Kega wrote:

Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Well, at that time there was enough noise around, so nothing had to be
added (just kidding).

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

But how does it work?

You can add noise in the digital domain when reducing the number of bits
and you can care for it on the analogue side of the A/D process - which
was done in the early days of digital recording. I.E. my Sony DAT recorder
DTC-59ES dating back to the early 90s had a special buffer amp (LF 412)
before the A/D chip just to add enough white noise to get over the
truncation of the LSB.

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...)

I use Adobe Audition (aka CoolEdit Pro) on my computer to process audio files
- normally in 32 bit floating point. When I need to select the word length it
lets me select the probability distribution function of added dither, the
color of the added noise and the number of bits to envolve in dithering.
And all this depends on the sampling rate used.

For instans when level is sufficient high you don't need any
dithering, do you.

If you have a sine wave at full scale you don't hear distortion that results
in lack of dither and you don't hear noise that results in adding dither.
However, if you have a music signal that ends in a fff and its reverb fades
into silence you will hear a considerable difference between dither/truncation.
But that's of cource no "sufficient high level".

Norbert

Kega wrote in message ...

My main point is that a loud sound (in a linear PCM system) has a finer
granularity than a faint one when it comes to how the ear percept the
sound.

This is based on two assumptions:

1. That the encoding of PCM IS "granular,"

2. That the ear itself is NOT "granular."

Both assumptions are completely, utterly and totally wrong.

First, NO competent PCM system suffers from "granularity," in that
no competent PCM system uses undithered sampling. DIthering itself
REMOVES all such "granular" artifacts from the resultant digital
stream, and you are left with simply a continuous representation
whose resolution is limited simply by the random variations within
the band.

Second, the implicit assumption is that the resolution of the ear
is limitless, and this is not only wrong, it's a preposterous
assumption. If the resolution were limitless, i.e., NO "granularity,"
then the ear would be capable of sensing infinitesimally small
sound pressure levels without limit. Such is clearly NOT the case and,
indeed, the resolution of the ear is quite poor, even by 16 bit PCM
standards. Consider, for example, the limitations in hearing resolution
imposed by masking: where tones only a few dozen dB down are completely
masked by proximal louder tones.

The decibel scale is a way to closer describe how the ear
functions.

False, the decibel scale is simply a way of expressing the ratio
of two power in a convenient fashion.

Kega wrote in message ...

My main point is that a loud sound (in a linear PCM system) has a finer
granularity than a faint one when it comes to how the ear percept the
sound.

This is based on two assumptions:

1. That the encoding of PCM IS "granular,"

2. That the ear itself is NOT "granular."

Both assumptions are completely, utterly and totally wrong.

First, NO competent PCM system suffers from "granularity," in that
no competent PCM system uses undithered sampling. DIthering itself
REMOVES all such "granular" artifacts from the resultant digital
stream, and you are left with simply a continuous representation
whose resolution is limited simply by the random variations within
the band.

Second, the implicit assumption is that the resolution of the ear
is limitless, and this is not only wrong, it's a preposterous
assumption. If the resolution were limitless, i.e., NO "granularity,"
then the ear would be capable of sensing infinitesimally small
sound pressure levels without limit. Such is clearly NOT the case and,
indeed, the resolution of the ear is quite poor, even by 16 bit PCM
standards. Consider, for example, the limitations in hearing resolution
imposed by masking: where tones only a few dozen dB down are completely
masked by proximal louder tones.

The decibel scale is a way to closer describe how the ear
functions.

False, the decibel scale is simply a way of expressing the ratio
of two power in a convenient fashion.

Kega wrote in message ...

My main point is that a loud sound (in a linear PCM system) has a finer
granularity than a faint one when it comes to how the ear percept the
sound.

This is based on two assumptions:

1. That the encoding of PCM IS "granular,"

2. That the ear itself is NOT "granular."

Both assumptions are completely, utterly and totally wrong.

First, NO competent PCM system suffers from "granularity," in that
no competent PCM system uses undithered sampling. DIthering itself
REMOVES all such "granular" artifacts from the resultant digital
stream, and you are left with simply a continuous representation
whose resolution is limited simply by the random variations within
the band.

Second, the implicit assumption is that the resolution of the ear
is limitless, and this is not only wrong, it's a preposterous
assumption. If the resolution were limitless, i.e., NO "granularity,"
then the ear would be capable of sensing infinitesimally small
sound pressure levels without limit. Such is clearly NOT the case and,
indeed, the resolution of the ear is quite poor, even by 16 bit PCM
standards. Consider, for example, the limitations in hearing resolution
imposed by masking: where tones only a few dozen dB down are completely
masked by proximal louder tones.

The decibel scale is a way to closer describe how the ear
functions.

False, the decibel scale is simply a way of expressing the ratio
of two power in a convenient fashion.

Kega wrote in message ...

My main point is that a loud sound (in a linear PCM system) has a finer
granularity than a faint one when it comes to how the ear percept the
sound.

This is based on two assumptions:

1. That the encoding of PCM IS "granular,"

2. That the ear itself is NOT "granular."

Both assumptions are completely, utterly and totally wrong.

First, NO competent PCM system suffers from "granularity," in that
no competent PCM system uses undithered sampling. DIthering itself
REMOVES all such "granular" artifacts from the resultant digital
stream, and you are left with simply a continuous representation
whose resolution is limited simply by the random variations within
the band.

Second, the implicit assumption is that the resolution of the ear
is limitless, and this is not only wrong, it's a preposterous
assumption. If the resolution were limitless, i.e., NO "granularity,"
then the ear would be capable of sensing infinitesimally small
sound pressure levels without limit. Such is clearly NOT the case and,
indeed, the resolution of the ear is quite poor, even by 16 bit PCM
standards. Consider, for example, the limitations in hearing resolution
imposed by masking: where tones only a few dozen dB down are completely
masked by proximal louder tones.

The decibel scale is a way to closer describe how the ear
functions.

False, the decibel scale is simply a way of expressing the ratio
of two power in a convenient fashion.

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

unitron wrote:

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

It gets worse, of course, because digital audio uses twos-complement
numbers in to express audio's AC nature. This results in 0x7FFF being
the largest (most positive) number we can express in 16 bits and is 32767
decimal. 0x8000 is the smallest (most negative) number and is -32768
decimal.

0xFFFF is -1 decimal and 0xFFFE is -2 decimal.

--
================================================== ======================
Michael Kesti | "And like, one and one don't make
| two, one and one make one."
| - The Who, Bargain

unitron wrote:

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

It gets worse, of course, because digital audio uses twos-complement
numbers in to express audio's AC nature. This results in 0x7FFF being
the largest (most positive) number we can express in 16 bits and is 32767
decimal. 0x8000 is the smallest (most negative) number and is -32768
decimal.

0xFFFF is -1 decimal and 0xFFFE is -2 decimal.

--
================================================== ======================
Michael Kesti | "And like, one and one don't make
| two, one and one make one."
| - The Who, Bargain

unitron wrote:

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

It gets worse, of course, because digital audio uses twos-complement
numbers in to express audio's AC nature. This results in 0x7FFF being
the largest (most positive) number we can express in 16 bits and is 32767
decimal. 0x8000 is the smallest (most negative) number and is -32768
decimal.

0xFFFF is -1 decimal and 0xFFFE is -2 decimal.

--
================================================== ======================
Michael Kesti | "And like, one and one don't make
| two, one and one make one."
| - The Who, Bargain

unitron wrote:

(Kega) wrote in message . com...
Laurence Payne wrote in message . ..
On Tue, 16 Mar 2004 07:12:14 -0000, (Dave Platt)
wrote:

Leaving a small fraction of a dB of digital headroom seems like good
practice,

What fraction of a dB would correspond to one bit under maximum?

Well if you mean you go from the value FFFF (hexadecimal) (=65536) to
FFFE (65535) then the decibel change will be (20*lg(65535/65536))
where lg is the logarithm using 10 as base. A rather small value
indeed.

Note that one step close to the maximum level (FFFF) is very small in
decibel compared to a step at the minumum level. A step between 0001
to 0002 is aprox 6 dB. You have doubbled to voltage value. The
quantization is linear but the ear's sensitivity is logarithmic.

Every time I try to teach myself algorithms again my eyes glaze over
but I do know that in hex FFFF = 65535 and that FFFE = 65534. Even
though we're talking about 65536 different possibilities, the lowest
one is 0, not 1, but it's easy to forget that you're supposed to start
counting at 0.

It gets worse, of course, because digital audio uses twos-complement
numbers in to express audio's AC nature. This results in 0x7FFF being
the largest (most positive) number we can express in 16 bits and is 32767
decimal. 0x8000 is the smallest (most negative) number and is -32768
decimal.

0xFFFF is -1 decimal and 0xFFFE is -2 decimal.

--
================================================== ======================
Michael Kesti | "And like, one and one don't make
| two, one and one make one."
| - The Who, Bargain

chung wrote:

Kega (myself) wrote:

....cut...

Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

But how does it work?

Try this article:

http://www.cadenzarecording.com/dither.html

Thank you. I have now read it and it was a very good one. It is such tip
that you gave us that makes it so enjoyable to participate in
newsgroups.

....cut...

Regards Kent

--

Remove all characters 'c' before using mail address.

chung wrote:

Kega (myself) wrote:

....cut...

Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

But how does it work?

Try this article:

http://www.cadenzarecording.com/dither.html

Thank you. I have now read it and it was a very good one. It is such tip
that you gave us that makes it so enjoyable to participate in
newsgroups.

....cut...

Regards Kent

--

Remove all characters 'c' before using mail address.

chung wrote:

Kega (myself) wrote:

....cut...

Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

But how does it work?

Try this article:

http://www.cadenzarecording.com/dither.html

Thank you. I have now read it and it was a very good one. It is such tip
that you gave us that makes it so enjoyable to participate in
newsgroups.

....cut...

Regards Kent

--

Remove all characters 'c' before using mail address.

chung wrote:

Kega (myself) wrote:

....cut...

Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

But how does it work?

Try this article:

http://www.cadenzarecording.com/dither.html

Thank you. I have now read it and it was a very good one. It is such tip
that you gave us that makes it so enjoyable to participate in
newsgroups.

....cut...

Regards Kent

--

Remove all characters 'c' before using mail address.

chung wrote in message ervers.com...
Randy Yates wrote:
chung writes:

By the way, dither does not have to be, and usually is not, white
noise.

I disgree. Show me one application in which it is not. For that one,
I'll show you a dozen that are.

Also, do not confuse the whiteness of a random signal with its distribution,
or pdf. These are independent of one another.

I was actually referring to the final noise spectrum, after noise
shaping is performed. I am not familiar with the TPDF dither commonly
used, and whether they are always white or not.

In the case of DSD/SACD, it is very non-white.

Do not confuse the quantization error spectrum with the dither spectrum.
Dither may be used in DSD A/D conversion, but it is almost certainly
white. However, due to the noise-shaping feedback loop, the overall
quantization error spectrum is of course non-white.

I was talking about the final spectrum, after noise shaping. Sorry if
that was not clear.

No, it wasn't at all clear. In fact, it was outright wrong.
If you were talking about the quantization noise spectrum, then why
did you say "dither"? That's like saying "Put the cat out" and
then asking why it wasn't clear you meant the dog. The quantization
noise spectrum and the dither spectrum are two completely different
animals.

--RY

chung wrote in message ervers.com...
Randy Yates wrote:
chung writes:

By the way, dither does not have to be, and usually is not, white
noise.

I disgree. Show me one application in which it is not. For that one,
I'll show you a dozen that are.

Also, do not confuse the whiteness of a random signal with its distribution,
or pdf. These are independent of one another.

I was actually referring to the final noise spectrum, after noise
shaping is performed. I am not familiar with the TPDF dither commonly
used, and whether they are always white or not.

In the case of DSD/SACD, it is very non-white.

Do not confuse the quantization error spectrum with the dither spectrum.
Dither may be used in DSD A/D conversion, but it is almost certainly
white. However, due to the noise-shaping feedback loop, the overall
quantization error spectrum is of course non-white.

I was talking about the final spectrum, after noise shaping. Sorry if
that was not clear.

No, it wasn't at all clear. In fact, it was outright wrong.
If you were talking about the quantization noise spectrum, then why
did you say "dither"? That's like saying "Put the cat out" and
then asking why it wasn't clear you meant the dog. The quantization
noise spectrum and the dither spectrum are two completely different
animals.

--RY

chung wrote in message ervers.com...
Randy Yates wrote:
chung writes:

By the way, dither does not have to be, and usually is not, white
noise.

I disgree. Show me one application in which it is not. For that one,
I'll show you a dozen that are.

Also, do not confuse the whiteness of a random signal with its distribution,
or pdf. These are independent of one another.

I was actually referring to the final noise spectrum, after noise
shaping is performed. I am not familiar with the TPDF dither commonly
used, and whether they are always white or not.

In the case of DSD/SACD, it is very non-white.

Do not confuse the quantization error spectrum with the dither spectrum.
Dither may be used in DSD A/D conversion, but it is almost certainly
white. However, due to the noise-shaping feedback loop, the overall
quantization error spectrum is of course non-white.

I was talking about the final spectrum, after noise shaping. Sorry if
that was not clear.

No, it wasn't at all clear. In fact, it was outright wrong.
If you were talking about the quantization noise spectrum, then why
did you say "dither"? That's like saying "Put the cat out" and
then asking why it wasn't clear you meant the dog. The quantization
noise spectrum and the dither spectrum are two completely different
animals.

--RY

chung wrote in message ervers.com...
Randy Yates wrote:
chung writes:

By the way, dither does not have to be, and usually is not, white
noise.

I disgree. Show me one application in which it is not. For that one,
I'll show you a dozen that are.

Also, do not confuse the whiteness of a random signal with its distribution,
or pdf. These are independent of one another.

I was actually referring to the final noise spectrum, after noise
shaping is performed. I am not familiar with the TPDF dither commonly
used, and whether they are always white or not.

In the case of DSD/SACD, it is very non-white.

Do not confuse the quantization error spectrum with the dither spectrum.
Dither may be used in DSD A/D conversion, but it is almost certainly
white. However, due to the noise-shaping feedback loop, the overall
quantization error spectrum is of course non-white.

I was talking about the final spectrum, after noise shaping. Sorry if
that was not clear.

No, it wasn't at all clear. In fact, it was outright wrong.
If you were talking about the quantization noise spectrum, then why
did you say "dither"? That's like saying "Put the cat out" and
then asking why it wasn't clear you meant the dog. The quantization
noise spectrum and the dither spectrum are two completely different
animals.

--RY

Kega writes:

chung wrote:

Kega (myself) wrote:


Note also that I have not in my reasing involved dithering and other
techniques to increase the quality in a 16 bit PCM at low signal values.


But you HAVE to consider dithering, which is a key part of PCM systems.
Dithering effectively transforms the quantization errors, from being
correlated to the signal, to noise. So you can't say that at lower input
levels, the harmonic distortion increases because the step sizes are
now relatively large.

In a properly dithered system, you do not see the harmonic distortion
terms. The system is linear, with a slightly higher noise floor.


Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Kent,

The basic university professor may not have been aware of it back
then.

From what I have been able gather, Robert Wannamaker's PhD thesis
is a landmark paper on the entire subject. Of course it gets deep, but
he does a pretty good job of explaining things before he gets into
the depth. He also has an excellent section on the history of quantization
in chapter one. Essentially he credits L.G. Roberts as the first one to
use dither (in video) back in 1962. The thesis is freely available at:

http://audiolab.uwaterloo.ca/~rob/phd.html

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

That is about as intuitive as it gets, and is right on.

But how does it work?

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...) For instans when level is sufficient high you don't need any
dithering, do you.

To answer your immediate question, yes, you do even for high-level signals.
To see what happens if you don't dither, write a quick Matlab script that
generates a perfect (at least to double-precision floating-point) sine wave,
quantize it to 16 bits, and look at the resulting spectrum. You'll see lots
of nasty spurs.

The business of examining dither involves the study of random signals
(AKA random processes or stochastic processes). There are two main
properties of a random process: 1) the amount of correlation from one
sample to the next (or between one time t1 and another t2 for a continuous
random process), and 2) the distribution (pdf, or probability density
function) of the process. It is property 1 we are describing when we
call a dither signal "white."

Rob shows that an nRPDF (the sum of n rectangular PDFs) white dither
will decorrelate the first n moments of the quantization error
spectrum from the input signal. In practice, n = 2, and 2RPDF is also
known as TPDF, or triangular PDF. So that means the first moment,
or the DC correlation, is removed, and also the second moment, which
is the so-called noise power modulation.

Hope this sparks some understanding/interest.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124

Kega writes:

chung wrote:

Kega (myself) wrote:


Note also that I have not in my reasing involved dithering and other
techniques to increase the quality in a 16 bit PCM at low signal values.


But you HAVE to consider dithering, which is a key part of PCM systems.
Dithering effectively transforms the quantization errors, from being
correlated to the signal, to noise. So you can't say that at lower input
levels, the harmonic distortion increases because the step sizes are
now relatively large.

In a properly dithered system, you do not see the harmonic distortion
terms. The system is linear, with a slightly higher noise floor.


Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Kent,

The basic university professor may not have been aware of it back
then.

From what I have been able gather, Robert Wannamaker's PhD thesis
is a landmark paper on the entire subject. Of course it gets deep, but
he does a pretty good job of explaining things before he gets into
the depth. He also has an excellent section on the history of quantization
in chapter one. Essentially he credits L.G. Roberts as the first one to
use dither (in video) back in 1962. The thesis is freely available at:

http://audiolab.uwaterloo.ca/~rob/phd.html

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

That is about as intuitive as it gets, and is right on.

But how does it work?

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...) For instans when level is sufficient high you don't need any
dithering, do you.

To answer your immediate question, yes, you do even for high-level signals.
To see what happens if you don't dither, write a quick Matlab script that
generates a perfect (at least to double-precision floating-point) sine wave,
quantize it to 16 bits, and look at the resulting spectrum. You'll see lots
of nasty spurs.

The business of examining dither involves the study of random signals
(AKA random processes or stochastic processes). There are two main
properties of a random process: 1) the amount of correlation from one
sample to the next (or between one time t1 and another t2 for a continuous
random process), and 2) the distribution (pdf, or probability density
function) of the process. It is property 1 we are describing when we
call a dither signal "white."

Rob shows that an nRPDF (the sum of n rectangular PDFs) white dither
will decorrelate the first n moments of the quantization error
spectrum from the input signal. In practice, n = 2, and 2RPDF is also
known as TPDF, or triangular PDF. So that means the first moment,
or the DC correlation, is removed, and also the second moment, which
is the so-called noise power modulation.

Hope this sparks some understanding/interest.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124

Kega writes:

chung wrote:

Kega (myself) wrote:


Note also that I have not in my reasing involved dithering and other
techniques to increase the quality in a 16 bit PCM at low signal values.


But you HAVE to consider dithering, which is a key part of PCM systems.
Dithering effectively transforms the quantization errors, from being
correlated to the signal, to noise. So you can't say that at lower input
levels, the harmonic distortion increases because the step sizes are
now relatively large.

In a properly dithered system, you do not see the harmonic distortion
terms. The system is linear, with a slightly higher noise floor.


Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Kent,

The basic university professor may not have been aware of it back
then.

From what I have been able gather, Robert Wannamaker's PhD thesis
is a landmark paper on the entire subject. Of course it gets deep, but
he does a pretty good job of explaining things before he gets into
the depth. He also has an excellent section on the history of quantization
in chapter one. Essentially he credits L.G. Roberts as the first one to
use dither (in video) back in 1962. The thesis is freely available at:

http://audiolab.uwaterloo.ca/~rob/phd.html

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

That is about as intuitive as it gets, and is right on.

But how does it work?

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...) For instans when level is sufficient high you don't need any
dithering, do you.

To answer your immediate question, yes, you do even for high-level signals.
To see what happens if you don't dither, write a quick Matlab script that
generates a perfect (at least to double-precision floating-point) sine wave,
quantize it to 16 bits, and look at the resulting spectrum. You'll see lots
of nasty spurs.

The business of examining dither involves the study of random signals
(AKA random processes or stochastic processes). There are two main
properties of a random process: 1) the amount of correlation from one
sample to the next (or between one time t1 and another t2 for a continuous
random process), and 2) the distribution (pdf, or probability density
function) of the process. It is property 1 we are describing when we
call a dither signal "white."

Rob shows that an nRPDF (the sum of n rectangular PDFs) white dither
will decorrelate the first n moments of the quantization error
spectrum from the input signal. In practice, n = 2, and 2RPDF is also
known as TPDF, or triangular PDF. So that means the first moment,
or the DC correlation, is removed, and also the second moment, which
is the so-called noise power modulation.

Hope this sparks some understanding/interest.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124

Kega writes:

chung wrote:

Kega (myself) wrote:


Note also that I have not in my reasing involved dithering and other
techniques to increase the quality in a 16 bit PCM at low signal values.


But you HAVE to consider dithering, which is a key part of PCM systems.
Dithering effectively transforms the quantization errors, from being
correlated to the signal, to noise. So you can't say that at lower input
levels, the harmonic distortion increases because the step sizes are
now relatively large.

In a properly dithered system, you do not see the harmonic distortion
terms. The system is linear, with a slightly higher noise floor.


Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Kent,

The basic university professor may not have been aware of it back
then.

From what I have been able gather, Robert Wannamaker's PhD thesis
is a landmark paper on the entire subject. Of course it gets deep, but
he does a pretty good job of explaining things before he gets into
the depth. He also has an excellent section on the history of quantization
in chapter one. Essentially he credits L.G. Roberts as the first one to
use dither (in video) back in 1962. The thesis is freely available at:

http://audiolab.uwaterloo.ca/~rob/phd.html

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

That is about as intuitive as it gets, and is right on.

But how does it work?

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...) For instans when level is sufficient high you don't need any
dithering, do you.

To answer your immediate question, yes, you do even for high-level signals.
To see what happens if you don't dither, write a quick Matlab script that
generates a perfect (at least to double-precision floating-point) sine wave,
quantize it to 16 bits, and look at the resulting spectrum. You'll see lots
of nasty spurs.

The business of examining dither involves the study of random signals
(AKA random processes or stochastic processes). There are two main
properties of a random process: 1) the amount of correlation from one
sample to the next (or between one time t1 and another t2 for a continuous
random process), and 2) the distribution (pdf, or probability density
function) of the process. It is property 1 we are describing when we
call a dither signal "white."

Rob shows that an nRPDF (the sum of n rectangular PDFs) white dither
will decorrelate the first n moments of the quantization error
spectrum from the input signal. In practice, n = 2, and 2RPDF is also
known as TPDF, or triangular PDF. So that means the first moment,
or the DC correlation, is removed, and also the second moment, which
is the so-called noise power modulation.

Hope this sparks some understanding/interest.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124