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Topic: Why RG 89.0 dB when it doesn't clip? (Read 22512 times)
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## Why RG 89.0 dB when it doesn't clip?

##### Reply #25 – 2008-05-31 06:02:14
A doubling in voltage is exactly 6dB, not "about 6.02dB". When did the laws of physics suddenly change?

Now don't get all Karl Rovian on us!

Is your calculator handy?

20 * log (2) =

## Why RG 89.0 dB when it doesn't clip?

##### Reply #26 – 2008-05-31 10:57:17
You're right. It's 6.02dB. I was deliberately lied to by every professional tutor who ever taught me about logs.

Cheers, Slipstreem.

## Why RG 89.0 dB when it doesn't clip?

##### Reply #27 – 2008-06-03 19:12:58

Since dynamic range is around 98dB in a Compact Disc, that must be the 0 dBFs which is the maximum digital level. If a signal goes over the range, it should clip...

...Am I still wrong???  Dohh!

I've read posts of Dynamic (big thanks) and still don't know what is the dynamic range of CD-DA (44.1kHz 16bit LPCM).

And, you said that 0 dBFS (max. possible digital level) is around 98dB and min. possible digital level is 0dB?

The dynamic range of CD-DA is infinite if properly dithered, though that's not useful to you.

Imagine a deep fade-out of a full-scale sine wave (i.e. 0 dBfs to start). If you don't dither, the signal must be rounded to the nearest quantization level. So from peaks at -32768 and +32767 it would reach -1 and 0 and turn into a square wave (truncation distortion is thus adding odd harmonics of the fundamental) then it suddenly drops to a level where the negative and positive peaks round to the same value, be it 0 or -1 and the sound stops completely.

In that situation, you have about 96.3 dB dynamic range. (Vp-pmax = 65536, Vp-pmin = 1, work out 20 * log(65536/1) to get dB) where the fundamental signal is present in some form, below which it's absent. In this circumstance, you can usefully consider dynamic range.

However, not dithering is bad practice and shouldn't be considered intrinsic to CD-DA performance.

If you don't dither, the quantization noise might be peaky and related to the signal, or completely cancel the signal when it dips below a peak-to-peak amplitude of about 1. When you use flat dither, this complicated distortion is exchanged for flat, white noise that is constant and uncorrelated with the original signal.

Imagine trying to view the signal waveform on an oscilloscope, whether properly dithered or not. Imagine trying to place a decision threshold (e.g. at a comparator input) to produce a logic-level output, say to count the cycles or generate a clock signal from the live waveform. That sort of engineering situation is where the idea of dynamic range is particularly useful - determining the gap between the noise floor and, say, a saturation level.

With a digital sampling oscilloscope supplied with a suitable clock source you could average the signal over numerous cycles (e.g. 16 or 64), and be able to discern signals below the unaveraged noise floor if they were properly dithered in the first place. But being able to see this isn't the same as dealing with the live waveform.

On many sampling oscilloscopes you can also perform FFT analysis for a spectral view and approximate frequency analysis. Likewise waveform averaging, that involves a form of averaging any white noise present in, say, the 1024-sample FFT window to spread it over the 511 or 512 frequency bins in the power spectrum (remember positive and negative frequencies end up in the same bin, hence the number of bins is half the number of samples in the FFT window). Dividing the power equally among 512 bins it will be at a level in each bin that is about 10 * log(1/512) = -27.1 dB lower than the supposed noise floor measured from the waveform view (the waveform view noise floor is over the whole bandwidth present (e.g. 22.050 kHz for CD-DA), while the FFT of the noise within one bin is over that bin's bandwidth (e.g. 22.05kHz/512 = 43 Hz for CD-DA with 1024-point FFT). So from -96 dBfs, we can resolve sinusoids around 27 dB lower - say -123 dBfs, which would add to the equal noise power in that bin bandwidth, giving a bin power of -120 dBfs, standing out about the relatively flat noise.

The maximum sinusoid we could see would be full scale, i.e. 0 dBfs. So the dynamic range when analysed by a 1024-point FFT is about 120 dB.

1024-point FFTs on CD-DA aren't far from how the ear perceives sound (frequency and time resolution of the ear are in the same ball park as those of the 1024-point FFT), so you might argue that for humans, CD-DA has around 120 dB of usable dynamic range (assuming adequate flat-spectrum dither), though the signal gradually and gracefully sinks into the noise floor without suddenly disappearing.

However, one can frequency-shape the noise spectrum while remain adequately dithered to concentrate the noise into high frequencies where the ear is insensitive and reduce the noise in the areas of peak sensitivity by perhaps 15-18 dB. Thus, the useful dynamic range of noise-shaped CDs might be in the region of 135-138 dB in the frequency regions where the ear tends to have it's widest dynamic range.

If you're not a human ear, you can go for much longer FFT lengths (smaller frequency bins) and move that white noise per bin down further, thereby have a greater the dynamic range.

So, take your pick and decide whether dynamic range is relevant to you.

For 1024-point FFT pictures and audio files to demonstrate visibility / audibilty of signals above the noise floor with various kinds of dither see the old post I referred to previously.

I'd tend to say that all of the following are true:
• True dynamic range of CD-DA is infinite providing it is adequately dithered, as tonal signals far below the apparent noise floor can be discerned correctly with sufficient averaging time (if synchronised) or autocorrelation averaging time (even if unsynchronised) or sufficient FFT size. Just name your dynamic range and we can calculate the required averaging time or FFT size.
• The effective signal-to-noise ratio (SNR) of CD-DA for tonal signals with adequate spectrally white dither is probably about 120 dB thanks to the frequency-selectivity of the ear - similar to a 1024-point FFT.
• With adequate strong ATH noise shaped dither, the SNR of CD-DA for tonal signals at frequencies where the ear is most sensitive, is approximately 135-138 dB at the expense of extra high noise floor (reduced SNR) at the mostly higher frequencies where the ear is far less sensitive to small signals anyway.
• For undithered (i.e. truncation-quantized) reproduction - not the case for real CD audio these days unless very badly done - CD-DA has about 96 dB of dynamic range for tonal signals, though the quietest signal before it jumps to silence is a square wave, there's 96 dB range on the FFT bin for the fundamental frequency. If the signal is not a test tone (e.g. real music), there usually will be a degree of self dithering, and the dynamic range will vary from time to time as will the level of quantization distortion, depending on the actual signal.

To put this in context, most 18 inch professional chainsaws are labelled at about 116 dB above the threshold of hearing, not far from the pain threshold. That means that 120 to 138 dB should be more than adequate for music reproduction. Recording and processing may benefit from greater bit-depths, but 16-bit/44.1 kHz should be ample for playback.
Dynamic – the artist formerly known as DickD

## Why RG 89.0 dB when it doesn't clip?

##### Reply #28 – 2008-06-03 19:32:14
Note that, in his great explanation, Dynamic has snook (is that the past tense of sneak?) in yet another scale - something related to (but not exactly) dB / Hz - loudness per frequency bin.

I think the confusion arises when people think dB means something more than it does (i.e. think it's a unit of measurement, like an inch, which it isn't).

Even when they realise it's just an easy way of writing a ratio, they still think that somehow everything that can be expressed in dB must be related somehow. Well, sometimes it is - but that relationship can be quite complex - e.g. the relationship between dB in ReplayGain and dB FS - so complicated, that it's near useless to think of the two as being correlated in any way.

Anyway, back to ReplayGain: the scale is what the scale is - instead of trying to guess whether it'll clip or not from some vague understanding of it, or relating it to some other barely related scale, try this: look in the column marked "clip?"

Cheers,
David.

## Why RG 89.0 dB when it doesn't clip?

##### Reply #29 – 2008-06-04 04:58:13
Note that, in his great explanation, Dynamic has snook (is that the past tense of sneak?) in yet another scale - something related to (but not exactly) dB / Hz - loudness per frequency bin.

Oh yes. The unit of dB / Hz is commonly used in engineering but it comes with danger for misunderstanding or unclear thinking, for you don't divide the number of decibels by the bandwidth as the units alone would tend to suggest, but must convert out of the logarithmic domain into linear power units or linear power ratio, which is why my explanation had to subtract 10 * log (512) in the decibel domain to divide the white noise power equally among 512 bins in the power spectrum.

I hope this small digression is acceptable in the Scientific/R&D sub-forum.

As David has pointed out the while dB based units can be really handy you need to be careful to think about the fact it's just a power ratio expressed in logarithmic terms and that to do any other mathematics based on these figures, you should convert into the linear domain first.

You must also bear in mind the reference level you are implicitly making the ratio relative to.

Furthermore, bear in mind that to Joe Public, there's little understanding of dB's peculiarities (rather like other logarithmic scales, such as the Richter scale for earthquake power, or like non-absolute linear scales like temperatures in °C or °F). A 4.0 earthquake is 1000 time less powerful than a 7.0 earthquake, I believe. It's not "twice as hot" in Madrid as in Oslo when it's 32°C and 16°C respectively (90°F and 61°F respectively, or in absolute temperature, 305 Kelvin and 289 Kelvin respectively).
Dynamic – the artist formerly known as DickD

## Why RG 89.0 dB when it doesn't clip?

##### Reply #30 – 2008-06-07 02:18:21
Thank you so much, Dynamic. I humbly appreciate your great input. Now I see what role a dithering plays in digital audio. We should post this kind of information on HA Wiki for future reference usage!!

However I am not so clear about this: how come a CD recording can clip when it has a dynamic range way wider than 96dB? Does a digital recording have a limited amount of volume it can output???

I must ask you guys a pardon for my endless questions regarding clipping/SNR/DR/etc, but some of these concepts just don't seem to elaborate well with each other in my brain. The learning curve is darn steep...

## Why RG 89.0 dB when it doesn't clip?

##### Reply #31 – 2008-06-07 03:57:40
However I am not so clear about this: how come a CD recording can clip when it has a dynamic range way wider than 96dB? Does a digital recording have a limited amount of volume it can output???

Quote
However, as the maximum amplitude of a CD is at a fixed level, the overall loudness can only be increased by reducing the dynamic range. This is done by pushing the lower level program material higher while the loudest peak sounds are either destroyed or severely diminished. Certain extreme uses of compression can cause distorting or clipping the waveform of the recording.

## Why RG 89.0 dB when it doesn't clip?

##### Reply #32 – 2008-06-08 01:02:13
Quote
However, as the maximum amplitude of a CD is at a fixed level, the overall loudness can only be increased by reducing the dynamic range. This is done by pushing the lower level program material higher while the loudest peak sounds are either destroyed or severely diminished. Certain extreme uses of compression can cause distorting or clipping the waveform of the recording.

Thank you, lvqcl.
So.. a CD does have a limited amplitude it can output then. What is the exact value of the maximum amplitude of a CD?? So if you dither a clipping sample adequately, can you make it not to clip? (By increasing SNR?)

## Why RG 89.0 dB when it doesn't clip?

##### Reply #33 – 2008-06-08 02:02:42
So.. a CD does have a limited amplitude it can output then. What is the exact value of the maximum amplitude of a CD??

Since CD has 16 bit, max. amplitude is +32767 or -32768. And, it is 0 dBFS by definition.

So if you dither a clipping sample adequately, can you make it not to clip? (By increasing SNR?)

No, of course. Dithering and noiseshaping can alter noise level, not max. level. Well, look at waveform in ANY audio editor.

## Why RG 89.0 dB when it doesn't clip?

##### Reply #34 – 2008-06-09 05:17:52
I will try to explain how I interpreted all these. If anything is wrong, please correct it:

CD (16bit/44kHz) has a max amplitude. Its dynamic range is originally 96dB. Dithering/noiseshaping can expand this range further, like upto 138dB, but dithering/noiseshaping can't expand a CD's physical limitation. (96dB) That is why a CD recording clips.

BTW, I found a previous discussion in HA regarding CD's true dynamic range:

http://www.hydrogenaudio.org/forums/index....showtopic=45165

## Why RG 89.0 dB when it doesn't clip?

##### Reply #35 – 2008-06-09 11:54:52
I will try to explain how I interpreted all these. If anything is wrong, please correct it:

CD (16bit/44kHz) has a max amplitude. Its dynamic range is originally 96dB. Dithering/noiseshaping can expand this range further, like upto 138dB, but dithering/noiseshaping can't expand a CD's physical limitation. (96dB) That is why a CD recording clips.

CD recording clips (like at these pictures) only if it was deliberately mastered so. Anybody can make CD that doesn't clip.
And I think it's better to say about 16 bit as a limitation, not 96 dB.

By the way: Wikipedia (http://en.wikipedia.org/wiki/Compact_Disc) says that "There was a long debate over whether to use 14 bit (Philips) or 16-bit (Sony) quantization..."