Principles of $\ell^1$ norm and $\ell^2$ norm subtraction

In this section, I demonstrate with a 1-D example that the attenuation of multiples with least-squares adaptive filtering is not effective when strong primaries are located in the neighborhood. This simple example helps to better understand the behavior of the adaptive scheme in more complicated cases.
 

• Shaping filters and the $\ell^2$ norm
• Shaping filters and the $\ell^1$ norm
• Results on a simple 1-D example