Relationship between filters, Fourier magnitude, and frequency
(This explanation is going to be rough around the edges so that I can build your intuition. There are subtleties involved, but this should be good enough to start you off).

Forget about the dB scale for a moment. Let us take a step back: 

Imagine that you have some signal that occupies a bandwidth from say, 50 Hz to 100 Hz. Its spectrum is flat across this band. That is, it has the same power at 50 Hz, as it does at 51 Hz, as it does at 52 Hz, etc etc. In this example, we say that it has a constant (flat) power-spectral-density within this band. Let us say that the value of the PSD in this band is 1 Watts / Hz. This means that across 1 Hz of frequency, we will measure 1 Watt in power. Across 50 to 100 Hz, we would measure of course, 50 Watts in power. (To compute your PSD values, they are simply the absolute value of your fourier amplitudes, squared). 

So far so good. 

Now, imagine a filter, that removes frequencies above 75 Hz and also removes frequencies below 50 Hz. It however keeps frequencies between 50 and 75 Hz. To "keep" a frequency, means it multiplies the power of a signal at that frequency by 1. To "remove" a frequency, means it multiplies the power of a signal at that frequency by 0. 

So, you have a signal that is 1 Watt/Hz from 50 to 100 Hz. And you pass it through a filter that multiplies all frequency powers from 50 to 75 by 1, ("keeps them"), and it also multiplies all frequency powers less than 50 and above 75 Hz by 0. ("removes them").

If you pass your signal through this filter, what might you get? Well, you just removed all the energy of your signal from 75 to 100 Hz. Previously those frequencies had a power spectral density of 1 Wattage/Hz, however now they are 0. You have just filtered your signal.

If I asked you at this point, "Plot for me, the PSD of your signal after your filtering", you would draw 1's for frequencies in the 50 to 75 Hz range, and draw 0's for all other frequencies. Now if I said, "I dont like this linear scale. I want you to draw this for me on a dB scale. A log scale." This means that you now simply take the log of the PSD axis. So everywhere we had 0 watts/Hz, they are now -infinity watts/Hz dBW/Hz, (db Watts), and everywhere you had 1 Watt/Hz, we now have 0 dBW /Hz. 

Taking it so dB scale doesn't change your frequency axis, only your fourier amplitude/power axis.