# Could not understand why noise cancellation must be at (fs-fc) for -60dB

#### TarikElec

Joined Oct 17, 2019
33
I have the overview of signal with cut-off frequency fc that I want to sample using an ADC with sampling frequency of fs, I have seen that some of my colleagues wanted to dumb any noise at -60dB at frequency fs-fc as you see it in the picture.
for my understanding of nyquist theorem, I need to damp any signal over fs/2 for how much -x dB I want. here I could not understand why it is at (fs-fc)

#### crutschow

Joined Mar 14, 2008
25,664
Aliasing of any signal or noise components above fs/2 occurs.
I believe fc is not the cutoff (-3dB) point of the anti-alias filter, it's the Nyquist cutoff or the same as fs/2.
So you want any signal/noise above fs/2 (which is also the same as fs-fc) to be below the noise floor of the ADC.
The -3dB filter cutoff frequency will thus be below fc by a factor determined by the filter rolloff characteristics and the amount of attenuation you need at fc.

#### Papabravo

Joined Feb 24, 2006
14,688
In a sampled data system you want to attenuate frequencies above fs/2 and fs, to prevent them from showing up in the sampled data as a mirror image. -60dB puts an explicit specification on the amount of attenuation in the transition band and the beginning of the stop band.

#### TarikElec

Joined Oct 17, 2019
33
In a sampled data system you want to attenuate frequencies above fs/2 and fs, to prevent them from showing up in the sampled data as a mirror image. -60dB puts an explicit specification on the amount of attenuation in the transition band and the beginning of the stop band.
Thank you for your reply. I understand about that we must attenuate frequencies above fs/2 and we want for example -60dB attenuation, but why specify exactly (fs-fc)? I could not understand that