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The estimated signal in Figure a resembles the true signal
very well, and so does the estimated noise.
It is easy to check that the energy (in a
sense) in Figure
a (e1=2) is less
than the energy (in a
sense) in Figure
a
(e1=3.2).
Figure
shows the shaping filter associated with the
norm. This filter is a spike at lag=0.
This simple 1-D example demonstrates that the
norm should
be utilized whenever significant amplitude differences exist between
multiples and primaries. In the next section, a synthetic
example where internal multiples are attenuated illustrates the
properties of the
subtraction.