Anti-alias filtering

[netrom]

I've been thinking about this one for a while. Even though I've had my share of Fourier analysis and signal theory at the university, the theory wasn't directly related to audio, and in addition it's been a few years since then.

I these days, you get converters that are 24/192 kHz, and I read here on this forum (I think) that the advantage of having such high sampling rate is that you can implement an anti-alias filter with less steep low pass (dB/oct), since all filters (except linear phase filters) will introduce artifacts like phase shift, Gibbs "shooting" etc (especially if you have a steep cut off at Nyquist).

But when you have a less steep low-pass curve at the Nyquist frequency, will you dampen the desired frequency sufficiently (and thus avoid "folding-back" frequencies over Nyquist), considering that 24 bit converters have an extremely great dynamic bandwidth?

[Ethan Winer]

I imagine you'll get more answers if you post in the Geekslutz section.

[netrom]

Ah. Maybe you're right. But it's not diode-geeky enough!

[Francis Vaughan]

Briefly, this is oft quoted, and wrong. It confuses oversampling with higher sample rates, and they are most definitely not the same thing.

If you sample at the Nyquist rate (or a small margin above it) you do indeed need a brick wall filter, and yes, there are no realisable filters that don't involve nasty issues in the passband. This is why modern digital devices run at much higher internal sample rates - it allows a trade-off between a range of issues, amongst them easing the design of the anti-alias (or in a DAC - reconstruction) filter.

However if you have a 96-kHz sample rate ADC it is currently implicit that this ADC has a frequency response that extends to 40-kHz odd. This means that it does not make use of the extra bandwidth to apply a slower anti-alias filter - rather it has simply scaled everything up by a factor of two from a 48-kHz ADC. Assuming that the ADC is otherwise identical in design to the 48-kHz version this might actually mean that an even more aggressive anti-alias filter is required at 96-kHz - not a lesser one - one with even worse passband ripple and phase anomalies.

Oversampling involves the use of higher internal sampling rates at lower bit resolution and the application of digital domain filtering (and noise shaping) to achieve the final result. This internal sampling rate is typically anything from 4 times to a hundred odd times faster than the nominal sample rate. The actual internal implementation striding the range from multi-bit to single bit delta sigma coders, and some in between.

[netrom]

Originally Posted by Francis Vaughan

Briefly, this is oft quoted, and wrong. It confuses oversampling with higher sample rates, and they are most definitely not the same thing.

If you sample at the Nyquist rate (or a small margin above it) you do indeed need a brick wall filter, and yes, there are no realisable filters that don't involve nasty issues in the passband. This is why modern digital devices run at much higher internal sample rates - it allows a trade-off between a range of issues, amongst them easing the design of the anti-alias (or in a DAC - reconstruction) filter.

However if you have a 96-kHz sample rate ADC it is currently implicit that this ADC has a frequency response that extends to 40-kHz odd. This means that it does not make use of the extra bandwidth to apply a slower anti-alias filter - rather it has simply scaled everything up by a factor of two from a 48-kHz ADC. Assuming that the ADC is otherwise identical in design to the 48-kHz version this might actually mean that an even more aggressive anti-alias filter is required at 96-kHz - not a lesser one - one with even worse passband ripple and phase anomalies.

Oversampling involves the use of higher internal sampling rates at lower bit resolution and the application of digital domain filtering (and noise shaping) to achieve the final result. This internal sampling rate is typically anything from 4 times to a hundred odd times faster than the nominal sample rate. The actual internal implementation striding the range from multi-bit to single bit delta sigma coders, and some in between.

Great response! Well, I guess I should learn a thing or two about oversampling then. Nowadays I guess it's easier and better to implement digital filters, compared to analog filters.

[JEGG]

Originally Posted by Francis Vaughan

.............. Assuming that the ADC is otherwise identical in design to the 48-kHz version this might actually mean that an even more aggressive anti-alias filter is required at 96-kHz - not a lesser one - one with even worse passband ripple and phase anomalies. .................

Could one argue that even with a steeper brick wall filter, the undesired effects would still occur far above the program material, and our hearing? And when down sampled, one gets 44.1 w/o the effects of a 20-k low pass filter? With 96-k and the right program material, I notice that not only is the upper end is far more open (but not necessarily extended), but also non HF material is more "solid" or "large," both being rather vague terms!

Originally Posted by Francis Vaughan

...............Oversampling involves the use of higher internal sampling rates at lower bit resolution and the application of digital domain filtering (and noise shaping) to achieve the final result. This internal sampling rate is typically anything from 4 times to a hundred odd times faster than the nominal sample rate. The actual internal implementation striding the range from multi-bit to single bit delta sigma coders, and some in between.

This is beginning to sound a bit (pun not intended) like the Korg. True?

And from the world of photography: Cameras come with a wide variety of Nyquist filters. Some "stronger," some not. The trade off is whether moire will be evident. Some cameras have to Nyquist filter at all.

Could a point be made for not extending mic response to 40, 50, or even 100-k, employing higher sampling rates than 44.1, and just forgetting the Nyquist filter altogether? Yes, I realize that's never going to happen. But it is happening in the photography word-admittedly, not common. But "weaker" Nyquist filters are common in the photography world.

[Francis Vaughan]

Originally Posted by JEGG

Could one argue that even with a steeper brick wall filter, the undesired effects would still occur far above the program material, and our hearing?

Sadly no. 96kHz is only double 48kHz. One octave. Not all that far. The phase effects can reach a long way back.

And when down sampled, one gets 44.1 w/o the effects of a 20-k low pass filter?

Depends. The down sampling starts to look a lot like an oversampling filter. But if you do this, why bother with the brick wall filter in the first place? It just adds grief for no useful effect.

With 96-k and the right program material, I notice that not only is the upper end is far more open (but not necessarily extended), but also non HF material is more "solid" or "large," both being rather vague terms!

You always need to be careful in making comparisons, because you have changed a huge amount in the ADC when changing sample rates, and the effects you hear are not necessarily a result of the sample rate change itself. They can come from the change in filters, change in resistance to second order effects - such as intermodulation - and so on. (I have personally often observed that changes to the high frequency reproduction appears to change low frequencies under certain circumstances - there is good psycho-acoustic theory as to why. It need not mean anything changed to the low frequencies in the recording chain.)

This is beginning to sound a bit (pun not intended) like the Korg. True?

If you mean it is like DSD, well sort of. But only in part. DSD omits the digital filter and simply preserves the output from the sigma delta codec.

And from the world of photography: Cameras come with a wide variety of Nyquist filters. Some "stronger," some not. The trade off is whether moire will be evident. Some cameras have to Nyquist filter at all.

Yes, this comes about because the aliasing arefacts are often reasonably benign - moire patterns. Unless you make a habit of photographing plaid fabrics you end up with a perceived sharper resolution, although it is sub-Nyquist and not real. In audio we don't have that luxury - the ear is particularly sensitive to the results. We get our perceptual slack in different places (different spaces in fact.)

Could a point be made for not extending mic response to 40, 50, or even 100-k, employing higher sampling rates than 44.1, and just forgetting the Nyquist filter altogether?

If you extended the sample rate and left the mic response alone, maybe. But if you extend them both you will get aliasing. The aliasing products can reach all the way down to DC even if they were generated from energy at high ultrasonic frequencies. That is the whole point of the problem. You must eliminate all energy that has a frequency higher than half the sample rate. Otherwise the energy folds down into the passband. The manner in which it folds down is a reflection. (Frequency difference.) Energy very close to the sample rate folds down to very low frequencies - so you always get stuff in the audio passband.

But "weaker" Nyquist filters are common in the photography world.

There was a spate of "weaker" reconstruction filters in high end audio years ago. It didn't last. Clearly a manufactured coloured sound, swept away by better conventional technology. As I wrote above, the trick to get a massaged "sharper" resolution in digital photography doesn't directly translate to audio. Digital photography uses the filter in part to cope with the vagaries of the Bayer pixel pattern. Use a Foveon X3 sensor and it isn't nearly as much an issue. That said, I still lust after an M8 - and it has no such filter either. (But I'm a medium format guy and I really lust after a Phase-one 645.)

[JEGG]

Thanks very much for that well considered reply!

[theblue1]

Great info, Francis!

Thanks.

[chrisj]

Originally Posted by JEGG

With 96-k and the right program material, I notice that not only is the upper end is far more open (but not necessarily extended), but also non HF material is more "solid" or "large," both being rather vague terms!

More samples at a given bit depth over a given time is much like having more bit depth with the same samples. If you're doing a low frequency, packing more samples into that area gives you a closer approximation of what that signal level is.

[JEGG]

Originally Posted by chrisj

More samples at a given bit depth over a given time is much like having more bit depth with the same samples. If you're doing a low frequency, packing more samples into that area gives you a closer approximation of what that signal level is.

Hmmm. Given that I am speaking well beyond my very limited knowledge:

I do see the logic of what you're saying, particularly in the context of DSD, the Korg, and so on; but my understanding of bit depth suggests that it has only to do with noise/dynamic range. Not resolution.

Would you or Francis have a go at explaining this?