2-D spectral signal estimation examples

Figure  shows the results of using equation () to predict the noise from the data from Figure . Notice that the result is significantly better than that shown in Figure , although some artifacts are seen near the first breaks. Almost no noise is seen in the signal section.

While the program using the 2-D filter version of equation () with the initial solution of zero required 250 iterations to get a reasonable result, the program using the initialized estimate needed only 25.

Figure  shows the results of using equation () to predict the signal from the data seen in Figure . The separation is also good, and only a little weakening of the data traces can be seen where the noise appears. A little of the signal that has not been perfectly predicted has leaked into the noise section. An improved result might be produced by using the output of this process as the input to another step of the same process, with the next step using the previous step's results as the first guess of the amplitude and noise. The new noise and amplitude scale factors might then be more accurate.

 

sf2wf.b
Figure 7 A simple example of separation of signal and noise using sine waves of different frequencies. The method of equation () was used. The plot on the top is the calculated signal, and the plot on the bottom is the noise that remained. The plot on the left has t² scaling, the plot on the right does not.

 

sf2wf.a
Figure 8 A simple example of separation of signal and noise using real data. The method of equation () was used. The plot on the top is the calculated signal, and the plot on the bottom is the noise that remained. The plot on the left has t² scaling, the plot on the right does not.