Frequency Modulation examples

Sources of Physiological Noise. Despite the apparent importance of Hb, in the literature, the change in HbO is most widely reported and sometimes is the sole response reported. HbO is sometimes preferred due to its higher sensitivity to NIR based measurements than Hb. However, HbO measurements are not without disadvantages. There have been some studies (see for example [77] [22] [23] [47]) which indicate the presence of low frequency modulation ( 0.1 Hz) of both vascular (Hb, HbO) and metabolic (cytocrhome-c-oxidase) responses to visual stimuli with unknown origin. The cause of these low frequency oscillations are... 

Here we will summarize some known results for the simplest example of random frequency modulation as defined by Eq. (2). Let us assume that the process 2( ) in Eq. (2) is a projection of a Markovian process characterized by the evolution operator T. This is possible in principle, because the dynamical motion of the environment can be described in terms of a Liouville operator. The set of variables defining the Markovian process is designated by X. If the variable fi itself is Markovian, X consists only of 2, but in general it has to be supplemented by additional variables to complete the set. Let the function W(x, X, t) be the probability or the probability density for finding the random variables x and X at the respective values at the time t. Then a systematic method of treating the problem, Eq. (2), is to rewrite it in the form... 

A number of attempts were made to develop cyclotrons that could accelerate protons up to energies on the order of a GeV (the proton rest mass). For example, the resonant frequency of the cyclotron could be decreased in proportion to the mass increase. Such a frequency-modulated (FM) cyclotron (synchrocyclotron)... 

The graphical representation of this protocol is shown schematically in Fig. 10.15. Signals from two amperometric electrodes, representing channel 1 (blue) and channel 2 (red) detect to electroactive species, which is delivered to them with frequency modulation of, for example, 1 Hz. The experiment is performed in the benchtop fluid setup shown in Fig. 10.16. The first interesting observation is the presence of higher harmonics in the coherence spectrum. They arise as the effect of nonsinusoidal modulation. A pure sine wave would transform to the frequency domain as a single line. Any other waveform of the same frequency will contain higher harmonics in the spectrum. 

We can divide synthesis techniques into four basic categories Additive (Linear), Subtractive, Nonlinear and Physical modeling. Synthesis algorithms depend critically on the implementation of oscillators. For example, in the implementation of Frequency Modulation (F.M.), the output of one oscillator will serve as the input to another. Since the number of real time oscillators depends on the number of simple oscillators, it is important to efficiently and speedily implement the realizations. 

Even more interesting sounds can be made by more complex usage of the FM formulas. With frequency modulation one might select more than one modulating waveform, or perhaps different waveforms than sinusoids. In addition, a complex amplitude modulation can be imposed. For example, one possibility is revealed in the trigonometric relation... 

In woodwinds, on the other hand, odd harmonics can be present and the bandwidth may decrease as the attack increases, higher frequencies first becoming prominent. Odd harmonics can be created by making the modulation frequency exceed the carrier. For example, the frequency modulation coOT = 2 coc gives only odd harmonics... 

Using amplitude or frequency modulation of a carrier at frequency tog, we can achieve exact frequency division if we make sidebands of the carrier to such low frequency that we can force the condition wg-nQ = (n+2) 2-a>g = 2 so that tog/ 2 = n+1. For example, if we examine Fig. 2, we can achieve exact frequency division by any means which locks the phase of the carrier to the phase of the amplitude modulation that is, the undulations of the carrier do not "slip" under the envelope of the amplitude modulation. A divider based on these principles would be quite useful if 2 is in the microwave region (or below) where precise frequency synthesis is possible. Since 2 and n could be freely chosen, any value of uig could be measured in a single device. 

The required extreme amplitude or frequency modulation might be accomplished with the interaction of an electromagnetic wave (at frequency Wg) with a single electron oscillating at frequency 2. For example, 2 might be the cyclotron frequency of the electron in a magnetic field. 

It passes through the sample absorption cell made of Pyrex with polyethylene windows and is detected with a liquid helium cooled bolometer. One of the lasers is frequency-modulated at 1 kHz and the detector output is processed with a lock-in amplifier, as shown. Far-infrared rotational spectra of CO, HC1 and HF have been recorded [67], and as an example of the excellent sensitivity achieved, we refer the reader to the spectrum of the OH radical [68] shown later in this chapter. Evenson s spectrometer operates over a wide range of the far-infrared region up to 9 THz, with excellent frequency stability. 

On the other hand, there are measurements in which signal and noise cannot be directly filtered and the signal has to be transposed onto a carrier wave to be shifted away from the noise frequencies (modulation). Then an amplifier is tuned to the frequency of the carrier wave and the amplified original signal is finally recovered (demodulation). The use of a chopper in optical spectrophotometers is a common example of this process [i]. Ref [i] Horowitz P, Hill W (2001) The art of electronics. Cambridge University Press, Cambridge... 

The first SMS experiments in 1989 utilized either of two powerful doublemodulation FM absorption techniques, laser frequency-modulation with Stark secondary modulation (FM-Stark) or frequency-modulation with ultrasonic strain secondary modulation (FM-US) [3,26]. The secondary modulation was required in order to remove the effects of residual amplitude modulation produced by the imperfect phase modulator. In contrast to fluorescence methods, Rayleigh and Raman scattering were unimportant. Figure 2.3B (specifically trace d) shows examples of the optical absorption spectrum from a single molecule of pentacene in p-terphenyl using the FM-Stark method. 

The frequency of a cyclotron can be modulated to take into account the variation in velocity and mass as relativistic effects increase in importance. At very high energies the radius becomes very large. This has led to two somewhat different accelerator designs. The frequency modulated (FM) or synchrocyclotron maintains the original cyclotron principle witih a spiral particle path, while in synchrotrons the particle path is fixed in a circular orbit Figure 13.10 is an example of the latter. 

As pointed out above, the most accurate and reliable information obtained by ENDOR is the resonance frequency that directly gives the hyperfine coupling con.stant. In this respect, the firequency-derivative ENDOR spectra obtained by cw-ENDOR detection by employing the frequency modulation scheme, are particularly important because of high-frequency resolution. Combined with ENDOR-induced ESR, the maximum ENDOR frequency, important in identifying the peak value of the spin density distribution, can be determined very accurately [7]. Specific examples are discussed in the cases of solitons in polyacetylene and polarons in poly(paraphenylene vinylene) in Sections 3.2 and 3.3. 

For an illustrative purpose, we choose a simple model of the spectral diffusion, which is called a two-state jump process or a dichotomic process. We assume that the frequency modulation can be either Aco(t) = v or Aco(t) = — V, and the flipping rate between these two frequency modulations is given by R. This model will be used as a working example for which an analytical solution is obtained later in Section V. 

The spectrum near 600 cm of the V2 band of the CH3 radical generated by a glow discharge in di-tert-butylperoxide (Yamada et. al. 1981) provides a second example of this selectivity. With Zeeman modulation all the observed lines arise from CH3, but with source frequency modulation many additional lines from diamagnetic species are detected in the same spectral region. 

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