Unknown waveform

There are other methods of detecdng unknown signals when different information about them is known. For example, if it is known that the signal is nearly monochromatic at any instant but sweeps from low to high frequencies with time, it can readily be detected by searching for tracks in a time-frequency plot. 

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An alternate approach to separation first assumes a priori frequency knowledge, and performs a least squares fit to the summed waveform with respect to the unknown sine-wave parameters which can be written as... 

To determine whether alternative ANN architectures can lead to improved resolution and successful agent detection, Radial Basis Function (RBF) networks [106] were considered for the same problem. RBFs are networks with one hidden layer associated with a specific, analytically known function. Each hidden layer node corresponds to a numerical evaluation of the chosen function at a set of parameters Gaussian waveforms are often the functions of choice in RBFs. The outputs of the nodes are multiplied by weights, summed, and added to a linear combination of the inputs, yielding the network outputs. The unknown parameters (multiplicative weights, means and spreads for the Gaussians, and coefficients for the linear combination of the inputs) are determined by training the RBF network to produce desired outputs for specific inputs. 

We have only been able to generate the square waveform because we knew the appropriate values for au and k for every harmonic. The converse problem, of finding unknown and (j)fc for a known waveform function x t) is termed Fourier analysis and will be described in section 10.1.4. 

In principal, the variances of the arrival time data are unknown unless they are estimated for each signal in a visual inspection of the waveforms. However, it is possible to estimate cj/ from the remaining discrepancies between observed travel times and calculated travel times t, " after source localization, divided by the degree of freedom of the problem with four unknown source parameters. For n observations it is... 

Any measured result of a grounding impedance involves unknown physical parameters, such as soil resistivities along the earth s surface, depth at which the impedance is buried, irregular waveforms of an applied current, and possible noise during a measurement. As a result, it is not possible to discuss uniformity of the measured results. A numerical simulation, however, is a very effective way to determine uncertainties. 

Many seismic events have very similar waveforms if they originate from the same or nearby sites. This could also be the case for volcanic events even though they might not be from exactly the same area. A known waveform shape can then be used to detect unknown arrivals by cross correlating the known wavelet with the signal of unknown events. An example of similar events is seen in Fig. 13. Despite the large distances, the signal shapes are nearly identical for the two events. 

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