker C, Fink G (1977) Oestradiol-17beta and pituitary responsiveness to luteinizing hormone releasing factor in the rat a study using rectangular pulses of oestradiol-17 beta monitored by non-chromatographic radioimmunoassay. J Endocrinol 73 441-453... 

Assume the transmitted signal is a coherent train comprised of three rectangular pulses. The first example refers to the case where the target is close to the baseline Or = —80°) of one of the two bistatic pairs. For a simple bistatic radar it is well known that this scenario is detrimental to its resolution performance. The two baselines are set to lOOfcm and the target is stationary with Rr = 50km. 

Figure 9.9. Sinusoidal excitation can be regarded as a succession of sufficiently narrow rectangular pulses in lime Then, at any particular time r, the fluorescence response to the train of pulses sinusoidally modulated is given by the superposition of all single-pulse responses initiated at times l < t.

Let us regard the sinusoidal excitation of Eq. (9.46) as a succession of sufficiently narrow rectangular pulses in time t as illustrated in Figure 9.9. Let us also assume linear regime conditions such that only a small fraction of molecules is excited in the steady state with negligible stimulated emission and excited state reactions. 

Sinusoidal excitation provides only one harmonic at the modulation frequency. In contrast, pulsed light provides a large number of harmonics of the excitation repetition frequency. The harmonic content, the number of harmonics and their amplitude, is determined by the pulse width and shape.(25) For example, a train of infinitely short pulses provides an infinite number of harmonics all with equal amplitude. A square wave provides only three modulation frequencies with sufficient amplitude to be usable. Equation (9.74) gives the harmonic content of a train of rectangular pulses R(t) of D duty cycle (pulse width divided by period) and RP peak value ... 

The common feature of the schemes in this category is that the excitation light applied to the fluorescent material is a high intensity delta function pulse (e.g., a laser pulse or that from a flash lamp) or an rectangular pulse, and the measurement is derived from the observation of the fluorescence decay after the removal of the excitation light. The following are the outlines of some typical schemes which are of this type and have been used in thermometry applications. 

Fig. 4.52. Time-domain (left) and frequency-domain (right) excitation waveforms (a), (b) rectangular pulses (c) chirp excitation (d), (e) SWIFT excitations, with (e) formed to eject a certain mass range from the cell. Reproduced from Ref. [201] by permission. John Wiley Sons, 1998.

Find the Laplace transformation of a rectangular pulse of height and duration T. ... 

If the input pulse is a rectangular pulse of height h and duration D, its Fourier transformation is simply... 

The second device comprised a set of three circumferentially located pintle-type injectors Keihin, 10450-PG7-0031) to inject fuel radially into the main duct of the first flow arrangement as near-rectangular pulses. The frequency and duration of fuel injection were software controlled, and the fuel flow from each injector was delivered close to the outer edge of the annular ring flame holder by a cross-jet of air (1.2 x 5 mm), directed along the duct axis with exit velocity up to 100 m/s. The amplitude of the oscillated input was limited by the volume injection rate of the injectors. Propane, rather than methane, provided up to 3.5 kW of the total heat release of around 100 kW. With fluid dynamic damping, the RMS of the oscillated fuel flow corresponded to a heat release of around 1.8 kW. 

The peak rf amplitude required to achieve optimum excitation with a selective excitation pulse is given in comparison to the rf amplitude required to achieve an on-resonance 90° flip-angle with a selective rectangular pulse, the simplest conceivable shape. 

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