With each infinite grid X: ⋯ < x _-1 < x ₀ < x ₁ < ⋯ we associate the system of trigonometric splines {T _j ^B} of class C ¹(α, β), the linear space T ^B (X) = ^def {ũ| ũ = ∑ _j c _jT _j ^B c _j ∞ ℝ ¹}, and the functionals g ⁽ⁱ⁾ (C ¹(α, β))*with the biorthogonality property: 〈g ⁽ⁱ⁾,T _j ^B〈 = δ _i,j (here α = ^def lim _{j→-∞ xj}, β = ^def lim _{j→+infin;xj}). For nested grids X̄ ⊂ X, we show that the corresponding spaces T ^B(X̄) are embedded in T ^B (X) and obtain decomposition and reconstruction formulas for the spline-wavelet expansion T ^B (X) = T ^B (X̄)+ ^. W derived with the help of the system of functionals indicated above.