We present results on transverse momentum correlations of charged particle pairs produced in Pb-Au collisions at 158$A$ GeV/$c$ at the Super Proton Synchrotron. The transverse momentum correlations have been studied as a function of collision centrality, angular separation of the particle pairs, transverse momentum and charge sign. We demonstrate that the results are in agreement with previous findings in scale-independent analyses at the same beam energy. Employing the two-particle momentum correlator $<Delta p_{t,i}, Delta p_{t,j}>$ and the cumulative $p_t$ variable $x(p_t)$, we identify, using the scale-dependent approach presented in this paper, different sources contributing to the measured correlations, such as quantum and Coulomb correlations, elliptic flow and mini-jet fragmentation.
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