As for this:
"This for example allows CD audio to be "brickwalled" with a near-perfect lowpass filter with a transition band of only a few hundred Hz"
Actually, no. This is incorrect. One of the benefits of oversampling is the ability to avoid high-order brickwall filters that have a sharp transition band. Because the filter can implemented at a higher frequency, it can be a lower order, gentler slope -- not a brickwall.
Hi,
In my understanding, it
is correct. Oversampling features sharp filters in the digital domain instead of analog, which is much easier,
and a gentler one in the analog domain.
Actually, I wouldn't agree with that, either. There is no such thing as a perfect filter, either digital or analog. There is always a trade off in phase, impulse response, etc. There is no free lunch. It's just the way the physics / math of signal processing theory works.
The trade-off between frequency response and transient accuracy is an old legend. There
never has been
any trade-off about transient accuracy. It is
all about frequency response.
The idea comes from a misinterpretation of the oscilloscope visualization of the output signal of a pure pulse. Visualisation produced with a resolution near the MHz. The pulse seems to smear more and more as and when the frequency response is extended close to the cutting frequency, with sharper and sharper filters.
But in reality, what we see isn't time-smearing, it is ringing. An audiogram visualisation of a musical signal with full frequency range (0 - 22050 Hz for a 44100 Hz digital stream) shows the difference : as and when the digital filter gets sharper, time smearing becomes more and more important on the 22050 Hz frequency line. The timing of everything under 22050 Hz remains perfectly accurate. No smearing at all.
the audible impact of a strong brickwall filter is as far as I know still to be determined. sure it can make a little mess where it is, but if that's 20khz who cares? I would believe that OS and slower low pass filter is in good part a money/make it simple thing. more than an actual need for audio reasons.
now when talking DACs as a whole, I'm all for OS.
A listening test about that once existed, and the audio samples should be remade if someone has the technical possibility to do it.
Take a musical sample with a lot of high frequencies, and make lowpassed versions of it at 8, 10, 12, 14, 16, 18 and 20 kHz using three kind of filters.
-A standard lowpass with a soft slope.
-A lowpass with a cosine frequency profile, as used in DACs or MP3 encoders, something like 0 dB at 19500 Hz, and minus infinite at 20500 Hz, for the 20 kHz version.
-A true Sinc brickwall : 0 dB at 19998 Hz, minus infinite at 20002 Hz.
I had the chance of listening to the two later ones. Though I could hear up to 14 kHz on pure sines, I could not distinguish the 13 kHz "cosine" filtered sample from the original one. Only at 12 khz could I hear the loss of treble.
The true brickwall version was extremely interesting : the 14 kHz version sounded exactly like the original, but with a permanent 14 kHz sine added on top of it, whose volume was modulated by the amount of high frequency in the original.
Ringing is just that : a bleep of a fixed frequency playing on top of the music, that is completely unchanged except for that additional note. Hearing it at 12, 13, 14 kHz etc. allows to understand exactly the sonic effect of a too sharp filter in a CD player : your speakers just play a bleep that you can't hear... and this only if your musical program actually contains energy at 22050 Hz. With nothing at this frequency on the CD, there will be no ringing at all, even with a true brickwall filter in your DAC.
My understanding is, oversampling to F= oversampling frequency->digital brickwall below f= original input audio frequency ->gentle analog filter to lowpass below F.
?
I don't understand your equation. I think that a standard DAC should take the original PCM samples, oversample using a sharp lowpass filter, convert to analog, then filter the analog output with a soft lowpass.