Converting PSD to dB scale I am taking the PSD of the output of an RTL-SDR with Welch's method.  The output is an array like: [1.34225796e-07   1.37964799e-07   1.24558405e-07, ....].  I'd like to convert this array to dB, so that I can find the point 3dB down from the center (which in this case is the first element of the array, because I am not using fftshift.)

How can I do this?  I don't understand the units given in the PSD in this case, nor how to convert them to dB (one problem follows the other).  I understand that the RTL-SDR output is not wrt some known unit (i.e. it's not dBm, but dBFS.)
A dB scale is simply a logarithmic scale.  Bels are base 10, and decibels are base $ 10^{1/10} $.  Because $log(a/b) = log(a) - log(b)$, a decibel scale converts ratios to intervals.  3 dB corresponds roughly to a factor of 2.  So, what you are really asking when you say looking for a dB value that is 3 dB down is equivalent to asking for where the raw value is half of the original raw value.  

Added:  The units of the raw values don't matter since you are taking a ratio.  Simply take $ dB = 10 \cdot \log( raw ) $ to convert to a dB scale.

One thing you have to be careful of when taking the log of PSD values is that the PSD may have a zero value which makes the log undefined, but can be thought of as negative infinity.

Hope this helps,

Ced