Solutions with initial estimates of zero

Here I offer some simple examples of the previous ideas. Figure  shows two sections. The first section, which represents the signal, has a signal filter $\st S$ calculated from it. The second section, which represents the noise, has a noise filter $\st N$ calculated from it. Notice that the signal and noise sections contain a common event of intermediate dip. The data consists of all three events and is shown in Figure . Figure  shows the result of calculating the signal using the system of regressions seen in equation (). Notice the event common to both the signal and noise does not appear in the calculated signal. Since the noise is just the signal subtracted from the noise, the common event appears in the noise section.

 

signalnoise Figure 1 The events on the left are defined as signal, the events on the right are defined as noise.

 

data Figure 2 The data, made up of both signal and noise.

 

separ7sa Figure 3 The calculated signal and noise using an initial solution of zero for the signal.

When noise is calculated with the system of regressions seen in equation (), the event common to both the definition of noise and signal does not appear in the calculated noise, but is seen in the signal, which is now the noise subtracted from the data.

 

separ7na Figure 4 The calculated signal and noise using an initial solution of zero for the noise.