Julf wrote: > Not quite sure what you are saying here. Are you talking about a > just-noticeable increase in noise level, or a just-noticeable change in > signal amplitude? The former might relate to the needed number of bits, > the latter less so. Noise level, Julf. Provided that the half lsb is spectrally flat by dithering of otherwise the only effect of quantisation is to add an error equivalent to spectrally-flat noise. This is quantisation 101. So the question is whether this noise will when added to the noise in the signal pre-quantisation, produce a noticeable increase. Incidentally if anyone thinks I'm going off piste here I can quote from a basic text http://www.dspguide.com/ch3/1.htm "First we will look at the effects of quantization. Any one sample in the digitized signal can have a maximum error of ±? LSB (Least Significant Bit, jargon for the distance between adjacent quantization levels). Figure (d) shows the quantization error for this particular example, found by subtracting (b) from (c), with the appropriate conversions. In other words, the digital output (c), is equivalent to the continuous input (b), plus a quantization error (d). An important feature of this analysis is that the quantization error appears very much like random noise.
This sets the stage for an important model of quantization error. *In most cases, quantization results in nothing more than the addition of a specific amount of random noise to the signal. *The additive noise is uniformly distributed between ±? LSB, has a mean of zero, and a standard deviation of 1/√12 LSB (~0.29 LSB). For example, passing an analog signal through an 8 bit digitizer adds an rms noise of: 0.29/256, or about 1/900 of the full scale value. A 12 bit conversion adds a noise of: 0.29/4096 ≈ 1/14,000, while a 16 bit conversion adds: 0.29/65536 ≈ 1/227,000. Since quantization error is a random noise, the number of bits determines the precision of the data. For example, you might make the statement: "We increased the precision of the measurement from 8 to 12 bits." This model is extremely powerful, because *the random noise generated by quantization will simply add to whatever noise is already present in the analog signal. *For example, imagine an analog signal with a maximum amplitude of 1.0 volts, and a random noise of 1.0 millivolts rms. Digitizing this signal to 8 bits results in 1.0 volts becoming digital number 255, and 1.0 millivolts becoming 0.255 LSB. As discussed in the last chapter, random noise signals are combined by adding their variances. That is, the signals are added in quadrature: √(A2 + B2) = C. The total noise on the digitized signal is therefore given by: √(0.2552 + 0.292) = 0.386 LSB. This is an increase of about 50% over the noise already in the analog signal. Digitizing this same signal to 12 bits would produce virtually no increase in the noise, and nothing would be lost due to quantization. When faced with the decision of how many bits are needed in a system, ask two questions: (1) How much noise is already present in the analog signal? (2) H*ow much noise can be tolerated in the digital signa*l?"* You will thereofre note that the point I posed in my first post remains, unmolested by the imaginary correction by Arnyk, namely that one cannot say that a channel has been perfectly captured just because its inherent noise level is the same as the noise which will be added by dithering. The only way of knowing that is by knowing the just noticeable level of increase *of noise* in that channel. This will undoubtedly vary with the level of the inherent noise and may be affected by whether the noise is shaped or not, but let's assume it's spectrally flat. I have had to go round the houses with this point but it's really not that complicated. Now where is the psycho-acoustic evidence of the just noticeable level of noise increase. I'm hoping that may trusty introduction to the psychology of hearing might have it in. In the absence of precisely determined levels I reckon that keeping the increase in noise to 1db seems sensible, which implies 16 bit being good to capture capture a self-dithering channel with a noise level of --90dB (or -87dB if we feel we have to add tpdf dither). Whether we have the evidence or not let me make this clear there is no privileged position in adding quantisation noise at a level equal to the inherent noise in the channel- this might be either above or below audibility givne that it doubles the noise level. Imagine a channel with noise at -18db: I'm pretty sure that quantising at 3 bits WILL audibly increase the noise in the channel. At 16 bit level the quantisation noise is demonstrably audible in really extreme cases (if playing at 120dB peak level- this can be shown using fletcher munson and is what sparked the interest in noise shaped dither) so reallly really strictly doubling it is probably an audible difference, albeit probably not at ordinary listening levels. * NB the non-noise model of quantisation error is irrelevant in this context because the issue is capturing an audio channel and this entails that the signal is either self-dithering or dithered. There is no point discussing incompetent digitisation. ------------------------------------------------------------------------ adamdea's Profile: http://forums.slimdevices.com/member.php?userid=37603 View this thread: http://forums.slimdevices.com/showthread.php?t=105717
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