Waveform synthesizer

To perform broadband FTMW spectroscopy we require a microwave source that can produce phase-locked linear frequency sweeps over an 11 GHz frequency range in times ranging from 100 ns to 1 ps (sweep rates of 10 ° - lO" MHz/s). The short sweep durations are required so that the sample is polarized on a time scale faster than the pure dephasing of the rotational free indnction decay (FID). Traditional microwave synthesized sweepers are typically limited to sweep rates of about 10 MHz/s. We have developed a microwave source based on a 4 Gs/s arbitrary waveform generator that can produce the required excitation pulses. A schematic of the microwave source is shown in Figure 1. 

Square wave voltammetry is always performed using a computer-controlled potentio-static system with functional elements organized essentially as in Figure 7.3.11. The computer provides for operator interaction, synthesizes the waveform, sequences the sampling and logging of data, computes difference currents, and handles reporting of results, either graphically or otherwise. In many systems, the computer also controls the electrode, especially if an SMDE is involved. 

Figure 2.3. Concatenative speech synthesis of the word synthesize (lower). The top waveform is an actual recording of the spoken synthesize. ...

Selecting carrier and modulator frequencies that are not related by simple integer ratios yields an inharmonic spectrum. For example, a carrier of 500 Hz, a modulator of 273 Hz, and an index of five yields frequencies of 500 (carrier), 227,46, 319, 592, 865, 1138, 1411 (negative sidebands) and 773, 1046,1319,1592,1865,2138,2411 (positive sidebands). Figure 10.13 shows a spectrogram of this FM tone, as the index of modulation is ramped from zero to five. The synthesized waveforms at 7 = 0 and 7= 5 are shown as well. 

By setting the modulation index high enough, huge numbers of sidebands are generated, and the aliasing and addition of these (in most cases) results in noise. Figure 10.14 shows the synthesized waveform and spectrum of an FM... 

Collisions of the mesh with other objects can be computed providing a suitable energy/penalty method is used to ensure passivity. The benefit of this method is that it can be used both for animation and sound computation. Figure 12.9 shows an animation of the bowl bouncing from a rigid floor surfece, and the resulting synthesized waveform and spectrogram. All were computed from the same simulation. 

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