Separating signal from noise in similar frequency range
As you have noticed, it is quite unlikely that you can filter your data with a standard frequency filter, thus a linear filter. 

Unless the signal and the noise are well separated in time, unless you have a model, you will probably need to resort to other techniques, such as nonlinear filtering, time-frequency or time-scale filtering, or add additional information or assumptions, such as thought signal or noise properties (to name a few: gaussianity, positivity, independence, sparsity), and bend to blind source separation, latent variable analysis, nonlinear matrix separation, etc.