Quote:
Originally Posted by Jon Hodgson  Dan,
thanks for that, perhaps you can give people here some more real world perspective on another aspect of conversion.
A repeating mantra of many people who either think that digital can never be good, or insist that sample rates should be as high as possible, is the one "there are no such things as perfect filters"....
So, typically speaking, how imperfect are these filters?
I think it would be good for people to get some perspective on the performance of real world anti-aliasing filters.... |
OK. I will respond, and it is going to be long and slightly technical and some folks may want to skip it. If it is too long, please read the last 2 paragraphs.
In the good old days (such as before 1990), filters were a real limiting issue. When and AD recorded at 44.1KHz, one needed to make sure and filter out the energy above 22.05KHz that, but at the same time, the goal was to pass all the energy below say 20KHz intact. That task is about analog filtering. It is really impractical and perhaps not even possible to do a good job of such a filter.
The transition band is only around 2KHz – pass 20KHz but block 22KHz, and that is a real problem. All analog filters are circuits based on a concept of poles and zeros. To simplify, a pole or zero means an attenuation slop of 6dB per octave (20dB per decade). So a single pole filter that passes 20KHz, would yield only 6dB attenuation at 40KHz. So take 10 poles, and you have 60dB attenuation at 40KHz. So with 60dB over 20Khz, you end up with only 6dB over 2KHz transition band. That is “almost doing nothing”.
So how about 20 poles? That would yield only 12 db at 22KHz. So lets try for 100 poles, and on paper we will have 60dB attenuation at 22KHz. That too is not good enough. Now, no one designed 100 poles filter. 10 pole was closer to reality. I never heard of a 20 pole design. There are reasons for that. Each pole calls for a precision cap, and for a precision resistor. In fact, most analog filters have at least 2 caps and 2 resistors in an op amp circuit, for a pair of poles. So 100 pole design would call for 50 op amps, 100 precision caps and 100 precision resistors.
You really do not want to send your audio through 50 op amps. The precision requirement of high order R an C values gets impractical, the power dissipation, the cost and so on is just too much.
Also, an ANALOG filter that is very near 20KHz, brings about some serious phase non linearity issues, which can be somewhat compensated for when the number of poles is not too high, but with more poles, the phase curve is also an issue.
Well, what we did is “our best”. One way to help matters was to move the pass band to say 17-18KHz, making the transition band wider (22-18=4KHz, twice that of 22-20=2KHz). We also tended to rationalize that instrument level at around 20-22KHz is lower then full scale, so the filter requirement is relaxed by a few dB.
To summarize, things were far from idea or desirable.
Around 1990, the new concept of up sampling and oversampling came about, and that virtually solved the AD anti aliasing filters and the DA anti imaging filter problems. Say I over sample by only a factor of 2, (88.2KHz sampling) then my requirement is to pass 20KHz and below but block 44.1KHz and above. The transition band is now 24.1KHz, and that is 12 times easier filtering (12 times less poles). But way stop there? Lets go for say 64fs or 128fs or 256fs or 512 fs or even 1024fs.
Lets try for a 256fs AD. The sample rate is around 11.2896MHz (Nyquist is at around 5.6MHz). Say we want to pass everything up to 50KHz (no longer restricted to a tight 20KHz). The transition band is now 5.6MHz – 40KHz = 5.56Mhz (the 50Khz pass band is almost un importent- almost out of the calculation). You now have 5 MHz range to drop from full low pass at 50KH to blocking the energy above 5MHz.
A pole has 20dB per decade slope, and we have 2 decades (50KH, 500Khz, 5MHz is 2 decade). So a single pole yield 40dB. Take 3 poles and you have 120dB attenuation of any energy above 5MHz. The filter is low order (3 poles) so it is practical, and one can do it all with a single or a pair of Opamps. Low order filers have more linear phase, and we placed the poles at 50KHz not at around 20KHz so with a good design, the phase issue are moved to frequencies above hearing…
Folks get confused because they point out that 192KHz as having higher transition band then say 96Khz. And here I am talking about 11.2896MHz. So what is going on? Well, the FRONT END of a modern AD, as well as the BACK END of a modern DA operate at very fast rates (in the many MHZ). It is true that the end result is at many more bits at much lower rates, but from a filter design stand point, form what is needed to avoide aliasing and imaging, it does not matter. The filter of an up sampling or oversampling device needs to reject the energy above the modulator rate not the “final” AD data rate or the “Initial” DA data rate.
But this is audio. Folks heard something 50 years ago, and they hang on to the false notions for the rest of their lives. The fact is that with modern AD and DA’s the filter for a 44.1KHz is very similar to a filter for a 96KHz.
Please note that I am answering you about the anti aliasing filters which are analog filters. I included anti imaging filters which are also analog and the situation is very similar to anti aliasing (one is for an AD the other for DA). There are 2 more filter types that are digital, one is in the AD decimation, the other is in DA up sampling.
The digital filters at a 44.1KHz are somewhat tight, but one can do a real fine job, if one is willing to put the needed processing resources in, especially if one stays away from real low latency conversion, which is usually not a needed feature. At 88.2KHz there is plenty of room to do a real fine job. One can make a perfectly linear phase digital filter, but for low latency, people do what they can to reduce time delay, and they “cut corners”, so the phase becomes less then linear. Some argue that it does not matter that much. I think it needs to be better quantified, it may not matter to 1 degree of phase, but it may matter at 10 degrees…
I am not saying that filters do not matter. Everything matters to some degree. But the analog filters of 20 years ago mattered a lot. In fact, the analog filters were the bottle knack in performance, and they imposed very difficult compromises. But in today’s world, analog filters issues are not the overwhelming factors, and it is not just due to slow and constant evolution, it is due to the introduction of newer concepts (up sampling and oversampling). The improvement was a “sudden large step up”.
It is long past due that audio professionals stop dragging concepts from 2 dozen years ago into discussions about today’s technology. So much of the chatter about audio is about things that mattered long ago and matter so much less now. Technology does move forwards as some of you folks realize. We now have air in the tires, and gears in the cars, some cars have automatic transmission :-)
Regards
Dan Lavry