| Author |
Message |
Guest
|
 Posted:
Sat Jan 01, 2005 1:50 am Post subject:
Noise floor / FFT relationship |
|
|
Newsgroups: comp.dsp, ...
This started out as a short question and now is 3 long ones...
1. I am playing with cool edit and this program
(http://digilander.libero.it/hsoft/ any better alternatives?) and some
USB audio devices and trying to figure out how to get a "real,
official" number for the noise floor and hence dynamic range (right?).
If I generate a wave at -10 dBFS on the level meters and wave display,
it also peaks at -10 dBFS on an FFT spectrum of that recording. This
makes sense to me. Is this true of the actual FFT, or was some math
done in between? (In other words, if the peak sample values of the
original waveform are 10000, say, would the peak samples of the FFT
with no weighting or other processing also be at 10000? I can test this
myself in matlab later.)
If I generate two added waves of different frequencies at -10 dBFS
each, the peaks on the spectrum are each at -10 dBFS, but the total
wave peaks the level meters at -4 dBFS, which makes sense to me, since
they are added and the level will rise by x2 = ~6 dB.
If I record a sample of quiet audio from my interface, I will get a
measurement that peaks at about -65, valleys at about -71, and visually
averages about -67. If I then do an FFT of that recording, I get a
mostly flat line at around -106 dBFS. I am trying to figure out what
the actual noise floor of this recording is, and its relationship to
the theoretical 96 dB dynamic range of 16-bit audio.
If I reduce a white noise signal to the point where it is only moving
up or down by one quantization level, that first quantization level
shows up on the scale as -90.5 dB or so, the level meter shows at -90.5
or so, and the spectrum shows up at -103.5. I know I'm
misunderstanding the 96 dB dynamic range, and I learned the
calculations in DSP classes in school, but I can't remember the theory
anymore. Can someone explain the relationship between these numbers?
2. If I try to measure the dynamic range of a system by measuring the
ratio between maximum sine wave and noise floor with a peak measuring
instrument, and do the same with an RMS measuring instrument, I will
get different results, right? Because the RMS and peak values of noise
are not the sqrt(2) ratio as the RMS and peak values of sine wave. The
RMS dynamic range measurement would generally be considered correct,
right? Do I need to worry about this with my digital measurements as
well, since all of them seem to be peak-mode measurements?
3. If you do a calculation (I forget what. square, absolute value,
then sqrt i think), you get the "power spectrum" of the FFT. This has
no relationship to electrical power, like in an amplifer, does it?
4. What effect does averaging the spectrum have on measurement
accuracy? Is averaging a realtime windowed FFT over many windows
mathematically the same as taking an FFT of the entire prerecorded
signal at once?
Anyone know a good reference for all of this kind of information? I
found only this so far: http://www.daqarta.com/aa0fspav.htm I would
get a good (used) book, too, if it were not that much. |
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Tim Wescott
Guest
|
| Posted:
Sat Jan 01, 2005 3:02 am Post subject:
Re: Noise floor / FFT relationship |
|
|
u035m4i02@sneakemail.com wrote:
| Quote: | Newsgroups: comp.dsp, ...
This started out as a short question and now is 3 long ones...
1. I am playing with cool edit and this program
(http://digilander.libero.it/hsoft/ any better alternatives?) and some
USB audio devices and trying to figure out how to get a "real,
official" number for the noise floor and hence dynamic range (right?).
|
Tee hee.
| Quote: |
If I generate a wave at -10 dBFS on the level meters and wave display,
it also peaks at -10 dBFS on an FFT spectrum of that recording. This
makes sense to me. Is this true of the actual FFT, or was some math
done in between? (In other words, if the peak sample values of the
original waveform are 10000, say, would the peak samples of the FFT
with no weighting or other processing also be at 10000? I can test this
myself in matlab later.)
|
There are a number of different ways to scale FFT's. With no
"officially accepted" way of scaling, it's the job of the designer to
pick a good one. Choosing one so that A sin(wt) works out to a line
that's A high at w is a good way to go.
| Quote: |
If I generate two added waves of different frequencies at -10 dBFS
each, the peaks on the spectrum are each at -10 dBFS, but the total
wave peaks the level meters at -4 dBFS, which makes sense to me, since
they are added and the level will rise by x2 = ~6 dB.
|
Yes, that's correct.
| Quote: |
If I record a sample of quiet audio from my interface, I will get a
measurement that peaks at about -65, valleys at about -71, and visually
averages about -67. If I then do an FFT of that recording, I get a
mostly flat line at around -106 dBFS. I am trying to figure out what
the actual noise floor of this recording is, and its relationship to
the theoretical 96 dB dynamic range of 16-bit audio.
|
It appears that your noise is white and bandlimited. This means that it
has finite energy that's evenly spread out in the FFT. In the time
domain you get a signal that crawls around all over the place -- this is
what you're seeing on your peak meter.
| Quote: |
If I reduce a white noise signal to the point where it is only moving
up or down by one quantization level, that first quantization level
shows up on the scale as -90.5 dB or so, the level meter shows at -90.5
or so, and the spectrum shows up at -103.5. I know I'm
misunderstanding the 96 dB dynamic range, and I learned the
calculations in DSP classes in school, but I can't remember the theory
anymore. Can someone explain the relationship between these numbers?
|
First misunderstanding: The 96dB is the difference between one LSB and
the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth -- or
about 90dB. The 0.5dB is just there to make you think (unrelated note:
A previous manager of mine maintained that "you should always
tolerance your wild-ass guesses" -- that way folks looking at your
preliminary drawings would think they're real).
| Quote: |
2. If I try to measure the dynamic range of a system by measuring the
ratio between maximum sine wave and noise floor with a peak measuring
instrument, and do the same with an RMS measuring instrument, I will
get different results, right?
|
That depends on how you choose to define things, so definitely "maybe"
-- keep in mind that you'll be RMSing the noise floor, too.
| Quote: | Because the RMS and peak values of noise
are not the sqrt(2) ratio as the RMS and peak values of sine wave. The
RMS dynamic range measurement would generally be considered correct,
right? Do I need to worry about this with my digital measurements as
well, since all of them seem to be peak-mode measurements?
|
Dunno -- the RMS measurement may be more "correct" but it's an
impossible spec -- your results will vary depending on whether your
audio contains square waves or Dirac delta distributions.
| Quote: |
3. If you do a calculation (I forget what. square, absolute value,
then sqrt i think), you get the "power spectrum" of the FFT. This has
no relationship to electrical power, like in an amplifer, does it?
|
Square, yes, and it has every relationship to electrical power.
Assuming that you've gotten your scaling right the sum of the squares of
the samples in the time domain should equal the sum of the squares of
the absolute values of the frequency bins in the FFT.
| Quote: |
4. What effect does averaging the spectrum have on measurement
accuracy?
|
Define "accuracy". For all practical purposes it probably enhances it.
| Quote: | Is averaging a realtime windowed FFT over many windows
mathematically the same as taking an FFT of the entire prerecorded
signal at once?
|
No. I haven't worked out the math for that one, but taking the FFT of
the entire signal then adding up groups of bins, or doing a
frequency-domain convolution of the result and subsampling it is more
closely equivalent -- but beyond assuring you that it ain't the same I
can't say.
| Quote: |
Anyone know a good reference for all of this kind of information? I
found only this so far: http://www.daqarta.com/aa0fspav.htm I would
get a good (used) book, too, if it were not that much.
|
For the academically inclined, "Signals and Systems" by Oppenheim,
Willsky and Young is a classic -- but I don't know how good it is for
self-study. Robert Lyons's "Understanding Digital Signal Processing" is
highly recommended on this group. I have a copy -- it's a solid book
and aimed more toward the practicing engineer who needs to pick the
stuff up.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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robert bristow-johnson
Guest
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Tim Wescott
Guest
|
| Posted:
Sat Jan 01, 2005 4:12 am Post subject:
Re: Noise floor / FFT relationship |
|
|
robert bristow-johnson wrote:
Sorry Rick.
And yes, it's a good book.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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Att
Guest
|
| Posted:
Sat Jan 01, 2005 5:36 am Post subject:
Re: Noise floor / FFT relationship |
|
|
<u035m4i02@sneakemail.com> wrote in message
news:1104526253.000219.67160@c13g2000cwb.googlegroups.com...
| Quote: | Newsgroups: comp.dsp, ...
If I record a sample of quiet audio from my interface, I will get a
measurement that peaks at about -65, valleys at about -71, and visually
averages about -67. If I then do an FFT of that recording, I get a
mostly flat line at around -106 dBFS. I am trying to figure out what
the actual noise floor of this recording is, and its relationship to
the theoretical 96 dB dynamic range of 16-bit audio.
|
Remember that the total noise is the sum (integral) of all the frequency
bins (delta frequency)
There is a classic paper by Fred Harris on the scaling required to find SNR
using various different windows. The scaling for hanning is 1.5 if I recall
correctly.
Also hanning will span the center bin over the tone and the bin on each
side.
You must use a tone that has an integer number of cycles in the FFT length
you chose.
You add up the power in all the bins that would not include the tone you are
looking at and remember to be wary of the DC component and his nearest
neighbor.
| Quote: | If I reduce a white noise signal to the point where it is only moving
up or down by one quantization level, that first quantization level
shows up on the scale as -90.5 dB or so, the level meter shows at -90.5
or so, and the spectrum shows up at -103.5. I know I'm
misunderstanding the 96 dB dynamic range, and I learned the
calculations in DSP classes in school, but I can't remember the theory
anymore. Can someone explain the relationship between these numbers?
|
Looks about right since you said -106 above and the quantization noise floor
would be for
errors of about 1/2 LSB or about 3 dB lower, unless I am off by a factor of
2 and
it should be -109 dB. |
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Att
Guest
|
| Posted:
Sat Jan 01, 2005 5:45 am Post subject:
Re: Noise floor / FFT relationship |
|
|
"Att" <david.g.shaw@att.net> wrote in message
news:9gmBd.1199963$Gx4.10930@bgtnsc04-news.ops.worldnet.att.net...
| Quote: |
u035m4i02@sneakemail.com> wrote in message
news:1104526253.000219.67160@c13g2000cwb.googlegroups.com...
Newsgroups: comp.dsp, ...
There is a classic paper by Fred Harris on the scaling required to find
SNR
using various different windows. The scaling for hanning is 1.5 if I
recall
correctly.
|
I found the reference.
Unfortunately it looks like a chapter from a book and I only have the
chapter.
"DATA WINDOWS: Finite Aperture Effects and Applications in Signal
Processing"
Fred Harris Sandiego State University. |
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Jon
Guest
|
| Posted:
Sat Jan 01, 2005 7:57 am Post subject:
Re: Noise floor / FFT relationship |
|
|
:-( Dost thou mock me? Or the idea of an "official" measurement?
| Quote: | There are a number of different ways to scale FFT's. With no
"officially accepted" way of scaling, it's the job of the designer to
pick a good one. Choosing one so that A sin(wt) works out to a line
that's A high at w is a good way to go.
|
Oh, right.
| Quote: | It appears that your noise is white and bandlimited. This means that it
has finite energy that's evenly spread out in the FFT. In the time
domain you get a signal that crawls around all over the place -- this is
what you're seeing on your peak meter.
|
Yes, I know.
So what is the noise floor measurement? :-)
What I'm looking for is a single number for the level of background
noise so I can have a definite SNR or dynamic range or noise floor.
(Which are all the same for digital, right? Maybe that idea is what you
are teeheeing about?) I guess an RMS measurement is typical. So I
can't get that value from either the peak measurement or the FFT
spectrum, can I?
| Quote: | First misunderstanding: The 96dB is the difference between one LSB and
the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth -- or
about 90dB. The 0.5dB is just there to make you think (unrelated note:
A previous manager of mine maintained that "you should always tolerance
your wild-ass guesses" -- that way folks looking at your preliminary
drawings would think they're real).
|
Oh I get it! I was thinking you start at zero and migrate up *or* down
one quantization level, but the 96 dB is moving between two adjacent
levels only, hence the +6 dB.
*Tries it* Eh. I think Cool Edit just absolute values it and measures
the peak value, whether both sides are moving or not. It still says
-90ish. Oh. Here in the "statistics" window it says "Average RMS Power
-96.34 dB". (Why is it "power"?)
But 96 is actually just the "6 dB per bit" approximation; the actual
dynamic range of 16-bit audio is apparently around 98 according to SNR =
(6.02M + 1.76) dB. But whatever. That's just being picky.
I still don't understand the relationship to the spectrum though. If I
make a variety of signals confined to two quantization levels, I get
pretty different spectrums, and pretty different values from the
statistics window. White noise makes a flat line at -123ish dB.
Repeating waves make spikeys that end near -95, so maybe that's what I'm
looking for, for a generalization of level vs spectrum. The level
varies between those two numbers? I'm not sure... (Remember I'm asking
4 things at once, so I am "looking for" several different things.)
| Quote: | That depends on how you choose to define things, so definitely "maybe"
-- keep in mind that you'll be RMSing the noise floor, too.
|
Yes. That's what I meant. I meant these two will give different values:
1. Maximum sine wave measures 0 dBFS peak, so dynamic range is whatever
the peak value of the noise floor is.
2. Maximum sine wave measures -3.01 dBFS RMS, so dynamic range is
whatever the RMS value of the noise floor is - 3 dB.
Right? Since the noise floor could be anything, so the RMS noise floor
will probably not be -3 dB from the peak noise floor. I believe 2 would
be the generally agreed upon definition of dynamic range. But not sure.
| Quote: | Dunno -- the RMS measurement may be more "correct" but it's an
impossible spec -- your results will vary depending on whether your
audio contains square waves or Dirac delta distributions.
|
What do you mean? I am talking about real life digital quantized
sampled audio, so there are no Diracs.
| Quote: | Define "accuracy". For all practical purposes it probably enhances it.
|
Ok. That's what I thought. It certainly makes it easier to spot
constant frequencies buried under the wildness of the noise floor. I
just meant accuracy to the average value of the noise floor... which...
I guess... by definition... never mind. :-)
| Quote: | No. I haven't worked out the math for that one, but taking the FFT of
the entire signal then adding up groups of bins, or doing a
frequency-domain convolution of the result and subsampling it is more
closely equivalent -- but beyond assuring you that it ain't the same I
can't say.
|
I mean using a realtime spectrum analyzer that windows and FFTs, then
displays the average of that and the last 100 similar results, or just
recording the entire length covered by those 100 windows and FFTing
that. I imagine they are different, but by how much?
| Quote: | For the academically inclined, "Signals and Systems" by Oppenheim,
Willsky and Young is a classic
|
Yes. Already have it.
| Quote: | -- but I don't know how good it is for
self-study. Robert Lyons's "Understanding Digital Signal Processing" is
highly recommended on this group. I have a copy -- it's a solid book
and aimed more toward the practicing engineer who needs to pick the
stuff up.
|
Alright. I'll look into it.
Jon
--
Include "newsgroup" in the subject line to reply by email (or get dumped
with the spam). |
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| Back to top |
|
|
Jon
Guest
|
| Posted:
Sat Jan 01, 2005 7:57 am Post subject:
Re: Noise floor / FFT relationship |
|
|
:-( Dost thou mock me? Or the idea of an "official" measurement?
| Quote: | There are a number of different ways to scale FFT's. With no
"officially accepted" way of scaling, it's the job of the designer to
pick a good one. Choosing one so that A sin(wt) works out to a line
that's A high at w is a good way to go.
|
Oh, right.
| Quote: | It appears that your noise is white and bandlimited. This means that it
has finite energy that's evenly spread out in the FFT. In the time
domain you get a signal that crawls around all over the place -- this is
what you're seeing on your peak meter.
|
Yes, I know.
So what is the noise floor measurement? :-)
What I'm looking for is a single number for the level of background
noise so I can have a definite SNR or dynamic range or noise floor.
(Which are all the same for digital, right? Maybe that idea is what you
are teeheeing about?) I guess an RMS measurement is typical. So I
can't get that value from either the peak measurement or the FFT
spectrum, can I?
| Quote: | First misunderstanding: The 96dB is the difference between one LSB and
the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth -- or
about 90dB. The 0.5dB is just there to make you think (unrelated note:
A previous manager of mine maintained that "you should always tolerance
your wild-ass guesses" -- that way folks looking at your preliminary
drawings would think they're real).
|
Oh I get it! I was thinking you start at zero and migrate up *or* down
one quantization level, but the 96 dB is moving between two adjacent
levels only, hence the +6 dB.
*Tries it* Eh. I think Cool Edit just absolute values it and measures
the peak value, whether both sides are moving or not. It still says
-90ish. Oh. Here in the "statistics" window it says "Average RMS Power
-96.34 dB". (Why is it "power"?)
But 96 is actually just the "6 dB per bit" approximation; the actual
dynamic range of 16-bit audio is apparently around 98 according to SNR =
(6.02M + 1.76) dB. But whatever. That's just being picky.
I still don't understand the relationship to the spectrum though. If I
make a variety of signals confined to two quantization levels, I get
pretty different spectrums, and pretty different values from the
statistics window. White noise makes a flat line at -123ish dB.
Repeating waves make spikeys that end near -95, so maybe that's what I'm
looking for, for a generalization of level vs spectrum. The level
varies between those two numbers? I'm not sure... (Remember I'm asking
4 things at once, so I am "looking for" several different things.)
| Quote: | That depends on how you choose to define things, so definitely "maybe"
-- keep in mind that you'll be RMSing the noise floor, too.
|
Yes. That's what I meant. I meant these two will give different values:
1. Maximum sine wave measures 0 dBFS peak, so dynamic range is whatever
the peak value of the noise floor is.
2. Maximum sine wave measures -3.01 dBFS RMS, so dynamic range is
whatever the RMS value of the noise floor is - 3 dB.
Right? Since the noise floor could be anything, so the RMS noise floor
will probably not be -3 dB from the peak noise floor. I believe 2 would
be the generally agreed upon definition of dynamic range. But not sure.
| Quote: | Dunno -- the RMS measurement may be more "correct" but it's an
impossible spec -- your results will vary depending on whether your
audio contains square waves or Dirac delta distributions.
|
What do you mean? I am talking about real life digital quantized
sampled audio, so there are no Diracs.
| Quote: | Define "accuracy". For all practical purposes it probably enhances it.
|
Ok. That's what I thought. It certainly makes it easier to spot
constant frequencies buried under the wildness of the noise floor. I
just meant accuracy to the average value of the noise floor... which...
I guess... by definition... never mind. :-)
| Quote: | No. I haven't worked out the math for that one, but taking the FFT of
the entire signal then adding up groups of bins, or doing a
frequency-domain convolution of the result and subsampling it is more
closely equivalent -- but beyond assuring you that it ain't the same I
can't say.
|
I mean using a realtime spectrum analyzer that windows and FFTs, then
displays the average of that and the last 100 similar results, or just
recording the entire length covered by those 100 windows and FFTing
that. I imagine they are different, but by how much?
| Quote: | For the academically inclined, "Signals and Systems" by Oppenheim,
Willsky and Young is a classic
|
Yes. Already have it.
| Quote: | -- but I don't know how good it is for
self-study. Robert Lyons's "Understanding Digital Signal Processing" is
highly recommended on this group. I have a copy -- it's a solid book
and aimed more toward the practicing engineer who needs to pick the
stuff up.
|
Alright. I'll look into it.
Jon
--
Include "newsgroup" in the subject line to reply by email (or get dumped
with the spam). |
|
| Back to top |
|
|
Jon
Guest
|
| Posted:
Sat Jan 01, 2005 7:57 am Post subject:
Re: Noise floor / FFT relationship |
|
|
:-( Dost thou mock me? Or the idea of an "official" measurement?
| Quote: | There are a number of different ways to scale FFT's. With no
"officially accepted" way of scaling, it's the job of the designer to
pick a good one. Choosing one so that A sin(wt) works out to a line
that's A high at w is a good way to go.
|
Oh, right.
| Quote: | It appears that your noise is white and bandlimited. This means that it
has finite energy that's evenly spread out in the FFT. In the time
domain you get a signal that crawls around all over the place -- this is
what you're seeing on your peak meter.
|
Yes, I know.
So what is the noise floor measurement? :-)
What I'm looking for is a single number for the level of background
noise so I can have a definite SNR or dynamic range or noise floor.
(Which are all the same for digital, right? Maybe that idea is what you
are teeheeing about?) I guess an RMS measurement is typical. So I
can't get that value from either the peak measurement or the FFT
spectrum, can I?
| Quote: | First misunderstanding: The 96dB is the difference between one LSB and
the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth -- or
about 90dB. The 0.5dB is just there to make you think (unrelated note:
A previous manager of mine maintained that "you should always tolerance
your wild-ass guesses" -- that way folks looking at your preliminary
drawings would think they're real).
|
Oh I get it! I was thinking you start at zero and migrate up *or* down
one quantization level, but the 96 dB is moving between two adjacent
levels only, hence the +6 dB.
*Tries it* Eh. I think Cool Edit just absolute values it and measures
the peak value, whether both sides are moving or not. It still says
-90ish. Oh. Here in the "statistics" window it says "Average RMS Power
-96.34 dB". (Why is it "power"?)
But 96 is actually just the "6 dB per bit" approximation; the actual
dynamic range of 16-bit audio is apparently around 98 according to SNR =
(6.02M + 1.76) dB. But whatever. That's just being picky.
I still don't understand the relationship to the spectrum though. If I
make a variety of signals confined to two quantization levels, I get
pretty different spectrums, and pretty different values from the
statistics window. White noise makes a flat line at -123ish dB.
Repeating waves make spikeys that end near -95, so maybe that's what I'm
looking for, for a generalization of level vs spectrum. The level
varies between those two numbers? I'm not sure... (Remember I'm asking
4 things at once, so I am "looking for" several different things.)
| Quote: | That depends on how you choose to define things, so definitely "maybe"
-- keep in mind that you'll be RMSing the noise floor, too.
|
Yes. That's what I meant. I meant these two will give different values:
1. Maximum sine wave measures 0 dBFS peak, so dynamic range is whatever
the peak value of the noise floor is.
2. Maximum sine wave measures -3.01 dBFS RMS, so dynamic range is
whatever the RMS value of the noise floor is - 3 dB.
Right? Since the noise floor could be anything, so the RMS noise floor
will probably not be -3 dB from the peak noise floor. I believe 2 would
be the generally agreed upon definition of dynamic range. But not sure.
| Quote: | Dunno -- the RMS measurement may be more "correct" but it's an
impossible spec -- your results will vary depending on whether your
audio contains square waves or Dirac delta distributions.
|
What do you mean? I am talking about real life digital quantized
sampled audio, so there are no Diracs.
| Quote: | Define "accuracy". For all practical purposes it probably enhances it.
|
Ok. That's what I thought. It certainly makes it easier to spot
constant frequencies buried under the wildness of the noise floor. I
just meant accuracy to the average value of the noise floor... which...
I guess... by definition... never mind. :-)
| Quote: | No. I haven't worked out the math for that one, but taking the FFT of
the entire signal then adding up groups of bins, or doing a
frequency-domain convolution of the result and subsampling it is more
closely equivalent -- but beyond assuring you that it ain't the same I
can't say.
|
I mean using a realtime spectrum analyzer that windows and FFTs, then
displays the average of that and the last 100 similar results, or just
recording the entire length covered by those 100 windows and FFTing
that. I imagine they are different, but by how much?
| Quote: | For the academically inclined, "Signals and Systems" by Oppenheim,
Willsky and Young is a classic
|
Yes. Already have it.
| Quote: | -- but I don't know how good it is for
self-study. Robert Lyons's "Understanding Digital Signal Processing" is
highly recommended on this group. I have a copy -- it's a solid book
and aimed more toward the practicing engineer who needs to pick the
stuff up.
|
Alright. I'll look into it.
Jon
--
Include "newsgroup" in the subject line to reply by email (or get dumped
with the spam). |
|
| Back to top |
|
|
Jon
Guest
|
| Posted:
Sat Jan 01, 2005 7:57 am Post subject:
Re: Noise floor / FFT relationship |
|
|
Re: My triple posting.
(Argh. Just installed Thunderbird.) |
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|
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Eric Jacobsen
Guest
|
| Posted:
Sat Jan 01, 2005 7:57 am Post subject:
Re: Noise floor / FFT relationship |
|
|
On Sat, 01 Jan 2005 03:11:09 GMT, Jon <u035m4i02@sneakemail.com>
wrote:
| Quote: | So what is the noise floor measurement? :-)
What I'm looking for is a single number for the level of background
noise so I can have a definite SNR or dynamic range or noise floor.
(Which are all the same for digital, right? Maybe that idea is what you
are teeheeing about?) I guess an RMS measurement is typical. So I
can't get that value from either the peak measurement or the FFT
spectrum, can I?
|
| Quote: | First misunderstanding: The 96dB is the difference between one LSB and
the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth -- or
about 90dB. The 0.5dB is just there to make you think (unrelated note:
A previous manager of mine maintained that "you should always tolerance
your wild-ass guesses" -- that way folks looking at your preliminary
drawings would think they're real).
Oh I get it! I was thinking you start at zero and migrate up *or* down
one quantization level, but the 96 dB is moving between two adjacent
levels only, hence the +6 dB.
*Tries it* Eh. I think Cool Edit just absolute values it and measures
the peak value, whether both sides are moving or not. It still says
-90ish. Oh. Here in the "statistics" window it says "Average RMS Power
-96.34 dB". (Why is it "power"?)
But 96 is actually just the "6 dB per bit" approximation; the actual
dynamic range of 16-bit audio is apparently around 98 according to SNR =
(6.02M + 1.76) dB. But whatever. That's just being picky.
I still don't understand the relationship to the spectrum though. If I
make a variety of signals confined to two quantization levels, I get
pretty different spectrums, and pretty different values from the
statistics window. White noise makes a flat line at -123ish dB.
Repeating waves make spikeys that end near -95, so maybe that's what I'm
looking for, for a generalization of level vs spectrum. The level
varies between those two numbers? I'm not sure... (Remember I'm asking
4 things at once, so I am "looking for" several different things.)
|
FFTs have processing gain proportional to the relationship between the
input bandwidth and the bandwidth of a single FFT bin. This was
mentioned in another reply to the effect that the total noise power is
the sum of the noise in each bin. So the longer the FFT the lower
the noise floor will be for the same input statistics. People
exploit this all the time to reveal low-level signals or spurious
responses that are otherwise difficult to see.
So a strict answer to your question depends on the length of the FFT
as well as the nature of any windowing used, additional averaging,
etc.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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Rune Allnor
Guest
|
| Posted:
Sat Jan 01, 2005 5:57 pm Post subject:
Re: Noise floor / FFT relationship |
|
|
Tim Wescott wrote:
| Quote: | u035m4i02@sneakemail.com wrote:
Newsgroups: comp.dsp, ...
4. What effect does averaging the spectrum have on measurement
accuracy?
Define "accuracy". For all practical purposes it probably enhances
it. |
For estimating the frequency of a narrow spectrum line, the accuracy
gets worse since the measurment sequences get shorter. This is
outperformed by the accuracy of the coefficients of the power
spectrum becoming way better for the averaged spectra.
| Quote: | Is averaging a realtime windowed FFT over many windows
mathematically the same as taking an FFT of the entire prerecorded
signal at once?
No. I haven't worked out the math for that one, but taking the FFT
of
the entire signal then adding up groups of bins, or doing a
frequency-domain convolution of the result and subsampling it is more
closely equivalent -- but beyond assuring you that it ain't the same
I
can't say.
|
The squared magitudes of the DFT of a sequence, call them P(f), have
a variance of on the order of
Var [P(f)] ~ P(f)^2.
Not that the DFT length does not appear in the variance, so there is
no improvement to be made by increasing the DFT length. A crude
argument is that when supplying N samples to the DFT, you compute N
coefficients in the spectrum, so the added number of coefficients
just balances the effects of the added data samples.
The simplest and most robust way of improving the spectrum estimate
is to average several independent power spectra.
| Quote: | Anyone know a good reference for all of this kind of information?
I
found only this so far: http://www.daqarta.com/aa0fspav.htm I
would
get a good (used) book, too, if it were not that much.
For the academically inclined, "Signals and Systems" by Oppenheim,
Willsky and Young is a classic -- but I don't know how good it is for
self-study. Robert Lyons's "Understanding Digital Signal Processing"
is
highly recommended on this group. I have a copy -- it's a solid book
and aimed more toward the practicing engineer who needs to pick the
stuff up.
|
These are good general-purpose DSP books. For estimating power spectra
I will recommend the book
Kay: Modern Spectral Estimation - Theory and Application
Prentice-Hall, 1988.
You would need a fair amount of general DSP as basis before trying
to tackle this book.
Rune |
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Tim Wescott
Guest
|
| Posted:
Sat Jan 01, 2005 11:34 pm Post subject:
Re: Noise floor / FFT relationship |
|
|
Jon wrote:
| Quote: | Tee hee.
:-( Dost thou mock me? Or the idea of an "official" measurement?
|
Neither. I'm a sadist, and I have a good imagination, and I know that
you're going to be pulling hair out before you get this all figured out.
I also have _some_ compassion, so I could have said "you poor bastard"
but I thought "tee hee" would indicate more holiday cheer.
| Quote: |
There are a number of different ways to scale FFT's. With no
"officially accepted" way of scaling, it's the job of the designer to
pick a good one. Choosing one so that A sin(wt) works out to a line
that's A high at w is a good way to go.
Oh, right.
It appears that your noise is white and bandlimited. This means that
it has finite energy that's evenly spread out in the FFT. In the time
domain you get a signal that crawls around all over the place -- this
is what you're seeing on your peak meter.
Yes, I know.
So what is the noise floor measurement? :-)
What I'm looking for is a single number for the level of background
noise so I can have a definite SNR or dynamic range or noise floor.
(Which are all the same for digital, right? Maybe that idea is what you
are teeheeing about?) I guess an RMS measurement is typical. So I
can't get that value from either the peak measurement or the FFT
spectrum, can I?
First misunderstanding: The 96dB is the difference between one LSB
and the full range, +max to -max. Your peak meter is just reading the
distance from 0 to one maximum or the other, that's 15 bits worth --
or about 90dB. The 0.5dB is just there to make you think (unrelated
note: A previous manager of mine maintained that "you should always
tolerance your wild-ass guesses" -- that way folks looking at your
preliminary drawings would think they're real).
Oh I get it! I was thinking you start at zero and migrate up *or* down
one quantization level, but the 96 dB is moving between two adjacent
levels only, hence the +6 dB.
*Tries it* Eh. I think Cool Edit just absolute values it and measures
the peak value, whether both sides are moving or not. It still says
-90ish. Oh. Here in the "statistics" window it says "Average RMS Power
-96.34 dB". (Why is it "power"?)
|
Because somebody's confused. If you RMS a voltage, or a current, or a
string of numbers, then you're finding the DC value that would burn up
the same amount of power when applied to a given resistor -- so 10VDC
applied to a 10 ohm resistor delivers 10W, and so does 10Vrms.
| Quote: |
But 96 is actually just the "6 dB per bit" approximation; the actual
dynamic range of 16-bit audio is apparently around 98 according to SNR =
(6.02M + 1.76) dB. But whatever. That's just being picky.
I still don't understand the relationship to the spectrum though. If I
make a variety of signals confined to two quantization levels, I get
pretty different spectrums, and pretty different values from the
statistics window. White noise makes a flat line at -123ish dB.
Repeating waves make spikeys that end near -95, so maybe that's what I'm
looking for, for a generalization of level vs spectrum. The level
varies between those two numbers? I'm not sure... (Remember I'm asking
4 things at once, so I am "looking for" several different things.)
That depends on how you choose to define things, so definitely "maybe"
-- keep in mind that you'll be RMSing the noise floor, too.
Yes. That's what I meant. I meant these two will give different values:
1. Maximum sine wave measures 0 dBFS peak, so dynamic range is whatever
the peak value of the noise floor is.
2. Maximum sine wave measures -3.01 dBFS RMS, so dynamic range is
whatever the RMS value of the noise floor is - 3 dB.
Right? Since the noise floor could be anything, so the RMS noise floor
will probably not be -3 dB from the peak noise floor. I believe 2 would
be the generally agreed upon definition of dynamic range. But not sure.
Dunno -- the RMS measurement may be more "correct" but it's an
impossible spec -- your results will vary depending on whether your
audio contains square waves or Dirac delta distributions.
What do you mean? I am talking about real life digital quantized
sampled audio, so there are no Diracs.
|
But there are drumbeats, which have a very high peak/RMS ratio. This is
your problem. A 1V RMS signal could be anything from 1.414*sin(wt) to a
train of pulses that are 100us wide and 32V high. There -- no Diracs,
but things that could be recorded if you had enough dynamic range, and
which have _identical_ RMS voltages.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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Jon Harris
Guest
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Jon Harris
Guest
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