  In this paper we study the knot Floer homology invariants of the twisted and
untwisted Whitehead doubles of an arbitrary knot K. We present a formula for
the filtered chain homotopy type of HFK(D(+,K,t)) in terms of the invariants
for K, where D(+,K,t) denotes the t-twisted positive-clasped Whitehead double
of K. In particular, the formula can be used iteratively and can be used to
compute the Floer homology of manifolds obtained by surgery on Whitehead
doubles. An immediate corollary is that tau(D(+,K,t))=1 if t< 2tau(K) and zero
otherwise, where tau is the Ozsv{\'a}th-Szab{\'o} concordance invariant. It
follows that the iterated untwisted Whitehead doubles of a knot satisfying
tau(K)>0 are not smoothly slice.
