1
$\begingroup$

I'm trying to understand this solved example from a book, given an analog signal $x(t) = 3\cos(100\pi t) $. This signal has a frequency of $50hz$. If sampled at $F_S=75Hz$ ,I obtain the discrete time signal $3\cos(\frac{2\pi n}{3}) $.

Now I am supposed to find the frequency $F $ lying in the range $0 < F < F_S/2 $ that yields identical samples. Now I get that this frequency will be $F = 25Hz$ by using $f = \frac{F}{F_S}$.

However, I learnt earlier that this frequency is supposed to satisfy the relation $F_k = F_o +kF_S$ for integer values for k, and as it is obvious, there seem to be no integer solutions for this. Where am I going wrong ?

Any help would be appreciated.

Book Reference : https://engineering.purdue.edu/~ee538/DSP_Text_3rdEdition.pdf

$\endgroup$
1
$\begingroup$

Note that the cosine has a positive and a negative frequency component. Consequently, in the range $[0,f_s/2]$ you get a component at $-50\textrm{ Hz}+75\textrm{ Hz}=25\textrm{ Hz}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.