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