The usual way is to multiply by a factor 1/max(signal), however, one of my colleagues told me to multiply by a factor:
(1-1/2^bitrate)/max(signal)
to take into account the quantization error.
This is for signals that are going to be saved again as audio files.
I would like to know the opinion of the experts, what do you think?
Thank you very much.
It really depends on what the objective of the normalisation is. Unless you have some way of explicitly calibrating the sound pressure level to which a quantisation level corresponds, you probably don't want to overcomplicate it. I would also suggest that normalising it to the peak absolute value is not a very useful approach under any circumstances - firstly, you probably have a small DC offset, so you want to first subtract the mean, and secondly, you may have some impulse noise present - which would give you a rather misleading result as you may end up with a very much lower-amplitude signal than you expect.
You could normalise signal power by computing the average power of the signal and then scaling the signal such that the average power is unity. However, if your signal is music or speech, this will tend to be skewed by quiet parts of the signal - it really only makes sense if the signal has a roughly constant power envelope. There is no 'correct' way to do this which is suitable for all cases.
The factor of (1-1/2^bitrate) is not there to compensate for quantization error but to facilitate conversion to a quantized signal. Thus, if you want to quantize to 16 bits two's complement (the most used quantization), the lowest possible value of the quantized signal is -32768 and the highest possible value of the quantized signal is +32767. If with max(signal) you mean the maximum absolute value in the waveform, the value of signal*(1-1/2^bitrate)/max(abs(signal)) is guaranteed to lie between -32767.5 and +32767.5 after multiplying by 32768, so if you round that to the nearest integer (with values of exactly +32767.5 to be rounded down) the result will fit into the range -32768..+32767. So the actual maximum multiplication factor to get the quantized signal is (1-1/2^bitrate) * (2^(bitrate-1))/max(abs(signal)). In the case above that's (1-1/65536)*32768*max(abs(signal)), or 32767.5/max(abs(signal)). After multiplying with the signal, take care to truncate the result to +32767 if it's +32767.5, because rounding up to +32768 in 16-bit two's complement actually gives you -32768 (this is another way of saying what I already said above).
A good reference on normalization of digital (audio) signals is: Leland B. Jackson, Digital Filters and Signal Processing, 3rd Edition, Kluwer Academic Publishers, 1996, pp. 388-392. After reading this, you will be able to decide for yourself what the best normalization is for your application. Success!
Also mind inter-sample peaks when trying to normalize with respect to a maximum amplitude value:
http://www.audiomisc.co.uk/HFN/OTTrevisited/results.html
Usually, speech signals are normalized according to the "ITU-T speech voltmeter tool" available in ITU-T Rec. P.56 (1993). It provides a signal that is normalized according to a reference level that is selected below the overload point..Thus, we define the term dBov (i.e. dB below overload point).
You can find information about this by following this link : http://www.itu.int/rec/T-REC-P.56-199303-S/en. To go further, a good overview of the problem of measuring the speech activity can be found in Peter Kabal's report (http://www-mmsp.ece.mcgill.ca/documents/Reports/1999/KabalR1999.pdf).
Find the R.M.S value of the audio signal over a period and use this parameter to normalize the signal. It may give the signal its statistical nature.
I am agree with Mr. Daniel Robert Franklin. It realy depends on the situation. For example, sometimes, you need to mind the min(signal), the linear normalized amplitude would be (signal-min)/(max-min).
Supporting the answer of Dr. Franklin, I would like to note that the issue of the normalization of process, that is non-stationary with respect to the dispersion, in a general way does not make sense. Also, level control in process of recording and mixing is not a normalization. The question is: what are you going to do with an audio signal?
I agree with Mr. Daniel Robert Franklin and few other researchers. Main question is what is your objective? Answer depends on that and no specific answer about the question
I fully agree with Dr. Daniel Robert Franklin particularly second paragraph.
You could normalise signal power by computing the average power of the signal and then scaling the signal such that the average power is unity. However, if your signal is music or speech, this will tend to be skewed by quiet parts of the signal - it really only makes sense if the signal has a roughly constant power envelope. There is no 'correct' way to do this which is suitable for all cases.
I would completely agree with Daniel Robert Franklin. It completely depends on the purpose. Most commendably used approach is normalizing for user preferred RMS level (Root Mean Square Level). Peak normalization is not an accepted procedures commendably (But completely depends on the purpose). If your are using a speech signal or Music signal. There are silent (quieter portions) portions which will skewed, effecting the RMS level. However, there is no 'correct' way to do this which is suitable for all cases.
I would rather advice you to check the most effective feature normalization techniques such as: Cepstral Mean Subtraction (CMS), RelAtive SpecTrAl (RASTA), kernel filtering, short time gaussianization, stochastic matching, and feature warping.
I think the variance of the signal gives the correct information about the signal.
https://www.hackaudio.com/digital-signal-processing/amplitude/peak-normalization/
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