Hello,
Perhaps Rob or others who understand this point can chip in and enlighten me.
I understand the claim that people hear down to 4 micro seconds resolution of audio but don't get how the Hugo can reconstruct the sounds form a 22 micro second sample? if a sound started and ended in between those 22 micro seconds - than we have no 'evidence' it ever existed, no?
I like the Hugo, but a bit puzzled.
Thanks!
Good question. Every time I talk about sampling, I specifically say that the interpolation filter, with an infinite number of taps, will perfectly (that is, completely perfectly, it will be the same signal just time shifted) reconstruct the original
bandwidth limited input signal. Now this bandwidth limited signal must have no output at all above the Nyquist frequency. So the interpolation is not trying to re-create information that is not already present at the point of sampling - but if you use an infinite tap length interpolation filter you will reconstruct the original bandwidth limited signal perfectly - so this means you have effectively not sampled the signal, and filled out the in-between data perfectly.
So in your case, you put a signal that has information only above the Nyquist frequency (say a 30 kHz tone) and you are sampling at 44.1k. Now you put this signal through a brick wall filter set to infinite attenuation above 22.05k, that will mean the output of the filter is zero. You then sample zero, the perfect interpolation then re-creates - zero, exactly as it should do. Now the point I am trying to make is if you have a finite tap length filter, then when it re-constructs the bandwidth limited signal, there will be timing errors in the reconstruction process, and these timing errors are significant. To illustrate this, imagine a 20 kHz tone burst. So the signal is zero, then it is full output (and yes in reality it would not be this way as it would have pre-ringing due to the brick wall filter but ignore this as I am trying to illustrate a point). Now if we happen to sample at the peaks, then we will get a full output, followed by a declining output. If we sample at the point it is zero, then we lose the missing transient, and the signal then builds up so that at a few hundred uS later we get peak output. Now lets take the worst case, a FIR filter with a tap length of 1, (it returns the data unchanged so no filtering) then we can see that the transient timing error is hundreds of uS. Now if we use an infinite tap length filter, then it will reconstruct the output of the brick wall filter perfectly, zero timing errors,
it would be as if we had not sampled the data at all. My point of view was that conventional filters, with limited taps of a hundred or so, would create time domain errors that would be audible.
Now I use the 4uS inter-aural delay as an illustration of the importance of timing to the ear/brain. I have no idea what levels of timing errors are significant - that is a 4uS error of -60 dB, or is it -80dB - or indeed whether its 4uS or 4nS - after all, if I gave you a DAC that had 4uS of timing error you would say that may be a problem - but if I then said 4uS of jitter (timing error is the same as jitter), then you would be horrified, that must be audible as people keep going on about femto clocks within DAC's...
So my approach has been very simple - to recognise that the FIR filter tap length is important for reconstructing the timing of transients, and to keep increasing the tap length until I can no longer hear any improvement, and secondly that the FIR interpolation algorithm itself has to be optimized to improve timing and maximize sound quality with a finite number of taps.
So in short, an infinite tap length filter will perfectly re-create the bandwidth limited signal, as if no sampling had taken place. It absolutely will not recreate the signal before the brick wall input filter - but my listening tests has shown that linear phase brick-wall filters are completely transparent anyway, if you do them correctly. The sound quality problem is not the initial brick wall filter, but the interpolation reconstruction filter. That's why red-book sounds so good with Hugo...
Hope this explains,
Rob