A study of the Dirac-Delta functions with polynomial argument for modeling the signal path-loss in mid-sized urban areas is presented. From the fundamental "spike" property of the Dirac-Delta functions, or simply Delta, the formulation of nonlinear input/output (I/O) integrals with unknown parameters applied to a scheme of urban zone containing buildings and delimited areas was empathized. The modeling assumes that the Delta function contains a polynomial argument with unknown parameters. The extracted parameters and compared to the ones obtained from Monte Carlo steps, in order to measure the resulting signal intensity degradation at the mid-sized urban areas. For a case of application, the obtained results are compared with the well-known models like Okumura-Hata thereby yielding averaged errors ranging between 2.6% and 12%, roughly.