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Simulation of Nonlinearities Factors to Consider in Software Integrating EAN/UCC-13 in Software Simulation of Nonlinearities Factors to Consider

Simulation of Nonlinearities Factors to Consider using barcode implementation for software control to generate, create ean-13 supplement 2 image in software applications. Web service There are a number of factors Software GS1-13 to be considered when one attempts to simulate the behavior of a nonlinearity. The simulation of nonlinearities is almost always performed in the time domain except for lters included in the model to account i i i i. i i TranterBook 2003/11/1 8 16:12 page 450 #468. Modeling and Simulation of Nonlinearities 12 . x (t ). d 2 y (t ) dt 2 dy ( t ) dt y(t). ln Figure 12.2 Assembled block diagram model for a nonlinearity. for frequency-selective behav EAN-13 for None ior. Filters, of course, can be simulated in the time domain or in the frequency domain. To illustrate some of the factors that must be considered in the process of modeling or simulating a nonlinearity, assume that the model takes the form of either the zero-memory model described by (12.

1) or the frequency-selective model shown in Figure 12.1..

Sampling Rate The rst factor we have to co Software EAN-13 nsider is the sampling rate. For a linear system we typically set the sampling rate at 8 to 16 times the bandwidth of the input signal. In the case of a nonlinearity of the form y(t) = x(t) 0.

2x3 (t) (12.4). where the input x(t) is a det erministic nite energy signal, the transform Y (f ) of the output y(t) will be given by Y (f ) = X(f ) 0.2X(f ) X(f ) X(f ) (12.5).

where denotes convolution. Th Software EAN-13 e triple convolution will lead to a threefold increase in the bandwidth of Y (f ) over the bandwidth of X(f ). This e ect is called spectral spreading and is an e ect of the nonlinearity.

If y(t) is to be represented adequately without excessive aliasing error, the sampling rate must be set on the basis of the bandwidth of y(t), which has much higher bandwidth than x(t). Thus, in setting the sampling rate for simulating a nonlinearity, we must take spectral spreading into account and set an appropriately high sampling rate. However, the sampling frequency actually required for simulation will not be as high as that indicated in this example (see Section 12.

2.2 on the zonal bandpass model)..

Cascading Another factor that we have t Software UPC-13 o consider is the e ect of cascading linear and nonlinear blocks as in Figure 12.1. If we are using, for example, the overlap and add technique for simulating the lters, we have to exercise caution.

We cannot process blocks i i i i. i i TranterBook 2003/11/1 8 16:12 page 451 #469. Section 12.2. Modeling and Simulation of Memoryless Nonlinearities of data through the rst lte ean13+5 for None r, then through the nonlinearity and the second lter, and perform overlap and add at the output of the second lter. This operation is incorrect, since the principle of superposition does not apply for nonlinearities. A correct processing technique is to apply overlap and add at the output of the rst lter, compute the time-domain samples representing the rst lter output, process these samples on a sample-by-sample basis through the memoryless nonlinearity, and apply the overlap and add technique to the second lter.

Note that this problem does not occur in the overlap and save method, since superposition is not applied.. Nonlinear Feedback Loops Feedback loops might require European Article Number 13 for None the insertion of a one-sample delay in the loop in order to avoid computational deadlocks (recall, from 6, the feedback path in a PLL simulation). A small delay in a linear feedback loop may not adversely a ect the simulation results. In a nonlinear system, however, a small delay in a feedback loop might not only signi cantly degrade the simulation results but might even lead to unstable behavior.

In order to avoid these e ects, the sampling rate must be increased, which, in e ect, decreases the delay.. Variable Sampling Rate and Interpolation If the model is a nonlinear d EAN-13 Supplement 5 for None i erential equation that is solved using numerical integration techniques, many numerical integration algorithms included in software packages such as SIMULINK will use a variable integration step size. The step size will be determined automatically at each step depending on the behavior of the solution. If the solution is well behaved locally, then a large step size might be used.

In order to avoid aliasing problems in downstream blocks, it might be necessary to interpolate the output and produce uniformly spaced samples of the output signal..
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