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The aim of this paper is to calculate (deterministically) the Hausdorff dimension of the scale-sparse Weierstrass-type functions $W_s\left(x\right):={\sum }_{j\ge 1}{\rho }^{-{\gamma }^{j}s}g({\rho }^{{\gamma }^j}x+{\theta }_j)$, where ρ > 1, γ > 1 and 0 < s < 1, and g is a periodic Lipschitz function satisfying some additional appropriate conditions.