Sampling and Filtering Discussion Split From MQA Thread

[bogi]

  

44 minutes ago, botrytis said:

I think I would listen to Mani - he is being very reasonable.

 

It'd not about listening to Mani, but about an explanation, which is understandable and fits to theory.

I think I found it. Every ADC contains not only anti aliasing analog filter at input, but also digital filter at output side. You can find it in any ADC block diagram. Without that digital filter the high frequency content would be present at digital output.

[manisandher]

22 hours ago, bogi said:

Point of oversampling is to make that distance bigger to allow easier analog filtering of D/A converter stage output.

 

22 hours ago, bogi said:

But if f_max > fs/2, spectral replicas are overlapping. It means at least part of the nearest replica appears in audio band. That is called aliasing into audio band.

 

You're conflating filtering in D/A conversion with filtering in A/D conversion. [Too] many people do this. There is a fundamental difference.

 

"Aliasing" does not occur in D/A conversion, it occurs during sampling (A/D conversion, or downsampling). Without an anti-aliasing filter, any aliasing will lie <fs/2. This is really bad news if fs=44.1kHz especially.

 

"Imaging" occurs in D/A conversion. Without an anti-imaging filter, any imaging will lie >fs/2. This may or maynot be bad news, depending on your playback chain.

 

How you could imagine that there's any content (signal, noise and/or distortion) >fs/2 in a digital audio file with a sample rate of fs is beyond me. But there you go.

 

Mani.

[Jud]

3 hours ago, manisandher said:

"Aliasing" does not occur in D/A conversion, it occurs during sampling (A/D conversion, or downsampling). Without an anti-aliasing filter, any aliasing will lie <fs/2. This is really bad news if fs=44.1kHz especially.

 

With modern ADCs operating in the MHz range, it would seem dreadfully sloppy to have aliasing in the audible band. What reason, then, for some well-thought-of filtering software done by (I think) reasonably intelligent people with (I think) a good knowledge of digital audio and filtering to include, for example, apodizing filters?

[manisandher]

8 hours ago, Jud said:

What reason, then, for some well-thought-of filtering software done by (I think) reasonably intelligent people with (I think) a good knowledge of digital audio and filtering to include, for example, apodizing filters?

 

I would think that RME have good knowledge of digital audio and filtering. From the manual for my ADI-2 Pro:

 

"On the AD side the ADI-2 Pro offers four filters: Short Delay Sharp, Short Delay Slow, Sharp and Slow... SD Sharp and Sharp offer the most linear frequency response and highest suppression of mirroring (aliasing) at high frequency input signals. SD Slow and Slow try to combine a high aliasing suppression with an optimal impulse response, but start to act early within the higher audible range at standard sample rates."

 

"Please also note that Slow and NOS filters cause much more aliasing into the audio band and out-of-band noise than Sharp filters."

 

[Highlighting mine.]

 

They use a single sample impulse as the analogue source signal to measure the impulse response, which is so far from anything occuring in the real world, and therefore real music, it's ridiculous IMO. (I'm sure this applies to electronic music too.)

 

These things are quite easy to test with software such as DeltaWave. It's easy to show that the best nulls are achieved using sharp/brickwall linear-phase filters (in both ADCs and DACs). But they've been around a long time and don't sound very sexy. I mean, which of "apodizing" or "FIR" sounds better from a marketing POV?

 

The only good reason I can think of for opting for anything other than a linear-phase filter is latency, which can be a consideration in professional audio and AV.

 

Mani.

[manisandher]

8 hours ago, Jud said:

 

With modern ADCs operating in the MHz range...

 

Yes, but remember, that's not the sample rate. My RME uses a modern S-D ADC chip, and yet there's aliasing in the audioband when using one of its 'sloppy' filters.

 

Mani.

[bogi]

12 hours ago, manisandher said:

How you could imagine that there's any content (signal, noise and/or distortion) >fs/2 in a digital audio file with a sample rate of fs is beyond me. But there you go.

Digital file represents all the spectral replicas from my last picture, but of course only the content below fs/2 is of interest. If you would convert it to analog without filtering, you would get those replicas at output too. DACs use filtering of high frequency content, therefore one can see full amplitude spectral replicas rather only in pictures describing sampling theory but not at usual DAC output. But that's the principle. Digital file codes them all.

 

12 hours ago, manisandher said:

You're conflating filtering in D/A conversion with filtering in A/D conversion.

My intention in that part of my post was to point to a difference between upsampling and downsampling in relation to spectral replicas and to point to relation of aliasing to overlapping spectral replicas.

Oversampling and delta sigma modulation is used in both delta sigma ADCs and DACs. So part of operations in both cases are similar. ADCs and DACs use both analog and digital filtering, just in reversed order.

[Jud]

6 hours ago, manisandher said:

They use a single sample impulse as the analogue source signal to measure the impulse response, which is so far from anything occuring in the real world, and therefore real music,

Have you done any analysis to determine, for example, what triggers the “Apod” counter In HQPlayer?

[manisandher]

50 minutes ago, Jud said:

Have you done any analysis to determine, for example, what triggers the “Apod” counter In HQPlayer?

 

It's been a long while since I looked into HQP's filters. Once I discovered that sharp FIR filters null to <-210dB in the audioband, I just stopped looking altogether. I'm totally content with all my ADCs/DACs being set to brickwall filters.

 

If/when I get some time, I might revisit this because I find it really interesting. And as you've said, there must be a reason why some really smart people offer filters other than sharp FIR. But right now, I can't see why from a SQ perspective.

 

Edit: Quite a while ago now, I recall sharing a few posts with @Miskaabout this - I asked why anything other than FIRs are used. I can't remember what he said exactly, but something about correcting errors in the audio, I think.

 

Mani.

[Archimago]

44 minutes ago, manisandher said:

 

It's been a long while since I looked into HQP's filters. Once I discovered that sharp FIR filters null to <-210dB in the audioband, I just stopped looking altogether. I'm totally content with all my ADCs/DACs being set to brickwall filters.

 

If/when I get some time, I might revisit this because I find it really interesting. And as you've said, there must be a reason why some really smart people offer filters other than sharp FIR. But right now, I can't see why from a SQ perspective.

 

Edit: Quite a while ago now, I recall sharing a few posts with @Miskaabout this - I asked why anything other than FIRs are used. I can't remember what he said exactly, but something about correcting errors in the audio, I think.

 

Mani.

 

Yeah Mani. If you find a good answer to this other than people not wanting to see Gibbs pre-ringing in the DAC impulse response output (not in itself a good reason IMO), let me know... 

[botrytis]

I love very open discussions like this. A good way to learn.

 

[Jud]

1 hour ago, manisandher said:

I can't remember what he said exactly, but something about correcting errors in the audio, I think.

Yep, he’s said as much here. What I’m curious about, since you’re not going to find the one-sample impulse in real music, is what sorts of errors those are. I know Miska has been less than complimentary about the results of some ADC processing for popular music.

[Currawong]

14 hours ago, bogi said:

Digital file represents all the spectral replicas from my last picture, but of course only the content below fs/2 is of interest. If you would convert it to analog without filtering, you would get those replicas at output too. DACs use filtering of high frequency content, therefore one can see full amplitude spectral replicas rather only in pictures describing sampling theory but not at usual DAC output. But that's the principle. Digital file codes them all.

What you're describing is caused by the DAC. It's not because there is higher frequency content in the data, as that's not physically possible. 

[danadam]

On 10/4/2023 at 8:14 PM, manisandher said:

How you could imagine that there's any content (signal, noise and/or distortion) >fs/2 in a digital audio file with a sample rate of fs is beyond me. But there you go.

I can see how it can be too abstract interpretation for some, but it makes sense to me. In that chapter on dpsguide.com they describe that the samples (the digital domain) are direct representation of the impulse train (the analog domain). The spectrum of the impulse train is infinite, with copies of the baseband at each side of multiples of fs, so the samples also represent an infinite spectrum with copies of the baseband at each side of multiplies of fs:

Quote

Now we need to examine the relationship between the impulse train and the discrete signal (an array of numbers). This one is easy; in terms of information content, they are identical. If one is known, it is trivial to calculate the other.

 

You get [0 - fs/2] frequencies in the DA process only after applying the anti-image filter. You may ask, what difference does it make, if in the end you do have to apply the anti-image filter. Well, the anti-image filter does not necessarily has to be a lowpass at fs/2. No one stops you (a general you) from using a bandpass filter to retain one of the images instead of the baseband. AFAICT that's actually how undersampling works. Of course in such case the corresponding anti-aliasing filter used during AD process would have to be a bandpass filter too.

 

In general case, I would rather say that a file with sampling frequency fs contains a signal with bandwidth fs/2 and not necessarily [0 - fs/2] frequencies. Where that bandwidth starts will depend on the application. But yes, in audio it will usually/always start at 0.

 

And just to be clear, no one is saying (certainly not @bogi) that a digital file can represent any arbitrary frequency above fs/2. That would be ridiculous. Only images/copies of the baseband, and that's a pretty big restriction.

 

That's just my view on it, so no worries, I won't try to convince anyone 🙂

 

[manisandher]

6 hours ago, danadam said:

I can see how it can be too abstract interpretation for some, but it makes sense to me...

 

I agree with everything you've written 🙂.

 

6 hours ago, danadam said:

... a file with sampling frequency fs contains a signal with bandwidth fs/2...

 

This is the point I've been making.

 

But I also totally agree with the following:

 

6 hours ago, danadam said:

The spectrum of the impulse train is infinite, with copies of the baseband at each side of multiples of fs, so the samples also represent an infinite spectrum with copies of the baseband at each side of multiplies of fs...

 

And this is where measurements of the analogue output of DAC into the MHz region become important (to prevent IMD).

 

Thanks for your post. I think it sums everything up nicely.

 

Mani.

[manisandher]

Reading back over @bogi's posts in this thread, I agree with everything, and think his explanations are actually very good.

 

But where we went wrong I think is here:

 

On 10/4/2023 at 6:46 AM, bogi said:

Without filtering you get set of spectral replicas at digital output, including the range (fs/2, f), and above fs, like demonstrated on pictures d and f in my previous post.

 

My feeling was that the digital output of the sampling process (ADC or downsampling) gives us the baseband, and nothing else. And my point was that the signal in the baseband only extends to fs/2.

 

Mani.

[bogi]

9 hours ago, Currawong said:

What you're describing is caused by the DAC. It's not because there is higher frequency content in the data, as that's not physically possible.

 

Not right. Sampling theory does not speak about DAC. It tells that the sampled digital content represents all the spectral replicas.

[manisandher]

[bogi]

20 minutes ago, manisandher said:

But where we went wrong I think is here:

 

On 10/4/2023 at 7:46 AM, bogi said:

Without filtering you get set of spectral replicas at digital output, including the range (fs/2, f), and above fs, like demonstrated on pictures d and f in my previous post.

 

25 minutes ago, manisandher said:

My feeling was that the digital output of the sampling process (ADC or downsampling) gives us the baseband, and nothing else. And my point was that the signal in the baseband only extends to fs/2.

 

It's about how we look at digital signal. If we look at it as to coding only, then yes, quantized signal levels in that code are related to baseband. But if we look what for signal is encoded by that code, it encodes all those spectral replicas.

 

Where I was initially incorrect was an assumption that with digital filtering one can remove spectral replicas. You can digitally filter signal only up to fs/2. Then the filtered effect will be reflected in spectral replicas too. With analog filtering you dont't get any fs related restriction.

 

[Shadorne]

On 10/2/2023 at 2:16 PM, manisandher said:

 

Yep.

 

 

The Gibbs Effect is not an artifact of filtering, but rather an inevitable consequence of bandlimiting. You could have a perfect anti-aliasing filter, and the Gibbs Effect will still exist.

 

As @Currawonghas said, it only peaks its ugly head with signals requiring a larger-than-Nyquist bandwidth, e.g. a square wave, which is made up of a fundamental plus an infinite series of odd harmonics. Clearly, this will be bandlimited by the ADC’s anti-aliasing filter, which will only allow a finite number of odd harmonics through before its Nyquist cutoff. This will cause a ripple around the sharp edges... irrespective of the anti-aliasing filter used.

 

All music signals reaching a DAC are necessarily bandlimited, so no additional 'ringing' can be added by any anti-imaging filter. Any talk of 'ringing' due to filters is nonsense.

 

Mani.

Good to see that some people clearly understand the urban myth of pre-ringing.

[Fokus]

Quote

15 hours ago, danadam said:

And just to be clear, no one is saying (certainly not @bogi) that a digital file can represent any arbitrary frequency above fs/2. That would be ridiculous. Only images/copies of the baseband, and that's a pretty big restriction.

 

 

 

This is actually not quite correct.

 

A system sampling at Fs can represent a signal of any frequency, provided that this signal's spectrum does not occupy a stretch exceeding Fs/2 in length on the frequency axis. In other words, the band of interest is no longer the traditional baseband 0 - Fs/2, but rather Fo - Fo+Fs/2. Upon reconstruction the correct image has to be selected by a band filter.

 

This property is used in telecomms, and also in MQA. This is exactly how they, given an Fs=96kHz original,  'fold' the signal range of 24-48kHz into an Fs=48kHz distribution file.

 

 

 

[bogi]

16 hours ago, danadam said:

Only images/copies of the baseband, and that's a pretty big restriction.

 

44 minutes ago, Fokus said:

This is actually not quite correct.
A system sampling at Fs can represent a signal of any frequency, provided that this signal's spectrum does not occupy a stretch exceeding Fs/2 in length on the frequency axis. In other words, the band of interest is no longer the traditional baseband 0 - Fs/2, but rather Fo - Fo+Fs/2. Upon reconstruction the correct image has to be selected by a band filter.

 

It looks to me that danadam is telling the same and that you both are speaking about the same restriction, only with different language.

When danadam's baseband is (0, fs/2) and two bands of it are processed/filtered differently, it is still true that without any filtering all spectral images reflect that baseband (they cannot be independent). That's danadam's point of view.

But those two bands (as parts of the same danadam's baseband) can contain independent signals, which can be filtered to be output as part of different spectral replicas (images). Thats Fokus's point of view.

 

At least how I understood it. :D

[Currawong]

22 hours ago, Fokus said:

This is actually not quite correct.

 

A system sampling at Fs can represent a signal of any frequency, provided that this signal's spectrum does not occupy a stretch exceeding Fs/2 in length on the frequency axis. In other words, the band of interest is no longer the traditional baseband 0 - Fs/2, but rather Fo - Fo+Fs/2. Upon reconstruction the correct image has to be selected by a band filter.

 

This property is used in telecomms, and also in MQA. This is exactly how they, given an Fs=96kHz original,  'fold' the signal range of 24-48kHz into an Fs=48kHz distribution file.

 

Are there some good, visual examples of this? When I've looked at MQA files, all I've seen is a strip of noise spanning a few dB at the highest frequencies, which supposedly contains the higher-frequency data. 

[Fokus]

23 hours ago, bogi said:

It looks to me that danadam is telling the same and that you both are speaking about the same restriction, only with different language

 

 

Actually, yes, we are saying the same.

 

I am not following this thread anymore, at least not with anything approaching full attention. I say the "no-one is saying ...:" and jumped on that.

 

1 hour ago, Currawong said:

 

Are there some good, visual examples of this?

 

What would you like to see?

 

I did most of my analysis in 2016-2017. As I have lost all interest in MQA years ago I did not keep all results, and neither do I remember exactly what results of others (Archi, Mansr, ...) were published how and where.

 

Below is the spectrum of some (now unknown) MQA track played through an MQA DAC and recorded back at 192kHz. The track was announced as 192kHz, and came in a 48kHz container. You can see that the 0-48kHz passband is genuine (e.g. the 28kHz spike, which is unique), and that everything above 48kHz is the (leakily filtered) first image of the base band. This corresponds to MQA being an effective channel for 96kHz sampled data, with very leaky upsampling above that.

 

None of this is a secret, or new, so I can barely imagine that this is what you want.

 

 

 

 

 

 

 

 

[botrytis]

But showing how bad the filters are is important and one of the defining characteristics of mqa.

[Tsarnik]

On 10/5/2023 at 3:38 PM, manisandher said:

 

It's been a long while since I looked into HQP's filters. Once I discovered that sharp FIR filters null to <-210dB in the audioband, I just stopped looking altogether. I'm totally content with all my ADCs/DACs being set to brickwall filters.

 

If/when I get some time, I might revisit this because I find it really interesting. And as you've said, there must be a reason why some really smart people offer filters other than sharp FIR. But right now, I can't see why from a SQ perspective.

 

Edit: Quite a while ago now, I recall sharing a few posts with @Miskaabout this - I asked why anything other than FIRs are used. I can't remember what he said exactly, but something about correcting errors in the audio, I think.

 

Mani.

Apart from baked-in aliases near Nyqist on some recordings that apodizing filters can help shaving off there are some old masterings with lots of glitches or loud masterings with digital clipping – thereby essentially containing illegal step functions that do will evoke the anti-imaging filter's famous step response. Similarly, there are some masterings with undamped energy right up to fs/2 so that even brickwall filters with a bandwidth of 0.99*fs/2 (and cut-off frequency <= fs/2) will get excited with.

 

So, if one wishes to reduce the 'dreaded ringing' with the playback of those recordings a broader transition band (e. g. a couple of thousand Hertz wide) can be chosen.

 

I am not making any claims about the ringing's audibility (or lack thereof). :-)