Feature Extraction And Signal Component Separation
Please see the attached file for details.
Below, you can see couple of samples of my signals.
If your method works on these samples, I can send you more sample signals depending on the progress in work.
Basically, given a sample signal, let’s say, y, our aim is to extract a pulse train with exact location of incidents.
Let’s assume
y(t) = H.x(t) + n
where in H.x(t), the dot notation "." indicates that of multiplication, y is the given signal, H is a matrix, x is the pulse train we are looking for, and n can be noise.
What we know is that, there has been an input pulse with a quick damping shape, s(t), with central frequency of 15 MHz.
s(t) passes through layers of a material and we get the echoes back.
The received signal will be y(t) as shown in Figure 1.
We know that there are desired features (echoes) as shown in Figure 2.
But due to physical and environmental conditions finding exact location of echoes is not straightforward.
It should be noted that when the transmitted signal first hits the object, we call it surface location; there will be a strong reflection.
And echoes are equally distributed (distance-wise) from the surface location.
However, in practice, there are some other pulses detected for the whole duration of the signal.
It can be due to noise and/or many other factors.
Please note that in reality, y(t) = s(t)*x(t) + n, where "*" is the convolution operation, s(t) is the transmitted pulse, x(t) is the pulse train we are looking for, and n is noise.
However, to model the problem in terms of sparsity solutions or to solve it via deconvolution techniques, it is also possible to assume a suitable model such as matrix H, where H.x(t) + n can offer the same y(t).
Note that in H.x(t), the dot notation "." indicated that of multiplication.
Figures 3 and 4 show two more examples of more challenging cases.
In Figure 3, the large pulse has the same negative phase as echoes, and therefore, it is not clear if it has been due to noise.
If we assume that he large pulse is the first echo then the pulse before that would be the surface however in that case surface is going to have less amplitude than the first echo which is odd.
Therefore, we need to make sure what the components of the mixture composed of, so that the final mixture is now in this shape.
Maybe there was some defects in the object etc...
Figure 4 is also another suspecious case in which there are several tiny pulses hard to say which ones are correct echoes.
If you are interested in the project, please contact me to receive some data.