How dBs are used in this instance.

When most people who have studied a little science hear talk of the Decibell they think of sound level meters that measure the local factory noise and tell you if it’s dangerous or not. So for instance the basic definition is as follows.

where  is agreed upon as the sound pressure level at 1kHz  of the threshold of hearing, P is the sound pressure you are measuring and  is the dB reading.

Have a look here

Now, the trouble is that Electrical Engineers use dBs a little differently. Because of this a few people (including the Times of London) have miss-interpreted my Spectral Density graph. Electrical Engineers use dBs as follows. Either

or

The latter expression is normally used to measure the gain of an amplifier at different frequencies – we measure the output and input voltages at increasing values of frequency  and plot the frequency response (Gain in dB versus frequency in Hz or radians/s).

In communication engineering (another branch of Electrical Engineering) we measure dB as the first of the above equations with dBPower. Signal to noise ratio is also measured in a similar way

So what about Power-Spectral density? Well, the dB used is just . It has no absolute meaning (ie the sound of a noisy restaurant!). Instead we use it to measure how harmonics differ – ie a comparison. For example third harmonic distortion might be 60dB down (ie lower in dB) on the fundamental – this would be a good thing for an audio signal – the ear could not pick this up. If I multiply the signal strength by 2 then the overall dBs increase but the relative dB differences stay the same. So please don’t confuse the Power Spectrum with the audio sound pressure spectrum – the latter is measured relative to an international agreed standard of sound pressure and the former is just a relative measure within the graph itself. I hope this clears things up.