The wikipedia article on noise shaping is worth a read.
Well SebastianG is obviously not on the same wavelength as I am on this, no pun intended.
I presume from this that the answer to my question is 'no', even a 20KHz low amplitude signal can benefit from dither in a 44.1KHz PCM environment, as much as a lower frequency source signal can benefit?
What I don't understand is "ultrasonic" "dither" like UV22. It "claims" to leave the quantisation noise level in the audio band unchanged (i.e. same RMS level as with no dither), adds dither noise only at ultrasonic frequencies, but still manages to decorrelate the quantisation noise from the signal (...) What I don't understand is how a couple of high frequency sine waves (which is all UV22 appears to be) can work as correctly decorrelating dither.
Why did you use noise shaped dither?If you push all the noise above ~16kHz, then it'll probably hide a 20kHz signal!
2Bdecided, are you sure the signal was at -100 dBFS ?I wouldn't expect it to show up at all after truncation to 16 bits (without dithering).
Did you notice that your graphs are showing -60dB rather than -100dB?I think you did not reduce the signal amplitude sufficiently.
2. The higher the frequency of the tone, the more difficult it was to hear it above the dither noise. In particular, the 20KHz tone tended to blend in with the dither, despite the whole file being played back at less than 1/5th speed, bringing the 20KHz tone into a more readily audible range. [It became a 3628Hz tone as a result of the slow playback.]I was surpised that the 20KHz tone showed up at a similar intensity level in the frequency analysis graph to lower frequency tones I tried. On the other hand, I could not fail to notice how much more difficult it was to hear the 20Khz tone above the dither noise compared with lower frequency tonesFor example, the 20KHz tone did not benefit from the dither as much as a 2KHz tone.I did not experiment with other varieties of dither. I suspect all forms of dither would struggle to make a low amplitude 20KHz waveform audible above dither/quantisation noise, where the format is 44.1/16 PCM.
The high frequency fall off you are hearing is due to your sound card, windows internal wave handling, and maybe your ears. The former two will fall off around the Nyquist frequency, whatever sample rate you choose for playback.
I see now that you in fact changed the scale on your frequency analysis plot by 40dB by changing the reference level. When I change the various settings to match yours, I do not get the clear graphs you get, but ones showing the noise at a much closer level to the signal. Anyway that is a detail I will not worry about.
Regarding an attitude of arrogance I suppose it may have been presumptuous of me to query your graphs
What you're doing by questioning whether dither "works" is questioning decades of work by people far more qualified than you or I. It's fair enough to question, and lots of "qualified" people have been wrong before, but the evidence in this case is overwhelming.
What I was querying is how effective it is for a signal approaching the Nyquist limit.
Quote from: MLXXX on 20 March, 2008, 11:18:29 AMWhat I was querying is how effective it is for a signal approaching the Nyquist limit.What do you mean by effective?
1. THD comes to mind (...)3. IMD (...)
2. S/N ratio comes to mind ....
.... I presume that you cannot dither a 20KHz tone without using noise at around 20KHz or beyond.
1. THD comes to mind, e.g. I would speculate that a low amplitude 10KHz tone would give more 2nd order harmonic than a 5Khz tone, after conversion to 44.1/16. I know this would depend on the particular dither protocol used, but as a general statement does this speculation have any validity?
I generated a 1 second long tone, I selected the entire waveform, and clicked "scan" in the frequency analysis window. This averages the results of the analysis windows across the selection, rather than just showing you the result from one analysis window (the middle one).Even with the reference changed from -40dB to 0dB, you shouldn't trust the graph 100%. It's nearly correctly for some settings, but not "calibrated". It'll jump around by a few dB if you change the window function, for example.
Can anyone confirm this or point out any mistakes I possibly made?I think I'm going to run some simulations...
In the case of the small 20 kHz signal, if one applied low frequency dither (i.e. send it through a low-pass filter before applying it) then the 20 kHz signal would sometimes be not present and other times present as a 1 lsb signal. On average, though, wouldn't it be present and in the correct amplitude and audible over the low-frequency dither?
First off, if ordinary triangular probability distribution function (TPDF) dither is used, the frequency components of the dither can exceed the Nyquist limit.
I do not understand your use of the phrase 'by definition'.
Cabbagerat, I have been wrong so many times previously in this thread it is not surprising to me that you commenced your post immediately above with the word 'No'.
I do not understand your use of the phrase 'by definition'. If you generate a set of random numbers at 44.1KHz you will generate instantaneous slew rates beyond what a continuous 22.05KHz wave would involve. Theoretically you could have a series of numbers as follows: +1, -1, +1, -1. [although the probability of that exact series would be extremely low]Intuitively [for me anyway], you need freedom of the dither to change its value as fast as possible, and not to be filtered down to 22.05KHz. A low amplitude continuous 22.05KHz wave (or a little below 22.05KHz) could lead to the following instantaneous samples at 44.1KHz sampling: +1, 0, -1, 0, +1, 0, -1, 0
Quote from: MLXXX on 25 March, 2008, 05:56:27 AMI do not understand your use of the phrase 'by definition'.I think I can answer this one. A series of samples at 44.1 khz cannot be used to represent any frequency above 22.05 khz because there will be a perfectly valid frequency below 22.05 khz which also goes through those exact same samples. Therefore 'by definition' all of the resulting frequencies are below the Nyquist limit.
I have come up with an anomaly. When I use my version of cool edit pro (2.00 build 2095) to generate a stereo sine wave it seems to generate the right channel differently. This is apparent when looking at the frequency distribution of the 32 or 24 bit wave immediately after it is generated: the right-hand channel has a 'fatter' distribution.
An interesting question is IMHO if it's actually worth using non-white dithers especially in the light of the noise shaping technique. To check this my idea was to compare plain "white TPD dither" with Wannamaker's "high pass TPD dither" (page 37)....So, in case I didn't make any mistakes the use of the "high pass dither" is preferable because the noise floor is lower by log10(3/2.61803)*10 = 0.59 dB. Of course, the 0.59 dB improvement is hardly noticable but it sure was a big surprise for me!
A continuous sine wave at 22.05KHz, sampled at 44.1KHz, could produces the samples [0, 0, 0, 0, 0, .....] or [1, -1, 1, -1, 1, -1, ......], or something inbetween - depending on the phase difference between it and the carrier. In fact, a sine wave at fs/2 Hz, sampled at fs Hz produces the samples [-sin(theta), sin(theta), -sin(theta), sin(theta), .....], where theta is the phase offset between the wave and the carrier. But that's just an aside. Critical sampling is a bit of a complication, and can be avoided entirely by defining your sampling theorem to require the signal to be bandlimited to less than fs/2 Hz.
The issue of "by definition" is that you cannot break the sampling theorem in any single rate digital system. Any (finite-valued) set of samples you can produce correspond to samples of a function bandlimited to half the system sampling rate. Be careful here, though - they might not correspond to samples of the bandlimited function you intended them to. This sounds like an arbitrary distinction, but I think it's fairly important. This is what I meant by "by definition": "by definition, all sampled signals are bandlimited".
Check the settings (all of them) in the tone generator. IIRC there's a difference between the left and right channels in the "default" settings. I can't remember what it is though (might be phase?), or why it would cause harmonics in the downconversion.If it is phase, that's why the initial frequency analysis looks "fatter" - it starts on a non-zero sample on the phase shifted channel only.Cheers,David.
The point I wish to concentrate on is simply this: is dither intended for use for a signal sampled at 44.1KHz pre-filtered to 22.05KHz or is it allowed to roam freely as generated.
Actually I was hoping to get a sample of raw TPDF dither, but I have not come across a sample on the net. Or at least a little bit of software that generates TPDF dither in isolation. I was then going to add that dither to a 24-bit signal in a relatively 'manual' dithering process, and save the mix to 16 bits without [further] dither.
seconds = 1;rate = 44100;sz = seconds*rate;x=(rand(1,sz)+rand(1,sz)-1)/32768;wavwrite('out.wav', x, rate, 24);