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Forums - Theory / composition / technique
Subject: RMS dB?
Viewing all 7 messages - View by pages of 10: 1
Original Message 1/7 20-Aug-04 @ 03:22 PM - RMS dB?
Can anyone give a SUCCINT definition of RMS dB? Maybe with a diagram.
Progs such as Cubase give the option of Peak or RMS meters, but what do the
little lights really mean?
I understand Peak dB ok, as a relative difference in power equal to ten times the
common logarithm of the ratio of two signal levels (or voltages). For power
(voltage) dB=10log10(V/Vref).
For amplitude (sound pressure) dB=20log10 (A/Aref) because squaring a value
doubles its logarithm.
Appending the suffix 'U' denotes that the ratio is relative to 0.775V RMS and 'V'
expresses the ratio relative to 1Volt RMS.
Simplifying the problem: If I take a 'pure' sine wave, my bad maths leads me to
think that any Root Mean Square dBV value over a complete cycle must equal
zero. I'm just bright enough to know I must have this wrong! But why is it wrong?
I checked several sites but can't find an explanation that makes me go "Oh of
course!" In fact, the more I've read the more I'm sure I've missed a vital clue.
This is what comes of having a virus and not making music!
Progs such as Cubase give the option of Peak or RMS meters, but what do the
little lights really mean?
I understand Peak dB ok, as a relative difference in power equal to ten times the
common logarithm of the ratio of two signal levels (or voltages). For power
(voltage) dB=10log10(V/Vref).
For amplitude (sound pressure) dB=20log10 (A/Aref) because squaring a value
doubles its logarithm.
Appending the suffix 'U' denotes that the ratio is relative to 0.775V RMS and 'V'
expresses the ratio relative to 1Volt RMS.
Simplifying the problem: If I take a 'pure' sine wave, my bad maths leads me to
think that any Root Mean Square dBV value over a complete cycle must equal
zero. I'm just bright enough to know I must have this wrong! But why is it wrong?
I checked several sites but can't find an explanation that makes me go "Oh of
course!" In fact, the more I've read the more I'm sure I've missed a vital clue.
This is what comes of having a virus and not making music!
Message 2/7 22-Aug-04 @ 11:33 PM - RE: RMS dB?
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Well in guitar amps the RMS is used to show the sustained power load that can be handled by the amp at various frequencies over several cycles.The peak rating is used to show the(no surprises here)peak power that can be handled at a specific frequency so it is less useful as a power measurement.The different power rating sytems use different sections of the sine wave peak rating uses the top of the sine wave,RMS uses a point at 3 quarter of the height of the sine wave hence the RMS measurement has become more widely used as it gives a better idea of the sustained power.
Message 3/7 24-Aug-04 @ 12:53 AM - RE: RMS dB?
RMS stands for Root Mean Square, and essentially it's an averaging function to give you an 'average' energy measurement of a wave. For example you can have a sine wave at #Hz that has a peak of -6db, and you can have a complex waveform that has the same amount of energy at the same frequency as that sine wave, but with more harmonic content, yet still having a peak of -6db, but because of all the energy in the other frequencies, even with the same peak, you have a higher RMS.
Lets's look at water for a moment. Peak measures the maximum amount of energy, like the crest of a wave, but imagine the difference between a steep but thin wave and that same height wave with ten times the amount of water underneath it. That thin wave will splash the tops of the trees and piss off the birds, but the thick wave has so much more energy in it that it will wipe out the trees and the town behind them. Peak will be the same for both, RMS quite different. Make sense?
Both peak and RMS are useful measurements. Hope this helps.
Ape
Lets's look at water for a moment. Peak measures the maximum amount of energy, like the crest of a wave, but imagine the difference between a steep but thin wave and that same height wave with ten times the amount of water underneath it. That thin wave will splash the tops of the trees and piss off the birds, but the thick wave has so much more energy in it that it will wipe out the trees and the town behind them. Peak will be the same for both, RMS quite different. Make sense?
Both peak and RMS are useful measurements. Hope this helps.
Ape
Message 4/7 24-Aug-04 @ 04:11 AM - RE: RMS dB?
Thanks both,
The analogy with the wave did the job! So now I've a bod that sits on a pier
wearing blinkers and counting waves, noticing their shape, height, gaps.... and
now how podgy they are!
Very clear on concept. Hope you're a teacher.
But what's the maths?
Root I know from terms such as 'square root' and 'cube root' etc. The phrase
begins with a word telling me a number. RMS begins with root!? The only
suggested number is the S bit.
Mean I know as a point in the middle of something - between two extremes (not an
average).
Square I know as a sum derived from multipying a number by itself.
So now, this might be a bozo question, but how is the RMS figure calculated?
Surely the Root of the Mean when Squared is the same as the Mean!? (If the Mean
is, say, 4 - its root (presumably squared) is 2, which when squared is 4.)
Or is it the square root of a point on the wave multiplied by the mean then
squared? But if so, over what length/duration is the mean taken? 1Hz? 1sec?
..be gentle
The analogy with the wave did the job! So now I've a bod that sits on a pier
wearing blinkers and counting waves, noticing their shape, height, gaps.... and
now how podgy they are!
Very clear on concept. Hope you're a teacher.
But what's the maths?
Root I know from terms such as 'square root' and 'cube root' etc. The phrase
begins with a word telling me a number. RMS begins with root!? The only
suggested number is the S bit.
Mean I know as a point in the middle of something - between two extremes (not an
average).
Square I know as a sum derived from multipying a number by itself.
So now, this might be a bozo question, but how is the RMS figure calculated?
Surely the Root of the Mean when Squared is the same as the Mean!? (If the Mean
is, say, 4 - its root (presumably squared) is 2, which when squared is 4.)
Or is it the square root of a point on the wave multiplied by the mean then
squared? But if so, over what length/duration is the mean taken? 1Hz? 1sec?
..be gentle
Message 5/7 24-Aug-04 @ 08:46 AM Edit: 24-Aug-04 | 08:47 AM - RE: RMS dB?
Here, ya geek, read this
If ya know me, you'll know that "geek" is a compliment.
If you can fully understand and utlitize this concept of peak vs. average (read: apparent) level, and achieve its balance in a recording, you're halfway to becoming a great mastering engineer
If ya know me, you'll know that "geek" is a compliment.
If you can fully understand and utlitize this concept of peak vs. average (read: apparent) level, and achieve its balance in a recording, you're halfway to becoming a great mastering engineer
Message 6/7 24-Aug-04 @ 08:39 PM - RE: RMS dB?
Root mean square (RMS)is a fundamental measurement
of the magnitude of an ac signal.Its defi nition can be
both practical and mathematical.Defi ned practically,the
rms value assigned to an ac signal is the amount of dc
required to produce an equivalent amount of heat in the
same load.
For time sampling signals,rms calculation involves
squaring the signal,taking the average,and obtaining the square root.
http://www.analog.com/UploadedFiles/Application_Notes/323300582AN578_a.pdf
of the magnitude of an ac signal.Its defi nition can be
both practical and mathematical.Defi ned practically,the
rms value assigned to an ac signal is the amount of dc
required to produce an equivalent amount of heat in the
same load.
For time sampling signals,rms calculation involves
squaring the signal,taking the average,and obtaining the square root.
http://www.analog.com/UploadedFiles/Application_Notes/323300582AN578_a.pdf
___________________________________
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Message 7/7 01-Sep-04 @ 03:14 AM - RE: RMS dB?
Thanks for taking the time to post those links both.
That's the maths all right - a bit wibble at first glance, but I think I get it now.
RMS is the square root of the mean of the squares of the values.
The final bit is the last peg so to speak. The more values the more accurate the
signal. RMS has escalating inaccuracies as the number of values that are used to
arrive at an average are reduced, and from the inherent latency of quantising a
continuous signal. (The higher sample rate produces a better quality but takes
more processing power/time - I've met that idea elsewhere!)
It was going really well until the equation pi over 2 x the square root of 2! Two
infinite numbers. God's teeth! Mind implodes. But then again, nothing is absolute
so why worry about one approximation over another abstract symbol?
I remember why I stopped studying maths.
That's the maths all right - a bit wibble at first glance, but I think I get it now.
RMS is the square root of the mean of the squares of the values.
The final bit is the last peg so to speak. The more values the more accurate the
signal. RMS has escalating inaccuracies as the number of values that are used to
arrive at an average are reduced, and from the inherent latency of quantising a
continuous signal. (The higher sample rate produces a better quality but takes
more processing power/time - I've met that idea elsewhere!)
It was going really well until the equation pi over 2 x the square root of 2! Two
infinite numbers. God's teeth! Mind implodes. But then again, nothing is absolute
so why worry about one approximation over another abstract symbol?
I remember why I stopped studying maths.
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