How to see if a .WAV file is saturated?

Hello everyone,

I have a .wav file that I want to see if its signal is saturated or not.

In case it is saturated I would like to change the gain in order to prevent the saturation.

Do you have any idea about how to do this?

Thank you in advance.

[Mathieu NOE]

hello

if you take the abs of the magnitude of your data and if this is very close to 1 for a good amount of samples (above 1% ?) , then you know it's clipped

Answer 1

[Walter Roberson]

You may have to choose your "very close to 1" to be fairly strict for "above 1%" to work out as a boundary

Nsamp = 30000;
Fs = 8000;
t = (0:Nsamp-1)./Fs;
F = 5;

sig1 = sin(F*2*pi*t);
plot(t, sig1); title('unsaturated 5Hz')

sig2 = max(min(sig1*1.5, 1), -1);
plot(t, sig2); title('saturated 5Hz')

mean(abs(sig1) > 0.99988) * 100

ans = 0.8733

mean(abs(sig2) > 0.99988) * 100

ans = 53.6233

If you use a boundary of 0.99987 then more than 1% of the original non-saturated sine is "close" to 1. But more than 50% of the 1.5 * saturated signal is.

load handel  %y, Fs
hNsamp = length(y);
hFs = y;
ht = (0:hNsamp-1)./Fs;

hsig1 = y;
plot(ht, hsig1); title('unsaturated Handel')

hsig2 = max(min(hsig1*1.5, 1), -1);
plot(ht, hsig2); title('saturated Handel')

mean(abs(hsig1) > 0.99988) * 100

ans = 0

mean(abs(hsig2) > 0.99988) * 100

ans = 0.2694

max(abs(hsig1))

ans = 0.8000

The original handel signal is -0.8 to +0.8 so none of it is "close" to 1 in the unsaturated version.

With 50% over-saturation, the peak would be 1.2 -- but even though this was constructed to be saturated (clipped) only about 1/4 of 1% is above the boundary that was needed for the pure sine wave.

We conclude from this that the strategy proposed by @Mathieu NOE cannot reliably distinguish clipping -- at least not by itself.

[Walter Roberson]

load handel  %y, Fs
hNsamp = length(y);
hFs = y;
ht = (0:hNsamp-1)./Fs;

hsig1 = rescale(y, -1, 1);    %what if we center and rescale?
plot(ht, hsig1); title('unsaturated Handel')

hsig2 = max(min(hsig1*1.5, 1), -1);
plot(ht, hsig2); title('saturated Handel')

mean(abs(hsig1) > 0.99988) * 100

ans = 0.0752

mean(abs(hsig2) > 0.99988) * 100

ans = 1.4826

max(abs(hsig1))

ans = 1

So centering and rescaling might help ?

[Ricardo Duarte]

Hello Walter,

I think your explanation solves part of my problem but I'm affraid that it do not solve the complete problem.

In fact what I need is to analyze all the WAV files in a folder and identify if the WAV files are saturated or not. In case of saturation I need to change the gain. If the file is not saturated I let the gain as it is.

Thank you in advance.

[Image Analyst]

There is no point to that. Once it's saturated, the values of the signal are lost. You don't know what values the signal would have had, had it not been clipped. You can multiply by a fraction to make it less than 1 but that will just make it quieter -- it will not restore whatever data was lost. To do that you'd have to re-record the sound and save in a new .wav file. If you have the opportunity to do that, then you can try that.

[Walter Roberson]

I could imagine that hypothetically one might need to identify saturation to know which rerecording needed to be done.

[Ricardo Duarte]

Hello Walter and Image Analyst,

This procedure is to be aplied in real time recordings and for that reason i think it will be possible to adjust the gain and then save the wave file in a new file. I was talking about the folder with several files as a way to test the procedure "offline" but the goal is to real time experiment.

So in that case, the only need is to multiply by a fraction?

Thank you in advance.

[Walter Roberson]

Imagine that you have a sine wave that is saturated. The peak value would be +/-1 to within round-off error. But compare that to a sine wave of the same frequency that was not saturated, whose peak was also +/- 1 to within round-off error.

In the non-saturated case if you had indefinite precision the sine wave would touch the peak for exactly one sample. But if you do not have indefinite precision...

Fs = 22100;
t = (0:Fs*3-1)/Fs;
F = 5;
y = sinpi(2*F*t);
plot(t, y); title('double precision'); ylim([-1.1 1.1])

yr = round(y*1024)/1024;
plot(t, yr); title('10 bit precision, overview'); ylim([-1.1 1.1])

plot(t(1050:1150),yr(1050:1150)); title('10 bit precision, zoom'); ylim([0.995 1.001])

So in this non-saturated case where you have 10-bit precision (because limite precision coming from the microphone), you get several samples in a row peaking a 1.

Compare that to what would happen if the signal was slightly oversaturated... you would also get several samples in a row that were 1.

Could you study min(diff(unique(yr))) to estimate quantization, and use that to model whether this staircase is "expected considering quantization" compared to "saturated" ? Maybe... if you knew you were dealing with a pure frequency.

Hmmmm... question for you:

If you were recording an old 8-bit video game that used square-wave sound synthesis, how would you know whether you had saturated or not?

Have you considered just using https://www.mathworks.com/help/audio/ref/audiolevelmeter-system-object.html ?

Or use https://www.mathworks.com/help/dsp/ref/timescope.html and manually adjust the gain controls before starting recording.

[Mathieu NOE]

Just one remark

a good audio engineer asks the musicians to play the loudest part of their music and then set the microphone sensivity and analog gains so that the levels recorded remains 10 to 12 dB below clip level (headroom)

that means , we usually don't use the full range of the wav file dynamics, max 25% in practice (most of the time). Naturally there is a micro loss of accuracy vs the case you would use 99% of the range, but at your ears it would probably remains unoticeable.

At the beginning of the CD era, the co-inventors had devised that even a resolution of 14 bits was enough.

So using wav format on 16 bits with only 25% dynamic usage is good enough for many cases. Only the purist would say (maybe) something against it.

[Walter Roberson]

@Mathieu NOE

Some purists complain about their 24 bit per sample audio file not being good enough... (Sorry, Neil Young!)