Digital Audio: bit depth

For every digital sample, our analog to digital converter asks “what is the amplitude?”.  The question that remains is, how is this amplitude represented? The answer is “bit depth” which determines both how many different amplitude levels/steps are possible and what the overall capacity of the system is…how loud of a signal it can tolerate.

For CD-quality sound, 16 bits are used.  This means we will have 2^16 (“two to the 16th power”) different amplitude values available to us, or 65,536 steps.  Since the number of steps is divided between positive and negative values (our crests and troughs from before) this means it is divided into 32,767 positive (plus zero) and 32,768 negative values. For each sample taken, the actual amplitude must be “rounded” to the nearest available level…producing another “error” relative to the original audio signal.  The signal is “quantized”. This “quantization error” produces as small amount of “quantization noise”, noise inherent to digital recording.  A digital system is totally noise-less on its own, but as soon as it is recording a signal, it makes these errors and ends up with this small amount of noise.

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The amount of inherent noise versus the system’s capacity for the desired signal is called the signal-to-noise ratio, a concept I will illustrate in the next installment.  The signal-to-noise determines both how loud and how soft a signal can be cleanly recorded. It determines the recording’s “dynamic range”.

The overall amplitude capacity of an digital system can be theoretically approximated as 6 decibels per bit.  For our 16-bit CD-quality signal, this means our system can tolerate 96 dB.

So, is 16-bits enough?  The threshold of hearing or the threshold of pain varies among individuals, but is often cited as 120 or 130 dB.  So it may be that–unlike the CD-quality sampling rate and its accommodation for the range of human hearing–our 16-bit system is not enough. If one is not careful when recording, a signal can easily exceed the maximum amplitude, producing “clipping”.  In clipping, the waveform hits its amplitude ceiling resulting is a cropped waveform.

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The changing peaks above the maximum amplitude end up flattened. The naturally fluctuation amplitude levels are just chopped off and the resulting sound is jarring and distorted.  Increasing the bit depth will provide more amplitude “headroom” for these louder signals. 24 bits, for example provide 2^24 (over 16 million!) amplitude steps and 144 dB of theoretical overall capacity (24 x 6 dB).  So, a higher bit depth has a higher tolerance for ampltude, up to and beyond our “threshold of pain”.

As an added benefit, this higher bit depth also results in less inherent noise (!!).  Our signal-to-noise, therefore gets a two-fold benefit: more capacity for our signal and less inherent noise.

The long and short of this is, if you have a higher- bit depth system available to you, absolutely use it.  Of the two possible changes one can make to a digital conversion system, sampling rate and bit depth, the increase in bit depth will have the most profound impact on audio quality.  You will also help increase the signal-to-noise ratio, avoid clipping, as the system can tolerate higher amplitudes before going over.

Further reading:

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