AES Fall Online Convention

Digital Audio Workstations (DAWs) are now using floating-point arithmetic for their signal processing. This allows for a far wider dynamic range within the DAW, and file storage. However, the way this processing might affect the audio signal is not so well known. The older fixed-point methods of processing are much better understood and applying remedies such as “dither” when the signal is rounded, is well known.

However, floating-point numbers are dynamic entities that depend on the instantaneous value of the audio signal. This means that the step size of the underlying digital word is continually changing dependent on the sample value. How does this affect the audio signal? What is the effect of adding such signals together? How might we apply “dither” to such signals?

The purpose of this tutorial is to look at floating point numbers and arithmetic in some detail with a view to gaining some insight into their effect on the audio signal.
We will look at both floating-point and fixed-point number formats in order to understand how they differ. We will also examine the performance of both formats to understand what penalties floating-point numbers impose for their greater dynamic range when compared to the equivalent sized fixed-point number.

We then look at how to add/subtract and multiply floating-point numbers with a view to understanding how add/subtract operations in particular can be an issue because, if they are not carefully implemented, they can cause significant damage to the audio signal.

Finally, we will look at how you might apply “dither” and noise-shaping in a floating point environment.

The tutorial will be at a level that should allow it to be understandable to; students, users of DAWs, and signal processing, and plug-in developers, and will allow them to use and program DAWs more effectively, mindful of audio quality.