  Based on the algebraic theory of signal processing, we recursively decompose
the discrete sine transform of first kind (DST-I) into small orthogonal block
operations. Using a diagrammatic language, we then second-quantize this
decomposition to construct a tensor network implementing the DST-I for
fermionic modes on a lattice. The complexity of the resulting network is shown
to scale as $\frac 54 n \log n$ (not considering swap gates), where $n$ is the
number of lattice sites. Our method provides a systematic approach of
generalizing Ferris' spectral tensor network for non-trivial boundary
conditions.
