Not sure I understand this right - is this basically treating both binary strings as square waves, converting them to the frequency domain and determining the offset as a pitch shift between the two spectrograms?
EDIT: err, I'm actually not sure about the pitch shift part, that's a bit of vocabulary I'm not familiar with. If you've seen the fast polynomial multiplication algo from CLRS, it's basically that. E.g. if we have strings 1101 and 0101, we can find the best alignment by looking at the exponent of the largest coefficient after multiplying
polynomial(1101)*polynomial(reverse(0101))
where polynomial(1101) = x^3 + x^2 - x + 1
and polynomial(reverse(0101)) = polynomial(1010) = x^3 - x^2 + x - 1
In essence, the fourier-transform is based on convolutions. F(eta) is essentially the convolution of f(x) with sin(eta x).* This is very loosely why the convolution theorem works.
[1] https://en.wikipedia.org/wiki/Convolution_theorem
* This excludes all cosine parts of the transform. Its neater to work in the complex domain and state that:
F(eta) = f(x) convolved with e^(eta i x)