When I calculate spectrum of a voltage signal using FFT and then I calculate periodogram using $$S_k=10\cdot log_{10}(\frac{1}{N}|X_k|^2)$$ where \$X_k\$ if the result of FFT and \$N\$ is number of samples, the resulting graph usually has "dB" on vertical axis. But what is the meaning of dB in this context?
Decibels usually refer to either power (dBm) or amplification/attenuation or multiple of some reference value. But in this case, it seems to me that it is neither of these.
It linearly depends on the number of samples (Because the result of Fourier transform is linearly dependent on \$N\$, then I square it, but only divide by \$N\$). So is it somehow proportional to the energy of the signal? If so, how is voltage converted to energy/power? It would require some impedance value to get power from voltage. Or should it be somehow normalized (is there a definition of what 0 dB should mean)?