Is it possible to discretely sample the function I had a few questions on sampling(I'm quite new witht his), I tried to answer them, I think that I did the first one correct , but not sure about the 2 other:
.
given the next functions,Is it possible to discretely sample the function? if so what is the maximal allowed distance between the samples? otherwise explain why?


$$f(x)=\sin(\alpha x)$$


For this one I said it is possible using Nyquist theorem, assumin $\alpha =2\pi f$ and $T=\frac{1}{f}=\frac{2\pi}{\omega} $ then the allowed distance is $\frac{T}{2}=\frac{\pi}{\omega}$

(hopefully i got this allright).

now from the second question I'm not sure.


$$f(x) =
\left \{ 
\begin{array}{cl}
1,  &amp; \text{$-1\leq x \leq 1$} \\
0, &amp; \text{else}
\end{array}
\right . 
$$


for this function I'm pretty sure the answer is it is not possible, since it is a straight line, so I'm not sure.. (please help me with this one).


$$f(x)= \mbox{convolution between function of question 1 , function of question 2.}$$


In this case I'm guessing it is possible since its the same as sampling first question function (only that it is sliced).
yes, with spacing between samples closer than $\frac{\pi}{\alpha}$.
no.  it's not sufficiently "bandlimited"
yes, the convolution of a sinusoid with anything is a sinusoid of the same frequency.  so it's "yes" for the same reason as 1.