I started studying DSP and the first things that came out were the differences between continuous and discrete time signals. So, I was wondering if I understood well these concepts before I keep going into more difficult topics.
The first thing I realized is that discrete-time signals replace the continuous parameter $t$ (time) for $n$ (sample) where $n$ is always an integer, leading this to two main differences:
Complex exponential sequences $Ae^{j\omega n}$ with frequencies $\omega + 2\pi k$ where $k$ is an integer are indistinguishable from one another since $e^{j2\pi n} = 1$ always. This is not true for continuous time signals since $e^{j2\pi t}$ can possibly be different from $1$.
Concerning periodicity, in the discrete time case, the fundamental period $N$ is always an integer equal to $\frac{k}{F}$ where $k$ is an integer, meaning that $N$ is not necessarily equal to $\frac{1}{F}$.
In the continuous case, this is not true since $T = \frac{1}{F}$.
So, my questions are:
- Am I correct about this two differences? If this is not the case, please explain it to me better.
- Are these two the more important to take into account, or am I missing something (else) big?