A trace representation of binary Jacobi sequences

We determine the trace function representation, or equivalently, the Fourier spectral sequences of binary Jacobi sequences of period pqpq, where pp and qq are two distinct odd primes. This includes the twin-prime sequences of period p(p+2)p(p+2) whenever both pp and p+2p+2 are primes, corresponding to cyclic Hadamard difference sets.