Sinusoidal wave analysis

In practice ultrasound is usually propagated through materials in the form of pulses rather than continuous sinusoidal waves. Pulses contain a spectrum of frequencies, and so if they are used to test materials that have frequency dependent properties the measured velocity and attenuation coefficient will be average values. This problem can be overcome by using Fourier Transform analysis of pulses to determine the frequency dependence of the ultrasonic properties. 

The RTD for a given reactor and flow rate can be established from response-type experiments. In these experiments the concentration of an inert tracer is disturbed in the feed stream and its effect on the effluent stream is measured. The three most common perturbations are a step function, a pulse (square wave), and a sinusoidal wave. The relationships between the observed concentration-vs-time curves and the RTD are examined here for step functions and pulses. The analysis of sinusoidal perturbations is more complex but is available in the literature. ... 

When a linear system is subjected to a sinusoidal input, its ultimate response (after a long time) is also a sustained sinusoidal wave. This characteristic, which will be proved in Section 17.2, constitutes the basis of frequency response analysis. 

With frequency response analysis we are interested primarily in determining how the features of the output sinusoidal wave (amplitude, phase shift) change with the frequency of the input sinusoid. In this chapter we deal only with the basic premises of frequency response analysis, leaving its use in controller design for Chapter 18. 

The thermal and thermomechanical properties of the polymer/HAp composites (glass transition temperature, melting and crystallization behaviour, thermal stability, crosslinking effects, phase composition, modulus, etc.) can be evaluated by thermal analysis methods, like TG, DSC and DMA. Recently, a modulated temperature DSC (MTDSC) technique has been developed that offers extended temperature profile capabilities by, for example, a sinusoidal wave superimposed on the normal linear temperature ramp [326]. The new capabilities of the MTDSC method in comparison with conventional DSC include separation of reversible and non-reversible thermal events, improved resolution of closely occurring and overlapping transitions, and increased sensitivity ofheat capacity measurements [92,327]. 

Harmonic analysis methods, such as STFT and wavelets, are not entirely adequate for the analysis of sounds with a high proportion of non-sinusoidal components and, to a certain extent, to non-harmonic combinations of partials. The nature of these signals is not compatible with the notion that sounds are composed of harmonically related and stable sinusoids. Formant analysis proposes an alternative method of representation. The sound is represented here in terms of an overall predictive mould that shapes a signal rich in partials, such as a pulse wave or white noise. The advantage of this method is that the predictive mould does not need to specify the frequencies of the spectrum precisely any value within a certain range may qualify. 

Some variation in thickness is always present in continuously extruded products. It may be too small to be of concern for the product application or it may not be measured or measurable with instrumentation in use. However, the result is always thickness that is varying in time periodically or continually (very long period of change.) For periodic variation, the thickness variation will have a wave shape, which may be irregular or regular (e.g., a simple sinusoidal wave shape.) Also, the period of the wave shape or disturbance may be regular or irregular (random.) Observation and analysis of these characteristics of the wave shape can be used to trace the source of the flow disturbances. 

Fig. 3.47 is comparable to Fig. 3.41 for sinusoidal ac polarography if the tilted shape provides a net compensation of the charging current one obtains a symmetric bell-shaped curve of I in the square-wave polarogram, similar to that depicted in Fig. 3.42. In fact, virtually all of the statements made before on the sinusoidal technique are valid for the square-wave mode except for the rigid shape of its wave this conclusion is according to expectation, especially as Fourier analysis reveals the square wave to be a summation of a series of only...

Perhaps the first detailed discussion of such a technique in fluorescent thermometry (shown in Figure 11.10) was given by Zhang et al. in their work(36) based on both mathematical analysis and experimental simulation. Examples of the electronic design of the corresponding system and the application of the technique in a ruby fluorescence-based fiber-optic sensor system are also listed. This shows that there is no difference in the measurement sensitivity between a system using square-wave modulation and one using sinusoidal modulation. However, the former performs a little better in terms of the measurement resolution. 

This circuit subtracts a 5 kHz sinusoid from a 1 kHz square wave. We would like to set up a Transient Analysis to run this circuit for 5 ms. Select PSpice and then New Simulation Profile from the Capture menus, enter a name for the profile, and then click the Create button. By default the Time Domain (Transienti Analysis type is selected. The dialog box below is set up to run the circuit for 5 ms (Run to time 5m). The maximum step size (Maximum Step Size) is not specified so that the simulation will finish as soon as possible. 

Sinusoidal voltammetry (SV) is an EC detection technique that is very similar to fast-scan cyclic voltammetry, differing only in the use of a large-amplitude sine wave as the excitation waveform and analysis performed in the frequency domain. Selectivity is then improved by using not only the applied potential window but also the frequency spectrum generated [28]. Brazill s group has performed a comparison between both constant potential amperometry and sinusoidal voltammetry [98]. 

Early approaches to music analysis relied on a running Fourier transform to measure sine-wave amplitude and frequency trajectories. This technique evolved into a filter-bank-based processor and ultimately to signal analysis/synthesis referred to as the phase vocoder [Flanagan and Golden, 1966], This section describes the history of the phase vocoder, its principles, and limitations that motivate sinusoidal analysis/synthesis. Other formulations and refinements of the phase vocoder are given in chapter 7. 

The purpose of this chapter is to describe the principles of signal analysis/synthesis based on a sine-wave representation and to describe its many speech and music applications. As stated, an important feature of the sinusoidal representation is that the aforementioned sound components can be expressed approximately by a sum of amplitude- and frequency-modulated sine waves. Moreover these sound components, as well as the source and filter contribution to their sine-wave representation, are separable by means of a sine-wave-based decomposition. This separability property is essential in applying sinusoidal analysis/synthesis in a number of areas. 

The preceding analysis views the problem of solving for the sine-wave amplitudes and phases in the frequency domain. Alternatively, the problem can be viewed in the time domain. It has been shown that [Quatieri and Danisewicz, 1990], for suitable window lengths, the vectors a andJ3 that satisfy Equation (9.75) also approximate the vectors that minimize the weighted mean square distance between the speech frame and the steady state sinusoidal model for summed vocalic speech with the sinusoidal frequency vector . Specifically, the following minimization is performed with respect to a andJ3... 

Another more sophisticated approach is to make a Fourier Transform analysis of the response in the way proposed by Bond et al. [84, 85]. In this case, the perturbation is a continuous function of time (a ramped square wave waveform) which combines a dc potential ramp with a square wave of potential that can be described as a combination of sinusoidal functions. Under these conditions, the faradaic contribution to the response generates even harmonics only (i.e., the non-faradaic current goes exclusively through odd harmonics). Thus, the analysis of the even harmonics will provide excellent faradaic-to-non-faradaic current ratios. 

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