We present a modified Temporal Deep Belief Networks (TDBN) for human motion analysis and synthesis by incorporating Sparse Encoding Symmetric Machines (SESM) improvement on its pre-training. SESM consisted of two important terms: regularization and sparsity. In this paper, we measure the effect of these two terms on the smoothness of synthesized (or generated) motion. The smoothness is measured as the standard deviation of five bones movements with three motion transitions. We also address how these two terms influence the free energy and reconstruction error profiles during pre-training of the Restricted Boltzmann Machines (RBM) layers and the Conditional RBM (CRBM) layers. For this purpose, we compare gait transitions by bifurcation experiments using four different TDBN settings: original TDBN; modified-TDBN(R): a TDBN with only regularization constraint; modified-TDBN(S): a TDBN with only sparsity constraint; and modified-TDBN(R+S): a TDBN with regularization plus sparsity constraints. These experiments shows that the modified-TDBN(R+S) reaches lower energy faster in RBM pre-training and reach lower reconstruction error in the CRBM training. Even though the smoothness of the synthesized motion from the modified-TDBN approaches is slightly less smooth than the original TDBN, they are more responsive to the action command to change a motion (from run to walk or vice versa) while preserving the smoothness during motion transitions without incurring much overhead computation time.