  In this paper, we study the soliton resolution conjecture for Type II
singular solutions $\overrightarrow{u}(t)$ to the focusing energy critical wave
equation in $R^d\times [0,T_+)$, with $3\leq d\leq 5$. Suppose that $u$ has a
singularity at $(x,t)=(0,T_+)$, we show that along a sequence of times
$t_n\uparrow T_+$ and in a neighborhood of $(0,T_+)$, $\overrightarrow{u}(t_n)$
can be decomposed as the sum of a regular part in the energy space, a finite
combination of modulated solitons (translation, scaling and Lorentz transform
of steady states) and a residue term which goes to zero in the Strichartz norm.
In addition, the residue term is asymptotically radial and can concentrate
energy only in a thin annulus near $|x|=T_+-t_n$. Our main tools include a
Morawetz estimate, similar to the one used for wave maps, and the use of a
virial identity to eliminate dispersive energy in $|x|<\lambda (T_+ -t_n)$ for
any $\lambda\in (0,1)$.
