> Can anyone explain the concept of Negative frequencies clearly. Do
> they really exist?
Here's the quick answer:
If you are expressing elements in frequency space as complex exponentials
(which is the kernel of the Fourier Transform) then to have sin(kt) or
cos(kt), you have to have the sum or difference of complex exponentials at
positive and negative frequencies.
So, the time domain cosine is a real sinusoid at a positive frequency.
But, in Fourier Transform spectral space, a real cosine is made up of
complex exponentials of equal amplitude at positive and negative equal
frequencies. You can find the identity in a trigonometry book of tables.
So, do they really exist? It depends on which domain you're looking at
them. In the time domain of real signals, I'd say no. In the frequency
domain, yes because of the observation above.