Novel use of singularity functions to model periodic phenomena in cash flow analysis

When seeking to properly consider the time value of money, typical periodic cash flows such as payments and interest charges are difficult to model. This paper explores a new signal function that employs singularity functions to express such intermittent phenomena. This flexible signal function allows manipulating the parameters of start and finish, amplitude, and period of the signal efficiently, so that payments and interest charges can be modeled accurately. This novel approach is beneficial in several ways. First, the new model can effectively incorporate shift and delay effects that may affect an activity. Second, it applies an exact interest calculation. Third, it can handle compounding in its accumulation. Finally, a comprehensive model is created that returns the cumulative balance including interest charges at all times. It is concluded that signal functions are a promising area for future research on modeling and optimizing the cash flows.