It’s entirely possible to take the Fourier transform of noise and see what sine waves you’d have to add together to reproduce the random data. So it’s not true that noise doesn’t contain sine waves; ideal “white noise” in particular contains every possible frequency at an equal volume.
You are right. We are interested in extracting a single sin wave superimposed over a noise. Fourier transform will get you a series for constructing any type of signal. I don’t think it can find that sin wave inside the noise. If you are given a noise with the sin wave and the same one without the sin wave, then I think you can find it. If you don’t have anything else to compare to, I don’t think there is any way to extract that information.
If you have a signal that repeats over and over again, you actually can eventually recover it through noise. I don’t know the exact math, but basically the noise will “average out” to nothing, while the signal will get stronger and stronger the more times it repeats.
It’s entirely possible to take the Fourier transform of noise and see what sine waves you’d have to add together to reproduce the random data. So it’s not true that noise doesn’t contain sine waves; ideal “white noise” in particular contains every possible frequency at an equal volume.
You are right. We are interested in extracting a single sin wave superimposed over a noise. Fourier transform will get you a series for constructing any type of signal. I don’t think it can find that sin wave inside the noise. If you are given a noise with the sin wave and the same one without the sin wave, then I think you can find it. If you don’t have anything else to compare to, I don’t think there is any way to extract that information.
If you have a signal that repeats over and over again, you actually can eventually recover it through noise. I don’t know the exact math, but basically the noise will “average out” to nothing, while the signal will get stronger and stronger the more times it repeats.