# Dumb question : What units is a digital signal's amplitude measured in?

If I’m outputting a signal, what unit is the waves amplitude in?

I think its either amps or watts?

Amps is current, watts is power consumption calculated by voltage x current, if memory serves me correctly.

Digital doesn’t really have an amplitude. 1 or -1 in floating point digital audio is considered to be 0dbfs, but once that goes out to a converter, the converter can have different reference levels which will then be converted into an analogue voltage depending on that setting. Hope that helps!

Hmm…

So say I had a signal and I was trying to measure ‘how much’ bass had been outputted over a given time period, is there any good measurement of that? If you used decibels, I don’t think you could get any meaningful information as you would probably just get something like -infinity.

You’re mixing a lot of terms. try by getting some basic DSP 101.

‘bass’ - usually refers to a subset of frequencies (low ones).

‘how much’ - we’d look for energy which is also a broad term the can be measured in many ways.

In order to find how much (‘power’) of a range of frequencies (‘bass’) is in a signal (within a specific period of time). you’d need to filter it (so you’ll get the area of frequencies you desire) or try some techniques converting it into frequencies (spectrum) - Fourier Transform.

Decibels - is also a broad term where in the digital domain we use dBFS.

If as @Fandusss suggested, you need a real world equivalent. there is none.
What sound engineers would usually do.
They will calibrate the analog stage to have some reference point with the digital domain.

lol I’m aware of how to filter and that bass is not a concrete term,

but thank you, I will look into calibrating.

You should concede that the question is quite unclear. First you’d have to specify what you mean by output, because there are at least two boundaries, one at the DAC and another at the speaker. At the digital level you have a stream of numbers. These values are proportional to the voltage at the DAC’s output, which is then (hopefully) proportional to the sound pressure at some distance from the speaker. How many volts and pascals correspond to a digital value of 1.0 depends on the electric and acoustic characteristics of the whole system, including the space. As you might know, the decibel is not a unit of anything, it’s a way of converting a magnitude to a logarithmic scale relative to a reference value. So for the digital signal you have dBFS (“full scale”), relative to 1.0. For voltage you have dBV (relative to 1 V) or dBu (relative to 0.77 V); for sound pressure, dB SPL (relative to 20 micropascals). People calibrate their systems so that 0 dBFS translate to some desired dBV and dB SPL at the chosen points of measurement. For all these magnitudes you don’t measure instantaneous values, but a positive average (RMS) over a given time window.

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Thank you this is very helpful.

I apologize if the question was too unclear.
For the output in this situation I am only concerned with the DAC stage.
I am currently taking the RMS of the DAC output. I’m looking to sum the RMS value over a given time period to make some arbitrary measurement of (again, sorry for lack of a better word) ‘how much’ signal was produced and outputted over that time period.

So I guess I’m trying to figure out what the units are of taking the RMS of the DAC output. From what I’ve gathered here it seems like there are no units, but it is proportional to the voltage (though how many volts and pascals is dependent on the system).

As far as a Juce-based Audio plugin/processor goes… you can go to your processBlock and call `buffer.getRMSlevel()`, which takes a few arguments; one of which is “numSamples”, as in, get the RMS amplitude level across the number of samples in time.

I guess if you popped it last on the master buss in your DAW, you’d be measuring the RMS level being fed to your DAC, which might be the kind of thing you are looking for?

Sorry if I’ve not understood the question fully

Sorry if I don’t quite understand the situation. I suppose you’re not putting a multimeter on the DAC’s out (aka the computer’s analog audio out), unless it’s a system you have no access to, in which case you could measure voltage, but it would make more sense to put an ADC on it (aka send it to a computer’s analog audio in). If you’re talking of a digital signal in your software, and the question is to which magnitude it translates in the real world, the answer is voltage (in volts or dBV) after the DAC and sound pressure (in pascals or dB SPL) after the speakers. How much of them is unknown for the software, but unless it’s calibration software, it doesn’t matter. You have a digital signal, you take the square root of some windowed average of the squares of it (aka the RMS): this is your average amplitude. If you take 20 * log10 of that, you have it in dB. Which dB? dBFS, because it’s a digital signal, so it’s just numbers.

Now, suppose you have measured that in your system, a digital signal with average amplitude 0.5 (-6.02 dBFS) produces an average voltage of 0.25 V (-12.04 dBV) at some point in the circuit, and an average pressure of 0.02 pascals (60 dB SPL) in the air. If your signal happens to have an average amplitude of 0.25 (half the measured reference, or 6.02 dB below, so -12.04 dBFS), your voltage and pressure will also be half (6.02 dB below) the reference: 0.125 V (-18.06 dBV) and 0.01 pascals (53.98 dB SPL). The point of using dB is that you forget about volts and pascals and only speak in relative values: half is -6, double is +6, for every form the signal takes along its way.

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