I have a rather simple question, sorry in advance if it's too easy. I'm working on a waveform generation project on MATLAB. When I look at the examples, I see that the time variables are defined like this;
t = 0:1/fs:T-1/fs;
What is the point of -1/fs?
It's a matter of personal preference.
Some prefer that the length $N$ of the vector $t$ matches $$N = \lfloor f_sT\rfloor$$ where $\lfloor\rfloor$denotes the $\mathrm{floor}()$ function. This is done so that $$\frac{N}{f_s} \leq T$$
Example 1: $f_sT$ is an integer: $f_s = 200\,\texttt{Hz}$, $T = 3\texttt{s}$ so $N = 600$:
t = 0:1/fs:T % length(t) = 601, which would give 601/200 = 3.005s
t = 0:1/fs:T-1/fs % length(t) = 600, which gives 3s
Example 2: $f_sT$ is not an integer: $f_s = 200\,\texttt{Hz}$, $T = 3.142\texttt{s}$ so $N = \lfloor628.4\rfloor = 628$:
t = 0:1/fs:T % length(t) = 629, which would give 629/200 = 3.145s
t = 0:1/fs:T-1/fs % length(t) = 628, which gives 628/200 = 3.14s
However, others prefer that the last sample of $t$ be as close to $T$
as possible:
With t = (0:1/fs:T), the very last sample of t will
be closer to T:
Example 1:
t = 0:1/fs:T % t(end) = 3s
t = 0:1/fs:T-1/fs % t(end) = 2.995s
Example 2:
t = 0:1/fs:T % t(end) = 3.14s
t = 0:1/fs:T-1/fs % t(end) = 3.135s
It really depends what they are trying to do, but I assume they simulate several chunks of duration T with sampling interval 1/fs.
So they need to make sure that the last sample of each chunk is not computed again as the first sample of the next chunk.
