If you want to be pedantic about it, chaos is not necessarily the opposite of order. The act of relying requires pattern matching and recognition, thus deducing a form of order. There is nothing to rely on when it’s just chaos. Noise vs a sin wave. The opposite of a sin wave is its inversion which cancels things out. A sin wave cannot exist within a noise because all the data points are replaced by additional random data.
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.
If you want to be pedantic about it, chaos is not necessarily the opposite of order. The act of relying requires pattern matching and recognition, thus deducing a form of order. There is nothing to rely on when it’s just chaos. Noise vs a sin wave. The opposite of a sin wave is its inversion which cancels things out. A sin wave cannot exist within a noise because all the data points are replaced by additional random data.
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.