Sampling Frequencies: f1, f2, f3 with fs=1000Hz

[electronic engineer]

Homework Statement

We have the following signal frequencies:

f1=18 Hz, f2=510 Hz, f3=1100 Hz

when using the sampling frequency fs=1000 Hz.

how would these signals be like?

my question is if I could use the same formula stated below for all the frequencies f1,f2,f3.. because the second and third ones are above the Nyquist Frequency fc=fs/2=500 Hz so there would be aliasing in this case.

and what about the graphs for these samplings?

Homework Equations

when using another sampling frequency fs=1002 Hz

and here also would be the same questions.

The Attempt at a Solution

I used the formula:

$$ S_{\Delta }(v)= f_{s}\sum_{n=-\infty}^{+\infty}(S(v-n*f_{s})) $$

for the first frequency f1= 18 Hz I had:

$$ S_{\Delta}(18)=1000\sum(S(18-n*1000)) $$

where $$ n=-\infty $$ to $$ +\infty $$

 

[haruspex]

how would these signals be like?

Do you mean, for each actual frequency, what is the lowest frequency that could yield the same sampling results?

 

[electronic engineer]

Do you mean, for each actual frequency, what is the lowest frequency that could yield the same sampling results?

No i mean for each actual frequency wha are the sampling results for fs=1000 Hz and then for fs=1002 Hz.