Fourier transform, same frequencies, different amplitudes

[Behrouz]

I understand that the Fourier transform is changing the domain (time/space) to frequency domain and provides the sin waves. I have seen the visualizations of Fourier transform and they are all showing the transform results as the list of frequencies and their amplitude. My question is, what if the result has same sin waves with similar frequencies, but different amplitudes; are they going to be summed up (added/subtracted) in the final result?

 

[Orodruin]

It is not really clear to me what your question is. Do you mean to ask what is the difference between two functions whose FTs differ by some constant or how different amplitudes in the same FT affect the result?

 

[Behrouz]

It is not really clear to me what your question is. Do you mean to ask what is the difference between two functions whose FTs differ by some constant or how different amplitudes in the same FT affect the result?

Thanks.
I mean the effect of different amplitudes (for similar frequencies) in the same FT.

 

[DrClaude]

Thanks.
I mean the effect of different amplitudes (for similar frequencies) in the same FT.

Sorry, but this is still not clear. If you have sine waves of different frequencies, each will lead to a peak at the corresponding frequency, the height of that peak will correspond to the amplitude of the sine wave, but the fact that frequencies are similar or not plays no role here.

Or are you talking about discrete Fourier transforms?

 

[FactChecker]

Two FTs with identical frequencies, but different amplitudes are associated with different signals in the time domain. If two time-domain signals are combined, their FTs can be added, frequency by frequency, to get the FT of the combined time-domain signal. That is because the FT is a linear operator.

 

[Grinkle]

what if the result has same sin waves with similar frequencies, but different amplitudes; are they going to be summed up (added/subtracted) in the final result?

My short answer is yes.

My longer answer is that for a discrete FT similar means close enough to be in the same bin. For continuous FT, similar means exact.

 

[Behrouz]

Thank you all.
No, it wasn't specifically for DFT.
I believe @FactChecker 's answer is what I was looking for in this case.
Thanks again.