Frequency modulation deviation

A phase modulation can also be expressed as frequency modulation. The corresponding frequency deviation is the time derivative of the modulated phase angle (Pm t). According to the basic relationships Afrequency deviation Af(f) with respect to the carrier frequency fg, commonly known as the Doppler frequency shift... 

Note that the stationarity assumption results in a spectrum consisting of identically shaped (window) pulses placed at the sine-wave frequencies. Most signals of interest however are generally nonstationary (e.g., the frequencies may change over the window extent due to amplitude and frequency modulation), and so the window transform may deviate from this fixed shape. Naylor and Porter [Naylor and Boll, 1986] have developed an extension of the approach of this section that accounts for the deviation from the ideal case. 

Figure 3.11a Stylised illustration of frequency modulation. The low frequency waveform A causes modulation of the carrier frequency B resulting in the frequency modulated waveform C whose frequency varies with time. The magnitude of the carrier frequency change is the deviation and the rate is the frequency of the modulating waveform A...

Frequency deviation The peak difference between modulated wave and the carrier frequency. Frequency modulation A system of modulation where the instantaneous radio frequency varies in proportion to the instantaneous amplitude of the modulating signal and the instantaneous radio frequency is independent of the frequency of the modulating signal. 

The spectrum analyzer is also well-suited for making accurate transmitter FM deviation measurements. This is accomphshed using the Bessel null method. The Bessel null is a mathematical function that describes the relationship between spectral lines in frequency modulation. The Bessel null technique is highly accurate it forms the basis for modulation monitor calibration. The concept behind the Bessel null method is to drive the carrier spectral line to zero by changing the modulating frequency. When the carrier amphtude is zero, the modulation index is given by a Bessel function. Deviation can be calculated from... 

Novotny et al. [41] used p-polarized reflection and modulated polarization infrared spectroscopy to examine the conformation of 1 -1,000 nm thick liquid polyperfluoropropy-lene oxide (PPFPO) on various solid surfaces, such as gold, silver, and silica surfaces. They found that the peak frequencies and relative intensities in the vibration spectra from thin polymer films were different from those from the bulk, suggesting that the molecular arrangement in the polymer hlms deviated from the bulk conformation. A two-layer model has been proposed where the hlms are composed of interfacial and bulk layers. The interfacial layer, with a thickness of 1-2 monolayers, has the molecular chains preferentially extended along the surface while the second layer above exhibits a normal bulk polymer conformation. 

Burke and his students (11) have published a proposal for solving the non-linearity problem associated with CC and the consequent correlation noise. They used a constant frequency multiple injection signal while this occurred, this frequency was modulated. Before each injection, a random number was generated to determine the magnitude and sign of the deviation from the carrier frequency for the next injection time. Thus, the next... 

The maximum instantaneous frequency deviation A (Umax is therefore given by A (i)max I(i>m. When the modulation index/is nonzero, side frequencies occur above and below the carrier 00c, and the number of side frequencies increases with increasing I. 

On a RDE, if the electrode is not uniformly active, then the individual sites can behave as if they were isolated UMEs embedded in the wall of a channel. Except, in this case, the solution velocity parallel to the wall varies with radial position of the electrode. For an electrode with an array of active sites, sufficiently separated, two relaxations are expected, as illustrated in Fig. 10.18. At sufficiently low modulation frequencies, the distance scale, SHm, of the perturbation of the hydrodynamic boundary layer is much larger than the size and spacing of the sites, so the electrode behaves as a uniform surface. A deviation is observed when hm becomes comparable to the spacing between the sites. Under these conditions, the surface responds to the perturbation as a set of isolated electrodes. 

Fig. 10.18. Effects of surface roughness on EHD impedance (amplitude ratio, H(p)IH(p- 0), and phase lag, 9, against scaled frequency, p and comparison with the behaviour of a uniform disc—asymptotic line marked (a) —and an array of UMEs— asymptotic line marked (b). The frequency shift is deduced from the displacement between the two sections of the phase angle diagram where the data superimpose for different n . The modulation frequency, to2, at which the data deviate from that of a uniform electrode, is related to the amplitude of the surface roughness or the spacing between the elements of the UME array. Data from Reference [121], for Fe(CN)i reduction on smooth Pt at 120 rpm 4 240 rpm, and on a rough, Pt-coated silver electrode (roughness scale 5 (im, disc diameter 6 mm) at O 120 rpm + 240 rpm A 500 rpm and x 1000 rpm.

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