A discrete-time exponential signal is defined as:
$ x(n) = A \alpha^n $
where $\alpha$ and $A$ are real numbers.
The evolution in time of the discrete-time exponential signal depends on the value of $\alpha$:
- $|\alpha| > 1$: the sequence $|x(n)|$ is increasing;
- $|\alpha| < 1$: the sequence $|x(n)|$ is decreasing;
- $\alpha > 0$: the samples of the sequence $x(n)$ all have the same $A$ sign;
- $\alpha < 0$: the samples of the sequence $x(n)$ are alternately positive and negative.