Harmonic Distortion of step-approximation to sine wave

[The Phantom]

On Sun, 16 May 2004 22:53:29 +0100, Don Pearce <complete@nonsense.com>
wrote:

On Sun, 16 May 2004 21:53:02 +0100, "John Jardine"
john@jjdesigns.fsnet.co.uk> wrote:


Norm Dresner <ndrez@att.net> wrote in message
news:N_Ppc.12678$hH.309261@bgtnsc04-news.ops.worldnet.att.net...
Is there any www-resource which gives values (or simple ways to calculate
the values) for the harmonic distortion of various step-approximations to
sine waves, e.g. 8-bit, 10-bit,...

TIA
Norm

Simply as you find it ...
8 bits can be no cleaner than one part in 256 parts. Therefore THD
=1/256th or 1/2%
12 bits is one part in 4096 parts = 0.025%
ect ect

Except of course that you naturally generate only a properly dithered
step approximation, in which case there is no harmonic distortion.

The usual definition of harmonic distortion (THD) used in the audio
business is: Total RMS of harmonics alone/Total RMS of wave

There is a website with some good graphics concerning dither and its
effects on harmonics: http://www.cadenzarecording.com/dither.html

Could you explain, perhaps with reference to some of that site's
figures, how dither of a single frequency sine wave can give a result
having no harmonic distortion?

 

[Ben Bradley]

On 31 May 2004 20:15:08 -0500, The Phantom <phantom@aol.com> wrote:

The usual definition of harmonic distortion (THD) used in the audio
business is: Total RMS of harmonics alone/Total RMS of wave

There is a website with some good graphics concerning dither and its
effects on harmonics: http://www.cadenzarecording.com/dither.html

Could you explain, perhaps with reference to some of that site's
figures, how dither of a single frequency sine wave can give a result
having no harmonic distortion?

Very short answer: The signal still has 'distortion', the dither
turns it into random noise, spread out over the whole available
bandwidth instead of being harmonically related to the sine wave.

Here are a couple more good dither links:

http://www.national.com/an/AN/AN-804.pdf

http://digido.com (Click on articles, then dither)

-----
http://mindspring.com/~benbradley

 

[The Phantom]

On Mon, 31 May 2004 21:48:13 -0400, Ben Bradley
<ben_nospam_bradley@mindspring.com> wrote:

On 31 May 2004 20:15:08 -0500, The Phantom <phantom@aol.com> wrote:

The usual definition of harmonic distortion (THD) used in the audio
business is: Total RMS of harmonics alone/Total RMS of wave

There is a website with some good graphics concerning dither and its
effects on harmonics: http://www.cadenzarecording.com/dither.html

Could you explain, perhaps with reference to some of that site's
figures, how dither of a single frequency sine wave can give a result
having no harmonic distortion?

Very short answer: The signal still has 'distortion', the dither
turns it into random noise, spread out over the whole available
bandwidth instead of being harmonically related to the sine wave.

Here are a couple more good dither links:

http://www.national.com/an/AN/AN-804.pdf

http://digido.com (Click on articles, then dither)

-----
http://mindspring.com/~benbradley

I can see that this question is going to hinge on precise
definitions of some technical terms. I think before getting into it,
I would like to list some of those terms and see what others think
they mean.
--------------------------------------

Harmonic Distortion

Intermodulation Distortion

Distortion (the unqualified word, note)

MSE (Mean Squared Error)

---------------------------------------

Having defined the terms, then what does it mean to say that a signal
has "harmonic distortion"

It's interesting to note that most of the "pre-digital era" harmonic
distortion analyzers work by nulling out the fundamental and then
measuring what's left.

Another way to do it would be to have a very good comb filter bank and
pass all the harmonics and only the harmonics and measure the result.

The first method measures THD+noise, while the second would presumably
measure only THD.

Suppose we applied the second method to Figure 9 at:
http://www.cadenzarecording.com/dither.html

What would we measure?

Would it be harmonic distortion?