Sinusoid signals

Fig. 4. The effect of temperature for Mng 6 Zng 3 Fe Fe on (a) initial magnetic permeabiUty, )J., measured on a polycrystalline toroid appHed as a core for a coil driven by a low (B <0.1 mT) ampHtude, low (10 kHz) frequency sinusoidal signal and (b) magnetocrystalline anisotropy constant, measured on a monocrystalline sphere showing the anisotropy/compensation temperature Tq and the Curie temperature, T. To convert joules to calories, divide by...

Fig. 5.12. Stress versus time responses (measured currents) for (a) fee 28.5-at. % Ni above 2.5 GPa (25 kbar), (b) below 2.5 GPa, and (c) for bcc 28.5-at. % Ni, reveal substantial differences in mechanical response. Such records at different input stresses are used to determine the various stress-volume relationships (after Graham et al. [67G01]). Time increases from right to left. Timing waves (upper sinusoidal signal) are 10 MHz.

More sophisticated instruments use special circuitry to obtain the rms values of non-sinusoidal signals. The current converter usually consists of low-value resistors in the input, and one of these is chosen as a shunt resistor... 

This system produces a steady laminar flow with a flat velocity profile at the burner exit for mean flow velocities up to 5m/s. Velocity fluctuations at the burner outlet are reduced to low levels as v /v< 0.01 on the central axis for free jet injection conditions. The burner is fed with a mixture of methane and air. Experiments-described in what follows are carried out at fixed equivalence ratios. Flow perturbations are produced by the loudspeaker driven by an amplifier, which is fed by a sinusoidal signal s)mthesizer. Velocity perturbations measured by laser doppler velocimetry (LDV) on the burner symmetry axis above the nozzle exit plane are also purely sinusoidal and their spectral... 

Fig. 3.42 represents the symmetric bell shape curve of 7, i.e., the genuine fundamental harmonic ac polarogram, which means the curve of only 7F discriminated for 7C, e.g., by means of phase-selective ac polarography. The term "fundamental is related to the character of the polarographic cell as a non-linearized network whose response is not purely sinusoidal but consists of the sum of a series of sinusoidal signals at first harmonic (o>) response, besides that of the second harmonic (2a>), the third harmonic (3a>), etc. 

This technique is of high accuracy and is meant to be used in precision measurement instrumentation, for it is inherently insensitive to the DC-offset and the AC-noise in the sinusoidal signal which can be substantially reduced by a great variety of electronic devices ranging from various electronic analogue filters, and digital filters to the most effective lock-in amplifiers. 

A typical measuring circuit is shown in Fig. 9.15. A signal generator supplies a sinusoidal signal with 600 fl output impedance. The current is amplified at sensitivity of 10 AfV. The ac voltages are measured by ac digital voltmeters. The experiment is performed with a PZT-4 tube, provided by EBL, Inc., with L = 25.4 mm, D = 12.7 mm, h = 0.50 mm, and Y= 7.5 X 10 N/m. The lowest resonance frequency is 5 kHz. The results of measurements are shown in Fig. 9.16. The current, about 1 xA, can easily be measured with 1% accuracy. The current from the two x quadrants agrees well with that from the two y quadrants. In terms of the units mentioned, the piezoelectric coefficient dn can be obtained from directly measurable quantities as ... 

This indicates that the oscillation, once set in motion, will be maintained with constant amplitude around the closed-loop for =. % = 0. If, however, the open-loop gain or AR of the system is greater than unity, the amplitude of the sinusoidal signal will increase around the control loop, whilst the phase shift will remain unaffected. Thus the amplitude of the signal will grow indefinitely, i.e. the system will be unstable. 

The describing function method is applicable to any non-linearity which has the characteristic that if the input is a sinusoidal signal then the output is a periodic function 38 401. Because of its simplicity and wide range of applicability, the describing function technique is one of the most versatile procedures for analysing non-linear effects. 

Cancelling of the signal. For a sinusoidal signal of frequency 0 (which is supposed to correspond to the center frequency of one of the filters of the filter-bank), it is easily checked (assuming that the additional noise power spectral density is sufficiently smooth) that Eq. 4.18 becomes... 

The first approach that need to be more precisely evaluated is the use of non-uniform filter banks [Petersen and Boll, 1981, Valiere, 1991], especially if they are applied in connection with perceptual criteria. Indeed, non-uniform filter banks allow a frequency dependent specification of the time-resolution/bandwidth compromise which could be adapted to the known features of our hearing system. The results of section 4.16 show that a high frequency-resolution is needed anyway, at least in the lower part of the spectrum, to ensure a sufficient separation of sinusoidal signal components from the noise. 

In the case of quasi-periodic sinusoidal signals, the buzziness can often be linked to the fact that the phase coherence between sinusoidal components is not preserved. Shape invariant modification techniques for quasi-periodic signals are an attempt to tackle this problem. As explained in 9.4.2, quasi-periodic signals such as speech voiced segments or sounds of musical instruments can be thought of as sinusoidal signals whose frequencies are multiples of a common fundamental COo(x), but with additional, slowly varying phases 0 (/) ... 

Restoration of a sinusoidal signal embedded in white noise 169... 

Figure 4.17 Restoration of a sinusoidal signal embedded in white noise (of power 0 dB). (a) The noisy signal (the dotted lines feature the filter bank characteristics) (b) The processed signal.

Short-time Fourier transform of a sinusoidal signal. When the signal corresponds to the model of Eq. (7.1), the short-time Fourier transform can be expressed in terms of the model parameters. Substituting Eq. (7.1) into Eq. (7.6) yields... 

Fig. 11.21. The Fourier transform the link between the time and frequency domain, (a) A simple sinusoidal signal (b) The first two components of a square...

Lastly it should be noted that the time or scan rate issue equally plagues time as well as frequency domain methods for obtaining Rf, since in the time domain measurement, the triangle waveform is simply the Fourier synthesis of a series of sinusoidal signal functions. However, voltage sweep, potential step, and impedance methods should all yield the same value of Rf when all the scan... 

From the experimental standpoint, the use of a.c. techniques offers many advantages. Sensitivity is much higher than in d.c. measurements, since phase-sensitive detection can be used and very small probe signals can be employed ( 5mV). The technique is therefore a truly equilibrium one, unlike cyclic voltammetry. An alternative approach to the commonly used sinusoidal signal superimposed on the selected d.c. potential is to use a potential step and to employ Laplace transform methods. Instrumentally, this is rather more demanding and the advantages are not clear [51]. Fourier transform methods have also been considered and their use will have advantages in terms of the time-scale for an experiment, especially at very low frequencies. 

If the fluorescence from the sample has a lifetime much shorter than a half period, the fluorescence signal will vary in a sinusoidal manner, without phase shift. If the decay time is comparable with that half period, the sinusoidal signal from the sample emission is phase-shifted with respect to the excitation. For a single exponential lifetime r, the fluorescence response from the sample is... 

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