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Karl Uppiano
 
Posts: n/a
Default Dithering Digital Audio

I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".

There seems to be commonly held misconception that dither is just the noise
we add to digital audio to cover up the real digital noise floor. This is
not true. I obviously can't go into all of the mathematical proofs here, and
that would be pointless anyway, since the information has been published in
many forms in many places by people like VanDerKooy and Lip****z. You can
Google them for more information.

Digital audio has no natural noise floor in the traditional sense. If you
feed silence into an un-dithered, ideal analog to digital (A/D) converter,
you'll get a sequence of binary samples representing zero, forever. If you
apply a very small input signal, you'll get a varying sequence of samples at
the output. The output sequence represents converter step values related to
the converters resolution, correlated in some way (but not musically or
audibly) to the input signal. Not until the signal significantly exceeds the
minimum converter resolution will the coded converter output samples begin
to represent the input signal as recognizable audio. When you run an A/D
converter at the lower limits of its resolution, the result is gross
intermodulation distortion, harmonic distortion and noise modulation.

From a perceptual standpoint, the previous paragraph can be put this way:
With zero input, the noise floor of an ideal A/D converter is infinite. When
the input signal amplitude happens to exceed the converter's minimum
resolution, the noise level jumps to some value dictated by the converter's
resolution (about -96dB in the case of a 16-bit converter). Furthermore, the
noise will be quite different in amplitude and spectral makeup from the
input signal. In other words, highly distorted, and probably not
recognizable by humans as the original input signal.

Dither adds a noise floor to a system that has no natural noise floor. In a
properly dithered system, a pseudo-random signal with a specific spectrum
and probability density (the likelihood of an occurrence a given amplitude)
keeps the converter always switching between adjacent bits. Because the
dither is wide-band and random, it doesn't matter whether the converter
represents it accurately or not. The output is also wide-band and random. It
isn't an accurate representation of the original dither, but two random
sequences are still just random sequences. The input sequence can be
numerically designed to produce the desired random output sequence.

The magic happens when you add the audio signal to this system. As we
already pointed out, A/D converters are highly non-linear when operated near
their lower resolution limits. This non-linearity gives rise to gross
intermodulation distortion, harmonic distortion and noise described earlier.
But what happens when you intermodulate (multiply) a signal with random
noise? You get the same signal, with noise added. It's not the same noise
you started with, but the noise is random, so it doesn't matter. The
important thing is, the signal is intact, except for the added noise. The
intermodulation products are distributed randomly, so they just add to the
noise slightly. The input signal would amplitude-modulate the dither unless
the dither has triangular probability density. This ingenious trick forces
the dither to self-modulate in the opposite direction as it gets pushed
towards or away from an A/D bit transition. The result is a very smooth
noise floor with the ability to linearly resolve correlated signals (tones,
i.e., musical notes) that are below the noise floor (and below the
resolution of the converter).

By the way, this discussion is all about A/D converters. That's where it
counts. The best D/A converter is only as good as the signal being sent to
it. Dither added after the fact cannot linearize or recover information lost
in an
improperly designed A/D converter. Your only hope at that point is to add
enough noise to cover it up. Fortunately, that noise level is probably
equivalent to that an analog master tape, so I guess it's not so bad,
really.

Having a good understanding of dither helps explain why CD audio, which has
been much maligned for being "so marginal" has been so successful. I tend
not to think of CD audio as marginal, I prefer to think of it as "optimal".
It's very elegant in the sense that it delivers extremely high quality
audio, without spending a single bit more than is theoretically required to
deliver it. We now have the storage densities and bandwidth to extend the
resolution and sampling rates. Aside from being great marketing tools, they
do give the design engineers more tolerance, which means we don't have to
work as hard to "get it right". Although I think CD audio is a great
delivery mechanism, it's probably inadequate for professional studio work,
where uncontrolled audio peaks are common, and mixing puts extreme demands
on dynamic range.

  #2   Report Post  
Ben Hoadley
 
Posts: n/a
Default Dithering Digital Audio

"Karl Uppiano" wrote in message news:on5Fb.6561$VB2.9687@attbi_s51...
I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".

There seems to be commonly held misconception that dither is just the noise
we add to digital audio to cover up the real digital noise floor. This is
not true. I obviously can't go into all of the mathematical proofs here, and
that would be pointless anyway, since the information has been published in
many forms in many places by people like VanDerKooy and Lip****z. You can
Google them for more information.

Digital audio has no natural noise floor in the traditional sense. If you
feed silence into an un-dithered, ideal analog to digital (A/D) converter,
you'll get a sequence of binary samples representing zero, forever. If you
apply a very small input signal, you'll get a varying sequence of samples at
the output. The output sequence represents converter step values related to
the converters resolution, correlated in some way (but not musically or
audibly) to the input signal. Not until the signal significantly exceeds the
minimum converter resolution will the coded converter output samples begin
to represent the input signal as recognizable audio. When you run an A/D
converter at the lower limits of its resolution, the result is gross
intermodulation distortion, harmonic distortion and noise modulation.

From a perceptual standpoint, the previous paragraph can be put this way:
With zero input, the noise floor of an ideal A/D converter is infinite. When
the input signal amplitude happens to exceed the converter's minimum
resolution, the noise level jumps to some value dictated by the converter's
resolution (about -96dB in the case of a 16-bit converter). Furthermore, the
noise will be quite different in amplitude and spectral makeup from the
input signal. In other words, highly distorted, and probably not
recognizable by humans as the original input signal.

Dither adds a noise floor to a system that has no natural noise floor. In a
properly dithered system, a pseudo-random signal with a specific spectrum
and probability density (the likelihood of an occurrence a given amplitude)
keeps the converter always switching between adjacent bits. Because the
dither is wide-band and random, it doesn't matter whether the converter
represents it accurately or not. The output is also wide-band and random. It
isn't an accurate representation of the original dither, but two random
sequences are still just random sequences. The input sequence can be
numerically designed to produce the desired random output sequence.

The magic happens when you add the audio signal to this system. As we
already pointed out, A/D converters are highly non-linear when operated near
their lower resolution limits. This non-linearity gives rise to gross
intermodulation distortion, harmonic distortion and noise described earlier.
But what happens when you intermodulate (multiply) a signal with random
noise? You get the same signal, with noise added. It's not the same noise
you started with, but the noise is random, so it doesn't matter. The
important thing is, the signal is intact, except for the added noise. The
intermodulation products are distributed randomly, so they just add to the
noise slightly. The input signal would amplitude-modulate the dither unless
the dither has triangular probability density. This ingenious trick forces
the dither to self-modulate in the opposite direction as it gets pushed
towards or away from an A/D bit transition. The result is a very smooth
noise floor with the ability to linearly resolve correlated signals (tones,
i.e., musical notes) that are below the noise floor (and below the
resolution of the converter).

By the way, this discussion is all about A/D converters. That's where it
counts. The best D/A converter is only as good as the signal being sent to
it. Dither added after the fact cannot linearize or recover information lost
in an
improperly designed A/D converter. Your only hope at that point is to add
enough noise to cover it up. Fortunately, that noise level is probably
equivalent to that an analog master tape, so I guess it's not so bad,
really.

Having a good understanding of dither helps explain why CD audio, which has
been much maligned for being "so marginal" has been so successful. I tend
not to think of CD audio as marginal, I prefer to think of it as "optimal".
It's very elegant in the sense that it delivers extremely high quality
audio, without spending a single bit more than is theoretically required to
deliver it. We now have the storage densities and bandwidth to extend the
resolution and sampling rates. Aside from being great marketing tools, they
do give the design engineers more tolerance, which means we don't have to
work as hard to "get it right". Although I think CD audio is a great
delivery mechanism, it's probably inadequate for professional studio work,
where uncontrolled audio peaks are common, and mixing puts extreme demands
on dynamic range.


Karl, this is an excellent article.
My initial assertation that the noise floor of cd's is ugly was
technically incorrect and I appologise. What I meant by noise floor is
actually "the point at which you can perceive uglyness unless its
dithered". The reason I called it "noise floor" is because we were
dealing with someone who didn't know what a volume knob did, so I
simplified the concept. (I am definitly not saying that the original
poster is simple, so no offence is intended).
Since we were talking about the play-back of cd's we can not assume
that all cd,s are propery dithered (they should be, and usually are).
You did say "if " so we agree.
When I said that the noise-floor of cd's is uglier than the noise
floor of vinyl ect. I did not mean that vinyl is better than cd as a
format. I was trying to explain in a simple way that the noise floor
of a cd is very diferent to the ones he might be familliar with, less
tolerable (somtimes) and therefore more critical to avoid.
I do not think that cd is a bad format. It is a good advance on
previous mediums for both practical and sonic reasons. However it is
not entirely optimal imho. The upper frequencies have to be filtered
so abruptly by both the ad and da converters that it is very
difficult, and therefore very expensive, to make them sound nice (to
my ears). If the original recording was done at a higher sampling
rate, and only converted down at the final mastering stage, the final
cd will(more likely) be smooth sounding in that regard. Then the only
limitation will be the da converter.
if we use dvda etc the filter can be a lot less steep, less expensive
and so hopfully more common. All the stuff people go on about upper
harmonics and all that, while being true, is far less important than
than the lack of harsh filters in my opinion.
I know true dither is not the same as tape hiss. I again was trying to
explain it in a way that I could understand when I was first learning.
I hope I don't get your heckles up any more. It seems I was
simplifying more than what would be to your liking. I agee with you
for the most part, Ithink cd's can sound excellent, but I can not say
that the format is "optimal" and I think mr Neve would agree with me.

  #3   Report Post  
Karl Uppiano
 
Posts: n/a
Default Dithering Digital Audio

I certainly did not mean to jump all over you, and I hope you did not get
that from my remarks. I just think a lot of mis-information about digital
audio gets its start with offhand remarks, and I am constantly poised to
pounce, I'm afraid. I first got involved with digital audio when I was in
college in the mid 1970's, before I was even aware of the Soundstream/Telarc
recordings. I was quite aware of the possibilities, and I was quite pleased
with the CD audio spec when it came out, although I was also painfully aware
of lots of poor implementations of it. I still think the Philips 4x
oversampling converters embody some of the most elegant engineering ever to
go into a consumer product.

Throughout the 80's I followed with great interest the developments by the
greats, such as VanDerKooy and Lip****z. Many of the CD releases in the
first decade of production did not incorporate these advances. They do now.
But these advances alone make the current CD audio format quite optimal, in
my opinion. Unfortunately, they are so esoteric (compared to the brute force
of 96kHz sample rates and 24-bit audio) that the marketers and casual users
can't be bothered. The sad part is that we ran the risk with SACD of losing
the "real" advancements in favor of the marketing bits and marketing sample
rates. Fortunately, it appears *that* gaffe may have been averted.

The nice thing about oversampled converters (dating all the way back to the
first Philips 4x oversampling machines) is that digital filters can handle
the extremely steep cutoff necessary for a 44.1kHz sample rate. Digital FIR
filters are completely phase linear, and can be made arbitrarily accurate
without too much expense. The only cost is how much memory you need to
implement it, and how fast of a processor you need to compute all the data
points to get the next filtered sample.

The analog filters required by an oversampling converter are thus much less
critical to design. I haven't done a recent poll on today's converters, but
64x oversampling is pretty common today. They use very sophisticated digital
filters, and the resulting highly oversampled output hardly needs filtering.
I just went out to the Analog Devices web site and looked at the data sheet
for the AD1853 D/A converter; it's fairly typical of what is used in lots of
DVD and CD players today. The recommended output filter will have Gaussian
response with a -3dB corner frequency of 75kHz. That's a decidedly
lackadaisical filter, with the transition band more than three octaves away
from the audio range.

"Ben Hoadley" wrote in message
news:5HmFb.172358$_M.778279@attbi_s54...
"Karl Uppiano" wrote in message

news:on5Fb.6561$VB2.9687@attbi_s51...
I decided to start a new thread about Digital Audio and Dithering from

the
thread "Volume and Dynamic Range Question".

There seems to be commonly held misconception that dither is just the

noise
we add to digital audio to cover up the real digital noise floor. This

is
not true. I obviously can't go into all of the mathematical proofs here,

and
that would be pointless anyway, since the information has been published

in
many forms in many places by people like VanDerKooy and Lip****z. You

can
Google them for more information.

Digital audio has no natural noise floor in the traditional sense. If

you
feed silence into an un-dithered, ideal analog to digital (A/D)

converter,
you'll get a sequence of binary samples representing zero, forever. If

you
apply a very small input signal, you'll get a varying sequence of

samples at
the output. The output sequence represents converter step values related

to
the converters resolution, correlated in some way (but not musically or
audibly) to the input signal. Not until the signal significantly exceeds

the
minimum converter resolution will the coded converter output samples

begin
to represent the input signal as recognizable audio. When you run an A/D
converter at the lower limits of its resolution, the result is gross
intermodulation distortion, harmonic distortion and noise modulation.

From a perceptual standpoint, the previous paragraph can be put this

way:
With zero input, the noise floor of an ideal A/D converter is infinite.

When
the input signal amplitude happens to exceed the converter's minimum
resolution, the noise level jumps to some value dictated by the

converter's
resolution (about -96dB in the case of a 16-bit converter). Furthermore,

the
noise will be quite different in amplitude and spectral makeup from the
input signal. In other words, highly distorted, and probably not
recognizable by humans as the original input signal.

Dither adds a noise floor to a system that has no natural noise floor.

In a
properly dithered system, a pseudo-random signal with a specific

spectrum
and probability density (the likelihood of an occurrence a given

amplitude)
keeps the converter always switching between adjacent bits. Because the
dither is wide-band and random, it doesn't matter whether the converter
represents it accurately or not. The output is also wide-band and

random. It
isn't an accurate representation of the original dither, but two random
sequences are still just random sequences. The input sequence can be
numerically designed to produce the desired random output sequence.

The magic happens when you add the audio signal to this system. As we
already pointed out, A/D converters are highly non-linear when operated

near
their lower resolution limits. This non-linearity gives rise to gross
intermodulation distortion, harmonic distortion and noise described

earlier.
But what happens when you intermodulate (multiply) a signal with random
noise? You get the same signal, with noise added. It's not the same

noise
you started with, but the noise is random, so it doesn't matter. The
important thing is, the signal is intact, except for the added noise.

The
intermodulation products are distributed randomly, so they just add to

the
noise slightly. The input signal would amplitude-modulate the dither

unless
the dither has triangular probability density. This ingenious trick

forces
the dither to self-modulate in the opposite direction as it gets pushed
towards or away from an A/D bit transition. The result is a very smooth
noise floor with the ability to linearly resolve correlated signals

(tones,
i.e., musical notes) that are below the noise floor (and below the
resolution of the converter).

By the way, this discussion is all about A/D converters. That's where it
counts. The best D/A converter is only as good as the signal being sent

to
it. Dither added after the fact cannot linearize or recover information

lost
in an
improperly designed A/D converter. Your only hope at that point is to

add
enough noise to cover it up. Fortunately, that noise level is probably
equivalent to that an analog master tape, so I guess it's not so bad,
really.

Having a good understanding of dither helps explain why CD audio, which

has
been much maligned for being "so marginal" has been so successful. I

tend
not to think of CD audio as marginal, I prefer to think of it as

"optimal".
It's very elegant in the sense that it delivers extremely high quality
audio, without spending a single bit more than is theoretically required

to
deliver it. We now have the storage densities and bandwidth to extend

the
resolution and sampling rates. Aside from being great marketing tools,

they
do give the design engineers more tolerance, which means we don't have

to
work as hard to "get it right". Although I think CD audio is a great
delivery mechanism, it's probably inadequate for professional studio

work,
where uncontrolled audio peaks are common, and mixing puts extreme

demands
on dynamic range.


Karl, this is an excellent article.
My initial assertation that the noise floor of cd's is ugly was
technically incorrect and I appologise. What I meant by noise floor is
actually "the point at which you can perceive uglyness unless its
dithered". The reason I called it "noise floor" is because we were
dealing with someone who didn't know what a volume knob did, so I
simplified the concept. (I am definitly not saying that the original
poster is simple, so no offence is intended).
Since we were talking about the play-back of cd's we can not assume
that all cd,s are propery dithered (they should be, and usually are).
You did say "if " so we agree.
When I said that the noise-floor of cd's is uglier than the noise
floor of vinyl ect. I did not mean that vinyl is better than cd as a
format. I was trying to explain in a simple way that the noise floor
of a cd is very diferent to the ones he might be familliar with, less
tolerable (somtimes) and therefore more critical to avoid.
I do not think that cd is a bad format. It is a good advance on
previous mediums for both practical and sonic reasons. However it is
not entirely optimal imho. The upper frequencies have to be filtered
so abruptly by both the ad and da converters that it is very
difficult, and therefore very expensive, to make them sound nice (to
my ears). If the original recording was done at a higher sampling
rate, and only converted down at the final mastering stage, the final
cd will(more likely) be smooth sounding in that regard. Then the only
limitation will be the da converter.
if we use dvda etc the filter can be a lot less steep, less expensive
and so hopfully more common. All the stuff people go on about upper
harmonics and all that, while being true, is far less important than
than the lack of harsh filters in my opinion.
I know true dither is not the same as tape hiss. I again was trying to
explain it in a way that I could understand when I was first learning.
I hope I don't get your heckles up any more. It seems I was
simplifying more than what would be to your liking. I agee with you
for the most part, Ithink cd's can sound excellent, but I can not say
that the format is "optimal" and I think mr Neve would agree with me.


  #4   Report Post  
Esp1
 
Posts: n/a
Default Dithering Digital Audio

"Ben Hoadley" skrev i melding
news:5HmFb.172358$_M.778279@attbi_s54...
"Karl Uppiano" wrote in message

news:on5Fb.6561$VB2.9687@attbi_s51...
I know true dither is not the same as tape hiss.


Think of dither as the digital brother of bias in analogue recorders. The
purpose is to linearize the transfer characteristics of the recording
process.

Espen B

  #5   Report Post  
Rajappa Iyer
 
Posts: n/a
Default Dithering Digital Audio

"Karl Uppiano" writes:

I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".


[ good explanation snipped ]

Incidentally, there's a nice explanation of dither with plots at

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

That should hopefully help in clearing up some misconceptions about
dither.

rsi
--
a.k.a. Rajappa Iyer.
Absinthe makes the tart grow fonder.



  #6   Report Post  
Bruno Putzeys
 
Posts: n/a
Default Dithering Digital Audio

I like to put it as "a correctly dithered converter has an infinite number
of bits in resolution"
If you take a perfectly linear 16-bit converter, you can feed it a 24 bit
signal and through dithering reproduce it faithfully.
If the 24 bit signal is correctly dithered, the system resolution is even
higher.
Noise is a different affair. If it's decorrelated it's noise. Any current
24bit converter has noise above 20 bits.

"Karl Uppiano" wrote in message
newsn5Fb.6561$VB2.9687@attbi_s51...
I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".

There seems to be commonly held misconception that dither is just the

noise
we add to digital audio to cover up the real digital noise floor. This is
not true. I obviously can't go into all of the mathematical proofs here,

and
that would be pointless anyway, since the information has been published

in
many forms in many places by people like VanDerKooy and Lip****z. You can
Google them for more information.

Digital audio has no natural noise floor in the traditional sense. If you
feed silence into an un-dithered, ideal analog to digital (A/D) converter,
you'll get a sequence of binary samples representing zero, forever. If you
apply a very small input signal, you'll get a varying sequence of samples

at
the output. The output sequence represents converter step values related

to
the converters resolution, correlated in some way (but not musically or
audibly) to the input signal. Not until the signal significantly exceeds

the
minimum converter resolution will the coded converter output samples begin
to represent the input signal as recognizable audio. When you run an A/D
converter at the lower limits of its resolution, the result is gross
intermodulation distortion, harmonic distortion and noise modulation.

From a perceptual standpoint, the previous paragraph can be put this way:
With zero input, the noise floor of an ideal A/D converter is infinite.

When
the input signal amplitude happens to exceed the converter's minimum
resolution, the noise level jumps to some value dictated by the

converter's
resolution (about -96dB in the case of a 16-bit converter). Furthermore,

the
noise will be quite different in amplitude and spectral makeup from the
input signal. In other words, highly distorted, and probably not
recognizable by humans as the original input signal.

Dither adds a noise floor to a system that has no natural noise floor. In

a
properly dithered system, a pseudo-random signal with a specific spectrum
and probability density (the likelihood of an occurrence a given

amplitude)
keeps the converter always switching between adjacent bits. Because the
dither is wide-band and random, it doesn't matter whether the converter
represents it accurately or not. The output is also wide-band and random.

It
isn't an accurate representation of the original dither, but two random
sequences are still just random sequences. The input sequence can be
numerically designed to produce the desired random output sequence.

The magic happens when you add the audio signal to this system. As we
already pointed out, A/D converters are highly non-linear when operated

near
their lower resolution limits. This non-linearity gives rise to gross
intermodulation distortion, harmonic distortion and noise described

earlier.
But what happens when you intermodulate (multiply) a signal with random
noise? You get the same signal, with noise added. It's not the same noise
you started with, but the noise is random, so it doesn't matter. The
important thing is, the signal is intact, except for the added noise. The
intermodulation products are distributed randomly, so they just add to the
noise slightly. The input signal would amplitude-modulate the dither

unless
the dither has triangular probability density. This ingenious trick forces
the dither to self-modulate in the opposite direction as it gets pushed
towards or away from an A/D bit transition. The result is a very smooth
noise floor with the ability to linearly resolve correlated signals

(tones,
i.e., musical notes) that are below the noise floor (and below the
resolution of the converter).

By the way, this discussion is all about A/D converters. That's where it
counts. The best D/A converter is only as good as the signal being sent to
it. Dither added after the fact cannot linearize or recover information

lost
in an
improperly designed A/D converter. Your only hope at that point is to add
enough noise to cover it up. Fortunately, that noise level is probably
equivalent to that an analog master tape, so I guess it's not so bad,
really.

Having a good understanding of dither helps explain why CD audio, which

has
been much maligned for being "so marginal" has been so successful. I tend
not to think of CD audio as marginal, I prefer to think of it as

"optimal".
It's very elegant in the sense that it delivers extremely high quality
audio, without spending a single bit more than is theoretically required

to
deliver it. We now have the storage densities and bandwidth to extend the
resolution and sampling rates. Aside from being great marketing tools,

they
do give the design engineers more tolerance, which means we don't have to
work as hard to "get it right". Although I think CD audio is a great
delivery mechanism, it's probably inadequate for professional studio work,
where uncontrolled audio peaks are common, and mixing puts extreme demands
on dynamic range.


  #7   Report Post  
Karl Uppiano
 
Posts: n/a
Default Dithering Digital Audio

"Bruno Putzeys" wrote in message
news:q%KFb.625555$Tr4.1618912@attbi_s03...
I like to put it as "a correctly dithered converter has an infinite number
of bits in resolution"
If you take a perfectly linear 16-bit converter, you can feed it a 24 bit
signal and through dithering reproduce it faithfully.
If the 24 bit signal is correctly dithered, the system resolution is even
higher.


I'm not sure if I completely agree. Or maybe I don't completely understand.
It's all a bit fuzzy (pun partially intended) when you start talking about
dither. The behavior is much more like analog in a lot of ways. Dither does
allow the reproduction (preservation might be a better word) of signals
below the implied resolution of an un-dithered converter. But there is a
danger: If you feed a 24-bit signal -- dithered for 24 bits -- into a 16-bit
D/A converter, you will end up with a raw, un-dithered signal. Any time you
re-quantize a digital signal it also needs to be re-dithered for the new
quantization format. If you go from 16 bits to 24 bits, it's OK, you'll have
the original 16-bit dithered signal. You won't get 24-bit performance, but
it won't be any worse than a properly dithered 16-bit recording.

Noise is a different affair. If it's decorrelated it's noise. Any current
24bit converter has noise above 20 bits.


"Marketing bits" have always been with us. For various reasons, most
converters don't deliver performance equal to the number of bits claimed. A
lot of the time, it's due to layout problems on the circuit board allowing
digital signals to be induced into critical analog circuitry. Mind you, the
noise is down more than 90dB or so, which is *excellent* by analog
standards. If it's correlated noise though, it's much more audible than
random noise, because the energy is concentrated at a single frequency or
group of frequencies, so the amplitude is higher. Noise is usually measured
as a weighted average, rendering overly optimistic numbers in cases like
this.

About ten years ago, I was at a design seminar put on by Crystal
Semiconductor, promoting one of their new 24-bit sigma-delta converters (for
laboratory data acquisition, not audio). In that application, they were
concerned about DC offsets, which, at 24-bit resolution, could be caused
simply by the thermocouple effects of a simple solder joint!

  #8   Report Post  
Stewart Pinkerton
 
Posts: n/a
Default Dithering Digital Audio

On Mon, 22 Dec 2003 23:20:54 GMT, "Bruno Putzeys"
wrote:

I like to put it as "a correctly dithered converter has an infinite number
of bits in resolution"


I shouldn't, if I were you! In a linear system, resolution and dynamic
range are inextricably linked.

If you take a perfectly linear 16-bit converter, you can feed it a 24 bit
signal and through dithering reproduce it faithfully.


No, you can *not* reproduce the dynamic range.

If the 24 bit signal is correctly dithered, the system resolution is even higher.


No, it isn't!

Noise is a different affair. If it's decorrelated it's noise. Any current
24bit converter has noise above 20 bits.


Very true, and this limits the resolution to 20 bits, regardless of
*narrow band* linearity below this level. Yes, you can recover tones
at anything up to 20dB below the noise floor, and they may be quite
undistorted, but this is not resolution in the universally accepted
sense, which is a function of full-bandwidth dynamic range.
--

Stewart Pinkerton | Music is Art - Audio is Engineering
  #9   Report Post  
Svante
 
Posts: n/a
Default Dithering Digital Audio

Rajappa Iyer wrote in message news:d9HFb.112679$8y1.349794@attbi_s52...
"Karl Uppiano" writes:

I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".


[ good explanation snipped ]

Incidentally, there's a nice explanation of dither with plots at

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

That should hopefully help in clearing up some misconceptions about
dither.

rsi


Hmmm... Figure 2 in that page has an error. The sine wave is not
quantised to 16 bits, it is quantised to 16 levels, or 4 bits. The
same error appears in the text at numerous places.
So I guess the page could add at least one misconception as well...
:-)

  #10   Report Post  
chung
 
Posts: n/a
Default Dithering Digital Audio

Svante wrote:
Rajappa Iyer wrote in message news:d9HFb.112679$8y1.349794@attbi_s52...
"Karl Uppiano" writes:

I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".


[ good explanation snipped ]

Incidentally, there's a nice explanation of dither with plots at

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

That should hopefully help in clearing up some misconceptions about
dither.

rsi


Hmmm... Figure 2 in that page has an error. The sine wave is not
quantised to 16 bits, it is quantised to 16 levels, or 4 bits. The
same error appears in the text at numerous places.
So I guess the page could add at least one misconception as well...
:-)


No, I don't think that was an error. The author was showing a low-level
sine wave. In other words, only the lowest 4 bits of the possible full
16 bits were used to represent the sine wave. You can think of the sine
wave as having a peak that is around -72dB relative to full scale.

What seems a little strange is that in fig. 8, there are now only 14
levels. But overall, the author did a good job of explaining dither.


  #11   Report Post  
Svante
 
Posts: n/a
Default Dithering Digital Audio

chung wrote in message ...
Svante wrote:
Rajappa Iyer wrote in message news:d9HFb.112679$8y1.349794@attbi_s52...
"Karl Uppiano" writes:

I decided to start a new thread about Digital Audio and Dithering from the
thread "Volume and Dynamic Range Question".

[ good explanation snipped ]

Incidentally, there's a nice explanation of dither with plots at

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

That should hopefully help in clearing up some misconceptions about
dither.

rsi


Hmmm... Figure 2 in that page has an error. The sine wave is not
quantised to 16 bits, it is quantised to 16 levels, or 4 bits. The
same error appears in the text at numerous places.
So I guess the page could add at least one misconception as well...
:-)


No, I don't think that was an error. The author was showing a low-level
sine wave. In other words, only the lowest 4 bits of the possible full
16 bits were used to represent the sine wave. You can think of the sine
wave as having a peak that is around -72dB relative to full scale.

What seems a little strange is that in fig. 8, there are now only 14
levels. But overall, the author did a good job of explaining dither.


Ahh, I should have read more carefully, I missed this sentence:
"In the picture below you'll see a 24 bit 100Hz sine wave recorded at
low levels for the ease of visual demonstration and explanation. "

...on the other hand, the spectral plots show that the sine wave has a
level of about -6 dB. Hmm... If the amplitude of the sine wave was -72
dB relative to full scale (which roughly would correspond to the
remaining 12 bits), this would mean that the author selected to use a
reference level somewhere in the neighborhood of -66 dB. Kind of
silly, IMO. The figures definitely lead me to beleive that we were
near full scale, but had poor resolution (4 bits).

  #12   Report Post  
Bruno Putzeys
 
Posts: n/a
Default Dithering Digital Audio

It's a matter of definition, as you probably realised after launching this
post. "Resolution" as audio folk use it these days no longer translates into
noise. It is used to denote the word length which the converter can accept
without becoming undithered. A 16bit converter fed 24 bit signals will
distort. When these are first dithered to 16 bits (and the converter is
linear) the distortion goes away. I've gotten used to that definition, hence
the statement. But in fact, you're right - this definition becomes
meaningless since the application of that definition gives "infinite
resolution" when dithering is correctly carried out.

Since resolution - for lack of proper standardisation has become such a
volatile item, one could propose that in addition to the "commercial
resolution", another, standardised spec be added as a fixture to data
sheets.
The most stringent definition would be ENOB - equivalent number of bits,
used to quantify noise, dnl and inl in one go. In audio this could be
derived from the worst-case THD+N.
A more common definition would be translating the unweighted DR into bits.

Any other suggestions? How to handle gain-ranging converters? Etc.
Constructive comments welcome. Others discouraged.

"Stewart Pinkerton" wrote in message
...
On Mon, 22 Dec 2003 23:20:54 GMT, "Bruno Putzeys"
wrote:

I like to put it as "a correctly dithered converter has an infinite

number
of bits in resolution"


I shouldn't, if I were you! In a linear system, resolution and dynamic
range are inextricably linked.

If you take a perfectly linear 16-bit converter, you can feed it a 24 bit
signal and through dithering reproduce it faithfully.


No, you can *not* reproduce the dynamic range.

If the 24 bit signal is correctly dithered, the system resolution is even

higher.

No, it isn't!

Noise is a different affair. If it's decorrelated it's noise. Any current
24bit converter has noise above 20 bits.


Very true, and this limits the resolution to 20 bits, regardless of
*narrow band* linearity below this level. Yes, you can recover tones
at anything up to 20dB below the noise floor, and they may be quite
undistorted, but this is not resolution in the universally accepted
sense, which is a function of full-bandwidth dynamic range.
--

Stewart Pinkerton | Music is Art - Audio is Engineering


  #13   Report Post  
Bruno Putzeys
 
Posts: n/a
Default Dithering Digital Audio

Dithering the 24 bit data to 16 bits of course... That a signal which is
correctly dithered to 24 bit is undithered with respect to 16 bits be
obvious.

"Karl Uppiano" wrote in message
news:5ELFb.456764$275.1339926@attbi_s53...
"Bruno Putzeys" wrote in message
news:q%KFb.625555$Tr4.1618912@attbi_s03...
I like to put it as "a correctly dithered converter has an infinite

number
of bits in resolution"
If you take a perfectly linear 16-bit converter, you can feed it a 24

bit
signal and through dithering reproduce it faithfully.
If the 24 bit signal is correctly dithered, the system resolution is

even
higher.


I'm not sure if I completely agree. Or maybe I don't completely

understand.
It's all a bit fuzzy (pun partially intended) when you start talking about
dither. The behavior is much more like analog in a lot of ways. Dither

does
allow the reproduction (preservation might be a better word) of signals
below the implied resolution of an un-dithered converter. But there is a
danger: If you feed a 24-bit signal -- dithered for 24 bits -- into a

16-bit
D/A converter, you will end up with a raw, un-dithered signal. Any time

you
re-quantize a digital signal it also needs to be re-dithered for the new
quantization format. If you go from 16 bits to 24 bits, it's OK, you'll

have
the original 16-bit dithered signal. You won't get 24-bit performance, but
it won't be any worse than a properly dithered 16-bit recording.

Noise is a different affair. If it's decorrelated it's noise. Any

current
24bit converter has noise above 20 bits.


"Marketing bits" have always been with us. For various reasons, most
converters don't deliver performance equal to the number of bits claimed.

A
lot of the time, it's due to layout problems on the circuit board allowing
digital signals to be induced into critical analog circuitry. Mind you,

the
noise is down more than 90dB or so, which is *excellent* by analog
standards. If it's correlated noise though, it's much more audible than
random noise, because the energy is concentrated at a single frequency or
group of frequencies, so the amplitude is higher. Noise is usually

measured
as a weighted average, rendering overly optimistic numbers in cases like
this.

About ten years ago, I was at a design seminar put on by Crystal
Semiconductor, promoting one of their new 24-bit sigma-delta converters

(for
laboratory data acquisition, not audio). In that application, they were
concerned about DC offsets, which, at 24-bit resolution, could be caused
simply by the thermocouple effects of a simple solder joint!


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