Difference Equations with Forward and Backward Differences and Their Usage in Digital Signal Processor Algorithms

In the paper the relation is given between linear difference equations with constant coefficients those obtained via the application of forward and backward differences. Relation is also established between input-output difference equations and state-space difference equations, which define the state of inner quantities of a discrete system. In conclusion, the state-space representation of a discrete system is given, which is suitable for implementing a discrete system in the microprocessor and digital signal processor. The resultant solution consists of the response to input signal and the response to non-zero initial conditions