This work investigates a generalized implementation of directive sources on discrete-time methods. Results based on previous work for sinusoidal sources have been extended to accomplish real life source requirements, which have a frequency-dependent pattern and show gradual transitions between the different directivities at successive frequencies. One of the main advantages of this method lies in its capacity to be applied to any discrete-time method, since it is based on a proper combination of impulse responses radiated from discrete positions, which, in turn, will produce a particular pressure distribution at far-field. Furthermore, some considerations about mesh-dispersion effects on source modeling are addressed using some examples.