Impulse response method

Step- and impulse-response methods. Chemisorption can conveniently be measured under flow conditions using transient techniques, in particular, step-response and impulse-response measurements. After pretreatment, pulses of probe gas are injected into a carrier gas stream passing through the reactor that contains the pre-treated. sample. The response is detected at the reactor exit. 

Figure 2.2 Impulse response method in a flow system.

When the impulse response method is used, the following standardized condition should be satisfied ... 

Blender distributor mixedness for impulse response method... 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

The FRF, G(tw), can be obtained by various methods such as finite element method (FEM), Timoshenko beam theory (Cao and Altintas 2004), impulse response method (Ewins 2001), or widely used frequency response analysis (Ewins 2001). Hybrid methods such as the receptance coupling substructure analysis (RCSA) (Schmitz and Duncan 2005) have also been utilized in practice. For example, excitation force generated in milling process can be estimated by an analytical model of the milling process (Altintas 2000). 

Fig. 6.5 Estimating the time delay using (left) the cross-correlation plot and (right) the impulse response method...

The equation system of eq.(6) can be used to find the input signal (for example a crack) corresponding to a measured output and a known impulse response of a system as well. This way gives a possibility to solve different inverse problems of the non-destructive eddy-current testing. Further developments will be shown the solving of eq.(6) by special numerical operations, like Gauss-Seidel-Method [4]. 

All described sensor probes scan an edge of the same material to get the characteristic step response of each system. The derivation of this curve (see eq.(4) ) causes the impulse responses. The measurement frequency is 100 kHz, the distance between sensor and structure 0. Chapter 4.2.1. and 4.2.2. compare several sensors and measurement methods and show the importance of the impulse response for the comparison. 

The following examples represent the importance of the impulse response for the comparison of different magnetic field sensors. For presentation in this paper only one data curve per method is selected and compared. The determined signals and the path x are related in the same way like in the previous chapter. 

Methods from the theory of LTI-systems are practicable for eddy-current material testing problems. The special role of the impulse response as a characteristic function of the system sensor-material is presented in the theory and for several examples. 

The method proposed by Papoulis [7] to determine h(t) as a function of its Fourier transform within a band, is a non-linear adaptive modification of a extrapolation method.[8] It takes advantage of the finite width of impulse responses in both time and frequency. 

Implementation Issues A critical factor in the successful application of any model-based technique is the availability of a suitaole dynamic model. In typical MPC applications, an empirical model is identified from data acquired during extensive plant tests. The experiments generally consist of a series of bump tests in the manipulated variables. Typically, the manipulated variables are adjusted one at a time and the plant tests require a period of one to three weeks. The step or impulse response coefficients are then calculated using linear-regression techniques such as least-sqiiares methods. However, details concerning the procedures utihzed in the plant tests and subsequent model identification are considered to be proprietary information. The scaling and conditioning of plant data for use in model identification and control calculations can be key factors in the success of the apphcation. 

The response-factor approach is based on a method in which the response factors represent the transfer functions of the wall due to unit impulse excitations. The real excitation is approximated by a superposition of such impulses (mostly of triangular shape), and the real response is determined by the superposition of the impulse responses (see Figs. 11.33 and 11.34). ... 

Since all tracer entered the system at the same time, t = 0, the response gives the distribution or range of residence times the tracer has spent in the system. Thus, by definition, eqn. (8) is the RTD of the tracer because the tracer behaves identically to the process fluid, it is also the system RTD. This was depicted previously in Fig. 3. Furthermore, eqn. (8) is general in that it shows that the inverse of a system transfer function is equal to the RTD of that system. To create a pulse of tracer which approximates to a dirac delta function may be difficult to achieve in practice, but the simplicity of the test and ease of interpreting results is a strong incentive for using impulse response testing methods. 

P. Veng-Pedersen, Novel deconvolution method for linear pharmacokinetic systems with polyexponential impulse response, J. Pharm. Sci.,... 

There are several other chemometric approaches to calibration transfer that will only be mentioned in passing here. An approach based on finite impulse response (FIR) filters, which does not require the analysis of standardization samples on any of the analyzers, has been shown to provide good results in several different applications.81 Furthermore, the effectiveness of three-way chemometric modeling methods for calibration transfer has been recently discussed.82 Three-way methods refer to those methods that apply to A -data that must be expressed as a third-order data array, rather than a matrix. Such data include excitation/emission fluorescence data (where the three orders are excitation wavelength, emission wavelength, and fluorescence intensity) and GC/MS data (where the three orders are retention time, mass/charge ratio, and mass spectrum intensity). It is important to note, however, that a series of spectral data that are continuously obtained on a process can be constructed as a third-order array, where the three orders are wavelength, intensity, and time. 

This paper has discussed algorithms for rendering reverberation in real-time. A straightforward method for simulating room acoustics is to sample a room impulse response and render the reverberation using convolution. Synthetic impulse responses can be created using auralization techniques. The availability of efficient, zero delay convolution algorithms make this a viable method for real-time room simulation. The drawback of this method is the lack of parameterized control over perceptually salient characteristics of the reverberation. This can be a problem when we attempt to use these systems in interactive virtual environments. 

Impulse (delta) response method The input signal is changed in the form of a delta function. This method is widely used in chemical engineering to investigate the residence time probability density distribution function. 

The method of Finite Fourier Transform with step and impulse responses (9) is used to solve Eq. (7) with boundary conditions (7a), (7b), and (17). The resulting dimensionless concentration profile of the desired product B is ... 

Thus, it becomes apparent the output and the impulse response are one-sided in the time domain and this property can be exploited in such studies. Solving linear system problems by Fourier transform is a convenient method. Unfortunately, there are many instances of input/ output functions for which the Fourier transform does not exist. This necessitates developing a general transform procedure that would apply to a wider class of functions than the Fourier transform does. This is the subject area of one-sided Laplace transform that is being discussed here as well. The idea used here is to multiply the function by an exponentially convergent factor and then using Fourier transform technique on this altered function. For causal functions that are zero for t < 0, an appropriate factor turns out to be where a > 0. This is how Laplace transform is constructed and is discussed. However, there is another reason for which we use another variant of Laplace transform, namely the bi-lateral Laplace transform. 

The mean residence time can be best evaluated by using the method of moments. In order to estimate the three parameters, tj>, N, and P, the experimental impulse response u(t) is, first, calculated numerically from the input and output signals on the basis of the following equation ... 

In the present work, we use the weighted-moments method to estimate parameters by fitting the theoretical Laplace domain moments to the experimentally generated moments for the impulse response. Thus, for the model without deadwater (equation 11), the Laplace transform for the response variable at the exit is (2) ... 

The methods for determining fluorescence lifetimes fall into three categories impulse-response [11], time-correlated photon coimting [12], and frequency-... 

Veng PP. Novel Deconvolution Method for Linear Pharmacokinetic Systems with Polyexponential Impulse Response.]Pharm Sci 1980 69 312-318. 

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