Why negative harmonics copies in sampling?

[yefj]

Hello, i have a signal of 120Mhz and sampling at 800Mhz. we look at the region of fs/2=400MHz so obvios we have harmonics of the fundamental which is 240 360. But in the document i see that there is another harmonic -4*120M+800M I cant see why we have negative harmonics and their copies. Upon what theory its based?
they say the -120M is the only one copied to the 0-400M region but i thought we could take also
-6*120M+fs=-720M+800M=80MHz
I cant see what why we have negative harmonics and which one is copied to the 0-fs/2 region.
Thanks.

 

[sutapanaki]

This is not a negative harmonic. It is aliasing of the 4th harmonic down into the Nyquist band from 0 to 400MHz. Your 4th harmonic is at 480MHz and after sampling it will alias to 320MHz.

 

[yefj]

Hello ,So follwong example where its told that our alias signal is fs/2.
So given our 4th harmonics af 480 and our nyquist frequincy is 800/2=400MHZ
480-400=80
400-80=320
SO the same thing could be done with the 5th harmonics 5*120M=600M
600M-400M=200M
400-200=200M which could be the nyquist range too
so is the 5th harmonics could be inside too?

 

[sutapanaki]

Aliasing is within 0 to 400MHz but it is actually measured with respect to Fs=N*800MHz. So, for the 4th harmonic you have 800-480=320MHz and it will alias to 320MHz. For the 5th harmonic 800-600=200MHz and aliases to 200MHz.
Also, if you had a component at 1120MHz, it will alias back again to 320MHz.

 

[yefj]

Hello sutapanaki,
Why you compare 480 with respect to 800(next nyquist frequncy) and not 400?
For 1120MHz you did the opposite you compared it to 800 instead of 1200.
so whe i compare it to the previos nyquist frequency and when to the next?
Thanks.

 

[FvM]

Alias frequencies of the input signal occur at +/-N*fs, as already explained. Your calculations in post #3 are all wrong. Alias frequencies can be negative, e.g. 720 - 800 = -80 MHz, but in a simple sampler, -80 MHz appears as +80 MHz. You need a homodyne detector (I/Q sampler) to separate positive and negative frequency components.

Respectively I would answer the initial question differently. There are no negative harmonics, but negative alias frequencies which can't be separated from positive frequencies by your system.

You may want to review the aliasing and folding chapter of a signal processing text book.