We present results for pseudodifferential operators on Rd whose symbol a(·,x)is almost periodic (a.p.) for each x ∈ Rd and belongs to a Hörmander class Smr,d. We studya linear transformation a 7→ U(a) from a symbol a(x,x) to a frequency-dependent matrixU(a)(x)l,l′ , indexed by (l,l′) ∈ L×L where L is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential operators to symbols of Fourier multiplieroperators acting on vector-valued function spaces. We show that the map preserves operatorpositivity and identity, respects operator composition and respects adjoints.