$How to calculate dB from audio signal amplitude (or its dbFS equivalent)$

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$How to calculate dB from audio signal amplitude (or its dbFS equivalent)$

Hello!

I am a software developer, and I am writing a software to measure the average perceived volume of an MP3 file using ReplayGain algorithm. I don't know that much about that topic myself, so if you know more than me, feel free to explain me any concept I might have misunderstood.

With that out of the way, I'd like to make a brief introduction to this topic:

An audio can be represented as a sequence of amplitude values, that is, numbers ranging from -1 to 1 (basically a wave). The ReplayGain algorithm transform these amplitude values using IIR filters to approximate their "absolute" amplitude with the amplitude for which human hears usually perceive the sound as (based on their frequency [Hz] and their overall power). The ReplainGain website has a great explanation of the application of these filters for those who are interested (see here).

As a last step, we calculate the RMS of the transformed audio samples (a very small fraction of a second of an audio) to find its average value. For audios with multiple channels, we just take the average of their channels.

With that said, how can I convert this average amplitude value to a (positive) dB scale? What do I need to know in advance and to consider when performing such conversion?

I am currently using these two functions I found on the internet to do that:

from a simple value: 20 * log10(x+ 1^-10), where x is the amplitude (ranging from -1 to 1)
from a squared value: 10 * log10(x + 1^-10), where x is the amplitude

The issue is that these functions convert the amplitude of the audio to dBFS, which is not what I was looking for because users usually expect to see positive dB values, not negative values.

And here am I, asking how can I convert either the amplitude values (-1 to 1) or the dBFS value into the dB scale. If you could explain me how do I figure out what noise floor to use (when calculating dBFS), and how to propertly calculate the dBFS value given the audio amplitude, I would be grateful.

It's important to point out that the software has access to the audio metadata such as bitrate, audio bit depth, etc, so these infos are available (if we need them to calculate these values).

Thanks in advance!

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Secretx

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Naturelover

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  Then what value do you think this question is worth? It's my first time using the website, I didn't know a good value to put.
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Naturelover

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Very low bounty!

Secretx

+1

Then what value do you think this question is worth? It's my first time using the website, I didn't know a good value to put.

Naturelover

0

If you are looking for someone to read the details you provided and provide a somewhat detailed answer to your question, it will take at least 30 minutes of time. Assuming a $50/hour rate for an expert, that would be at least $25.
Secretx

+1

Then what value do you think this question is worth? It's my first time using the website, I didn't know a good value to put.
Naturelover

0

If you are looking for someone to read the details you provided and provide a somewhat detailed answer to your question, it will take at least 30 minutes of time. Assuming a $50/hour rate for an expert, that would be at least $25.

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There are various ways to do this. In general, you can do the following:

For calculating decibels (dB) from amplitude:
$\text{dB} = 20 \cdot \log_{10}\left(\frac{\text{Amplitude}}{\text{Reference Amplitude}}\right) $

For dBFS (decibels relative to full scale):
$\text{dBFS} = 20 \cdot \log_{10}\left(\frac{\text{Signal Amplitude}}{\text{Full Scale Amplitude}}\right)$

In your case, to convert amplitude values to a positive dB scale, you need to consider the reference level or full scale of your audio. The dB scale is a logarithmic scale that measures the ratio of a value to a reference value. For audio, the reference value is typically the maximum possible amplitude, which corresponds to 0 dBFS (decibels full scale).

So, first you can convert your amplitude values to dBFS using the formula:

$dBFS = 20 \times log10(|x|)$

where x is the amplitude value ranging from -1 to 1. This gives you a value in the range of -infinity to 0 dBFS.

To make the values positive, you need to then adjust the scale. One common way is to add a constant value to the dBFS result. This constant represents the maximum possible amplitude in dBFS.

If your audio is 16-bit, the maximum amplitude is 32767 (for signed 16-bit). For 24-bit, it's 8388607. Adjusting the formula accordingly:

$dBpositive = dBFS + 20 \times log10(max amplitude) $

Instead of adding a constant for the maximum amplitude, you can also add a reference level. Choose a reference level that makes sense for your application. For example, you might choose the level at which the audio is considered "normal" or "average." The new formula becomes:

$dBpositive = dBFS - referencelevel$

You said you have access to audio metadata. Since you have access to those, you can use the information such as bitrate and bit depth to determine the maximum possible amplitude. For example, for 16-bit audio, the maximum amplitude is $2^{15} −1$ .

This approach allows you to set a reference level that aligns with your application's context, and it considers the metadata to determine the maximum possible amplitude. Adjust the reference_level_dB variable to suit your needs.

Here is a simple Python code to do all of the above:

----------------------------------------------------------------------------------
import math

def amplitude_to_positive_dB(amplitude, reference_level_dB):
dBFS = 20 * math.log10(abs(amplitude))
dB_positive = dBFS - reference_level_dB
return dB_positive

#Example: Reference level = -60 dB, amplitude value=0.5
amplitude = 0.5
reference_level_dB = -60
result_dB = amplitude_to_positive_dB(amplitude, reference_level_dB)
print("Positive dB value:", result_dB)
----------------------------------------------------------------------------------

Adjust the reference_level_dB variable to set the reference level that makes sense for your application. This way, you're representing the amplitude relative to your chosen reference level in a positive dB scale.

For more context, please see these videos which explain these very well:

https://www.youtube.com/watch?v=jZSjtQz8-7E (all 7 parts)

Kav10

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$How to calculate dB from audio signal amplitude (or its dbFS equivalent)$

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