bobkatz wrote on Wed, 02 March 2005 22:49 |
Yeah, it's true. Gerzon knew about it long ago and I believe it has been written up in Waves' literature as well.
While a zany signal (square wave) could be made to theoretically produce +3 dBFS on the analog side, with most practical musical sources I've found the dBFS+ signals can be prevented by dropping the ceiling on an L2 or any decent digital limiter, to -0.3 dBFS. TC designed their new brickwall limiter to prevent the intersample peaks and it's very effective so you don't need to drop the ceiling (on the TC it's just an output fader, which you can leave at 0 dB).
BK
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Yes there is a problem, and I agree with you that the best way to prevent it is to stay a couple of dB from clipping when doing AD, as I believe was stated by Bob a few times.
Regarding the mechanism of the problem and the reasoning behind it, I do not think it is well understood, so I will try to clarify a couple of points:
1. I heard people refer to it as an analog filter problems. I do not think it is correct. An analog filter, when fed a clipped sine wave, will track it down pretty well, and the exception is that the sharp corners on the wave (where the clip starts and stops) will be somewhat "rounded". Sharp corners require infinite bandwidth, which the analog filter does not have (thus the rounding).
I do not see any reason or mechanism by which the analog filter will try and "fill in" the clipped part. Analog filters do not have inertia and they do not resonate.
2. The problem occurs during the interpolating filter process. An unity gain FIR (LPF) will have the sum of its coefficients equal 1. That way, if one enters all 1 (full scale) DC signal, each coefficient is multiplied by 1 and if the sum of the coefficients is 1, the output will also be 1.
However, an FIR will have some of it's coefficients positive and the rest are negative (a sinc function envelop). The sum is 1 or less as long as the signal is "legal".
But what would happen if we could for example do the following: We line up the data (momentarily) so that all the positive coefficients are multiplying data values of +1, and all the negative coefficients are lined up with data values of -1?
The sum will me greater then 1, because all the negative coefficients became positive for that specific moment. Some filters will output a value of over 2!
Of course such a worse case signal is impossible to come by - it is in fact the absolute value of the sync function of the FIR multiplied by a huge value (such as 2^24). But a clipped signal, especially with high frequency content can yield some serious "overs", as much as 3dB on rare occasions. The data does not need to be all clipped (1's and -1's). The problem has a lot to do with both clipping and alignment of the data cycles with the filter coefficient cycles. It works out to a bigger problem for higher frequencies (with a clip).
The reports of 12dB overs are plain wrong, and 6 dB is also wrong. But 3dB can happen in the real world.
The interpulator (upsampler) designer can not ignore that effect. They receive say a 44.1KHz signal that is, by definition, music to be played. You up sample and if the signal was clipped the outcome could exceed the limits of the compute engine (+/-1). That waveform will not even try to follow the original signal waveform. It will follow the FIR coefficient curve interaction with the signal. But one way or another, you run out of code (over 1 stays at 1, under -1 stays at -1). The analog part of the DA gets an upsampled clipped signal.
The best way to avoid it is to scale the data down by say 3dB before the interpolation. But given that many DA's in homes and cars are not scaled, it would be good if the recording and mastering stay away from full scale by a couple of dB.
This is an engineering comment. I really do not want to speak about mastering - I am not a mastering engineer. I know a lot of mastering people over drive their converters to make the music louder (on a relative scale). They probably don't think about the fact that the end customer may have up to 3dB more clipping then a studio with quality DA.
Regards
Dan Lavry