# How to do addition of sound pressure RMS in a DFT

Based on this answer. Once you have your DFT in the unit sound pressure RMS, what is the correct method for getting the sound pressure RMS sum over multiple bins (if for example you're trying to get the total RMS over a frequency band)?

$$E_x=\sum_{k=0}^{N-1}\lvert x[k]\rvert ^2=\frac{1}{N}\sum_{k}^{N-1}\lvert X[k]\rvert^2.$$
$$\textrm{RMS}_{x}=\sqrt{\sum_{k=0}^{N-1}\lvert X[k]\rvert^2}.$$
You can compute the RMS of a range of bins $[i,j]$ by constraining $k$.
$$\textrm{RMS}_{x_{ij}}=\sqrt{\sum_{k=i}^{j}\lvert X[k]\rvert^2}.$$