Use Gram-Schmidt orthogonalization to remove the extracted chirp signal from the signal mixtures (i.e., the columns of z) in Example 6.4. First, listen to the remaining signal mixture. Does it sound like the gong? Apply the ICA steps of Example 6.4 to extract the second signal and listen to it using soundsc
Example 6.4
The following example was adapted from the projection pursuit MATLAB code found in Stone [2004], and it uses a gradient ascent method to find the weight vector that maximizes the kurtosis. The idea is that a projection with maximum kurtosis would show nonnormal structure. It should be noted that we are looking for a 1D projection, and only one signal will be found at each application of the procedure. To find more than one source signal, we would need to apply something similar to the structure removal process, as we explain shortly. We already created a mixture of signals based on the chirp and gong signals that are included in the basic MATLAB software. The data are saved in the file called icaexample.mat.
This file has several signal arrays, along with the frequency N. One is the matrix of signal mixtures x, where each column corresponds to amplitudes recorded at a receiver. We show one of the signal mixtures at the top of Figure 6.7. The file also contains the original unmixed signal matrix G, where the first column is the chirp signal and the second corresponds to the gong. Finally, as in projection pursuit, we spherized the data, producing the matrix z. See the online version of this example for the MATLAB code that was used to create the mixture of signals and the matrix z. The steps to extract a source signal from z are shown here:
The extracted signal is shown at the bottom of Figure 6.7. We can verify that the extracted signal matches the chirp by listening to it. This is done using the following commands.
We extracted just one signal in the previous example, but we probably want to find more. After all, this is the idea behind blind source separation. We can extract multiple source signals by first removing the current extracted signal from each of the remaining mixtures using Gram-Schmidt