# PSD - Correct Formula for removing Noise

Ok, so finally some things are making sense.

I'm trying to scale the results, which I have done by the following equation:

$$PS_{rms} = \frac{2 \cdot \left |y _{m} \right |^{2}}{ S_{1}^{2} } m = 0.....N/2$$

Where $y_{m} = (re*re+im*im)$

This produces the following: (Sorry about the axis - I have not had time to do these)

Prior to scaling the results, I got the following: Essentially, so far, so good (I hope!)

Now I want to remove the noise around the signal, in theory, so that the main peaks are just showing and remove all the peaks that are not. So in theory, I would just be left between points (60 - 80).

I have been trying to read, and, understand the "Section 10: Averaging and overlapping" in this paper: http://www.rssd.esa.int/SP/LISAPATHFINDER/docs/Data_Analysis/GH_FFT.pdf

It assumes that the usual remedy is to take the average of $M$ elements and reduce the standard deviation of the averaged result by a factor of $1 / \sqrt{M}$ however, what would be $M$ in this case? How could I therefore reduce the standard deviation, in order to remove noise from the result of scaling the PSD?

This is the only part to which I am now confused about, I essentially need to reduce the noise levels at the start of the result, and, at the end of the result thus giving me only the important peaks within the signal.