The classical Fourier transform is, in essence, a way to
take data and extract components (in the form of complex
exponentials) which are invariant under cyclic shifts. We consider
a case in which the components must instead be invariant under
automorphisms of a binary tree. We present a technique by which a
slightly relaxed form of the generalized Fourier transform in this
case can eventually be computed using only simple tools from linear
algebra, which has possible advantages in computational efficiency.