You have several ways how to do it, but no one had predict which one will be the best for your task. First of all, you can do do frequency analysis, you will see some storng (maybe not perfect and dirty) peaks of the signal. Usually the 'background' signal is located in the lower frequencies, the 'useful signal' somewhere in the midle, and the random noise usually occupies the higher frequencies. You can also use filtration of several windows (Gauss, Blackwel, Hamming,...), but than you need to specify the size of the window, which should be dependedt on the size of the object you are looking for. Or you can use the morphological operations, like Beucher segmentation, watershed, entropy maximization, Otzu thresholding, to separete the noise and background from hthe signal. Sometimes it works perfectly, sometimes it is not enough. Or you can tra to do the kernel decomposition if you know the base distribution (Gaussioan, power law,...). Or just simple fitting (polynomial, Savitzky-Golay, Gaussian,..) if you know hte typical signal plot. So, so many ways, and some of them will not work in your case. Try to type in google scholar the keywords of you topic and one of the method I proposed. You will se if there is somethong already done, so you do not have to test what was already tested. You can use it, it will fit to your case. Or you can try the one, the they omitted, mayby it will be the one. Who knows. Regards Jan.

Be careful, what might appear to be noise in the spectrum, could actually be false artefacts (i.e. side-lobes) due to the finite (rectangular) time window. Try applying a tapered window function (e.g. Hann, Hamming) to the data before you take the FFT and see if this reduces the "noise" level..

I'm assuming you are still doing spectral analysis here, as per your earlier question.