# If a signal is added to another in the freq. domain, how to filter it out?

I have two signals, $x$ and $y$. I know that $F(x)=F(s)+F(n)$ and $F(y)=F(n)$, where $s$ is the 'clean' signal, $n$ is the added noise and $F$ donate Fourier Transform.

To obtain the clean signal, I am trying the following: $s=F^{-1}[F(x)-F(y)]$. Is there any better way that I should try?

• You're basically asking, if you have a noisy signal $y=x+n$, and the noise $n$ is given, is there any better way to reconstruct $x$ than by computing $y-n$? The answer is no, you have indeed found the best way. – Matt L. Jul 25 '15 at 6:28
• Are you sure that you have the $F(y) = F(n)$ including both phase and amplitude information, or just $|F(y)| = |F(n)|$ meaning that you only have spectral power density known? – mbaitoff Jul 25 '15 at 20:32
• You might have a representation of the noise if it is random. It might be more specific if it is colored. I suggest that you will use some simple filtering. – Moti Jul 26 '15 at 6:35