Time domain signal model

The time-domain signal model is again given by Eq. (101), which can also be written as... 

Using either the time domain input signal or the output of the analysis filter bank, an estimate of the actual (time dependent) masked threshold is computed using rules known from psychoacoustics. This is called the perceptual model of the perceptual encoding system. 

This chapter is organized as follows By reference to a signal model, time-scale and pitch-scale modifications are defined in the first part. The second part presents frequency-domain techniques while the third part describes time-domain techniques. In the fourth part, the limitations of time-domain and frequency-domain methods are discussed along with improvements proposed in the last few years. 

Kates, 1991b] Kates, J. (1991b). A time-domain digital cochlear model. IEEE Trans. Signal Processing, 39( 12) 2573—2592. 

The goat of the signal processing is the parameter determination of the state of mixedness (i.e. Bodenstein number, mean residence time, etc.). The identiflcation of the model parameters is done by using an off-line identification scheme. The identification can take place either in the time or in the frequency domain. Since the convolution in the time domain becomes a multiplication in the frequency domain, it is advantageous to execute the identification in the frequency domain to save computational costs. Additionally, the presentation of the results in the frequency domain offers new insights. 

Barnes, M.S., Colter, T.J. and Elta, M.E. (1987) Large-Signal Time-Domain Modeling of Low-Pressure rf Glow-Discharges. /. Appl. Phys., 61, 81-89. 

The previous discussions of the signal are nicely illustrated by an extremely simple model analysis using real fields and signals for two Lorenzian resonances at frequencies a and b. The sample is irradiated with two very short pulses whose spectra are flat. The real generated field from the sample is the real part of Eq. (21) or Eq. (33) with T set equal to zero for convenience since is in any case a multiplicative factor. In time-domain interferometry, this is measured directly along the indicated time axes as described above. In spectral interferometry the real generated field along with a real local oscillator field, delayed by time d, is dispersed (i.e., Fourier-transformed) by a monochromator, then squared by the detection to yield a spectrum on the array detector at each value of t ... 

Equations (27) and (28) or alternatively Eq. (31) provide the most general formal expression for any type of 4WM process. They show that the nonlinear response function R(t3,t2,t 1), or its Fourier transform (cum + a>n + (oq,com + tu ,aim), contains the complete microscopic information relevant to the calculation of any 4WM signal. As indicated earlier, the various 4WM techniques differ by the choice of ks and ojs and by the temporal characteristics of the incoming fields E, (t), E2(t), and 3(t). A detailed analysis of the response function and of the nonlinear signal will be made in the following sections for specific models. At this point we shall consider the two limiting cases of ideal time-domain and frequency-domain 4WM. In an ideal time-domain 4WM, the durations of the incoming fields are infinitely short, that is,... 

When we use continuous analog controllers, all signals in a loop are continuous in time. Then the dynamic behavior of each component in the loop (process, measuring device, controller, final control element), as well as the response of the overall control system, can be effectively analyzed by continuous models (differential equations in the time domain or transfer functions in the Laplace domain). 

The process has continuous input and output signals, and consequently it can be described by continuous models (differential equations in the time domain, transfer functions in the Laplace domain). 

One important comment should be made at this point. These least-squares methods are cening the best fit in the time domain, and they tend to give models that are more accurate at low frequencies than near the ultimate frequency, so you should be caretui n ) our testing to make sure that your input signal has a signilicant frequency conter r.ec ar the ultimate frequency. 

Sm(0) is the signal intensity of the experiment m at the time domain origin. This factor enables a comparison of the relative intrinsic sensitivities of different APSY-NMR experiments that are detected on the same nucleus, and can thus help to identify high-sensitivity experiments. Values for Sm(0) can be estimated either experimentally, e.g., from ID NMR spectra of the time domain origins, or from model calculations [41]. Table 2 lists calculated values for different amide proton-detected experiments. 

To summarize, as a model of multidimensional FID signal, one can use an oscillatory function consisting of multiple, decaying components of various amplitudes. The spectrum of such a signal is built of Lorentzian peaks centered at frequency coordinates corresponding to component frequencies. Peak heights are proportional to component amplitudes in time domain. Peak half-widths are the inverse of signal decay rates. 

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