The problem of reconstructing a signal ψ(x) from its magnitude |ψ(x)| is of considerable interest to engineers and physicists.This article concerns the problem of determining a time-limited signal f with period 2π when |f(e~(ix))| is known for x ∈ [-π,π].It is shown that the conditions |g(e~(ix))| = |f(e~(ix))| and |g(e~(i(x+b))) - g(e~(ix))| = |f(e~(i(x+b)) - f(e~(ix))|,b ≠ 2π,together imply that either g = wf or g = vf,where both w and v have period b.Furthermore,if is irrational then the functions w and v reduce to some constants c_1 and c_2,respectively; if is rational then w takes the form W = e~(iα)B_1(e~(ix))B_2(e~(ix)) and v takes the form e~(i(x2πN/b+α))B_1(e~(ix))B_2(e~(ix)),where B_1 and B_2 are Blaschke products.