Explain "Floating Point"

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Soundtech98

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#148884 3-Jul-2014 21:36

Hi, I hope this question is in the right forum.

Anyway, I have been looking at some pro audio equipment and came across the word "Floating Point" (as in 40-Bit Floating Point for example).
It probably has something to do with the resolution of the recording, could somebody please give me a detailed explanation of the word using the 40-Bit Floating Point example to help me understand the theory behind all of this once and for all.

Cheers.

tardtasticx

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#1079685 3-Jul-2014 22:54

I think its to do with how well a computer can digitally represent sound ? Like, it can give a more accurate sample of the analogue audio at a given moment.

So for example, 40bit floating point could register up to 40 different types of sound/variations in the sound or something (?) per interval, making for a more crisp sound than 32bit floating point for e.g.

This diagram might help, the digital representation is the grey box, the analogue is the red line. The grey boxes want to be as close to that red line as possible. Sometimes due to sampling time etc some parts will get cut off and you lose a bit of sound, but floating point will be able to better match that red line for a better digital representation of the analogue sound. Depending on the bit level used to encode it, then you will get different results.

I haven't looked into this terribly much but I think this is what I remember being told in first semester of BCS degree lol.

If thats not on the right track I apologise in advance.

Lias

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#1079687 3-Jul-2014 23:07

https://en.wikipedia.org/wiki/Audio_bit_depth#Floating_point

and

https://en.wikipedia.org/wiki/Floating_point

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mclean

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#1079784 4-Jul-2014 09:59

Using Tardtasticx's diagram, which you could say is a 15-bit fixed point processor:

The grey output signal is a reasonable representation of the red input signal. Now imagine if the red input signal reduces to a low level one with a swing of say +/- 1, ie a swing between 6 and 8 on the diagram. This fixed point processor can only output at discrete values of 6, 7 or 8 so the processor really struggles. The output will be square waves more or less, which means a very noisy output signal.

A floating point processor is not stuck on these discrete output values. When is sees a low level input signal it can "re-scale" its conversion so that all 15 output values are squeezed in to the space between 6 and 8. Obviously these output levels are no longer integers, hence the "floating point". Now it can produce a good digital representation of the input signal. You could say that this floating point approach gives a better dynamic range because it works better with low level signals.

The downside is that the processor has the additional overhead of figuring out how to "re-scale" the conversion, depending on the sort of input signal it is seeing.

This is a gross simplification. The quality of the conversion with either method depends more on the quality of the software in the processor. The general consensus in the audio world seems to be that for equivalent levels of complexity/cost the fixed point processor is better.

As I said, it's very much more complex than this explanation!

RunningMan

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#1081036 4-Jul-2014 15:33

mclean: Using Tardtasticx's diagram, which you could say is a 15-bit fixed point processor:

Not quite - there's 16 discrete values on the graph (0-15), which would be represented by 4 bits, not 15. 2^4 = 16

mclean

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#1081047 4-Jul-2014 15:53

RunningMan: Not quite - there's 16 discrete values on the graph (0-15), which would be represented by 4 bits, not 15. 2^4 = 16

Yep.