[music-dsp] 32 bit floats >>> 24 bit integer

[Nigel Redmon]

Thanks, I like your improvement--it also reinforces the fact that the  
problem gets imprinted permanently if you truncate first, and dither  
just becomes a distraction on top of that.

BTW, I came up with the hand-waving analogy a couple of years ago  
[wow, time flies--my little web article is dated 1996: http:// 
www.earlevel.com/Digital%20Audio/Dither.html] after some serious  
thinking about a good way to describe the process intuitively. After  
writing is up, I got the idea to do a web search to see if that  
analogy had been used before, and found that it had. I was  
disappointed that I wasn't the first to think of it, but heck, it's  
still a good analogy. I looks like it might have been this page that  
I found it in:

http://www.tc.umn.edu/~erick205/Papers/paper.html

"Let the text on this page represent the amplitude of the signal to  
be quantized. Also, let the space between your slightly spread  
fingers represent valid quantization intervals. Now place your hand  
across the text. Amplitude information has been irrecoverably lost  
due to quantization. Now provide dither to the signal by quickly  
moving your hand up and down along the plane of the page. The  
amplitude information that was lost has been retrieved at the expense  
of adding a slight amount of noise to the system--your blurred  
fingers. So even though some noise has been added, we have eliminated  
the distortion due to quantization error with the result being a  
cleaner, more accurate signal."


On Jan 20, 2006, at 1:54 PM, Shay Green wrote:
> Nigel Redmon wrote:
>> I'll add an intuitive way to see why dither works, and why you can't
>> dither after the truncation:
>>
>> Close one eye and hold your hand up in front of the computer screen
>> with your fingers spread so that they obscure some of the words on  
>> the
>> screen--you won't be able to read everything. Now wag your hand side
>> to side quickly--now you can read everything, at the expense of
>> "noise"--the blur of your fingers going back and forth.
>>
>> Now, imagine that you have you hand up there still again, blocking
>> parts of the text. Imagine that you take a picture of what you can
>> see, or otherwise remove what's hidden by your fingers at the moment.
>> Now wagging your hand side to side will just add blur to picture--
>> what had been hidden by your fingers has been lost.
>
> I love this! The last part can be improved - just hold your other hand
> still behind the first. Then moving the first hand doesn't do  
> anything to
> uncover what is hidden by the second.