Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Nika Aldrich]

Chuck wrote on Wed, 16 June 2004 06:32

On the practical side,, yes, the DF1704 is an oversampling filter. Yes it feeds the PCM1704 DAC. Yes I have gentle analog filters behind the DAC. The idea of an oversampling filter actually IS that you don't need an analog brickwall filter behind your DAC anymore.

Chuck,

The problem with base rate sampling is as Dennis identified - it is very difficult to design a base-rate, analog reconstruction filter that meets the ripple requirements, the steep attenuation requirements, and the phase requirements simultaneously.  The advantage of oversampling is that we can use a linear-phase, digital reconstruction filter to do half the work, effectively tackling the steep-slope requirements of the filter.  In an 8x DAC this ensures that no frequency content is present between 20kHz and 384kHz, but upon reconstruction, material above 384kHz will still be present.  An analog filter needs to remove all of that content in order to complete the reconstruction process.

In your diagrams on your webpage you clearly did not have any reconstruction at all.  Look, for example, at the second graphic on the page - that of the 6kHz waveform.  That diagram has no filtering on it at all and represents only the sample points - not the waveform that the sample points represent.  The same is true with all of the "green" diagrams on your page.

Moving on to the oscilloscope shots, notice the difference between the "green" 21kHz diagram and the 21kHz oscilloscope shot.  The oscilloscope photo shows SOME reconstruction filtering in place (as you said, 8x filtering) but still has illegal frequency content above 384kHz.  That illegal content makes it look amplitude modulated.  Notice the difference in the amplitude modulation when SOME filtering is done as opposed to no filtering being done?  When COMPLETE filtering is done you will notice the AM disappears completely, as the AM inherently contains frequency content that is out of bounds of the Nyquist frequency.  The same is true with the 22kHz waveforms you show.  The AM is greatly attenuated in your photograph as opposed to the "green" figure because you have done SOME filtering.  Finish the process.

Quote:

I am not measuring with poor equipment. I have tried several DACs of my own make and other products. I have tried with old and modern R2Rs and modern sigma-delta DACs (f.e. DSD1791).

If you are getting amplitude modulation then the reconstruction filtering is not complete.  It's kind of simple.

Nika.

[Nika Aldrich]

Chuck wrote on Wed, 16 June 2004 06:58

"A well-known consequence of the sampling theorem is that a signal cannot be both bandlimited and time-limited..."

Right.  And tell me, when you put an IIR filter on the DAC output, is the waveform actually time-limited?  

Further, it is acceptable for the waveform to not be band-limited, so long as the frequency content above N creates aliasing that is below the dynamic range of the system.  You know that an FIR filter will inherently have frequency content in the stop-band.  We just care that that frequency content creates aliasing that is below audibility.

Quote:

Well, for being used with Shannon's theorem of being completely describable by samples of at least (for Nika) twice the speed, it must be bandlimited.

See above.  Both of my above statements apply - first it doesn't have to be time limited.  While the sample points may be of specific time, once the filter is applied it is no longer a time-limited waveform.  That's where the "ringing" you speak of comes in.  The longer the "ringing" the more accurate the reconstruction.

Further, however, it is fine for aliasing to exist, so long as it is amplitude limited.

Quote:

Does that mean, that it is not possible to perfectly bandlimit a piece of music (that I call truly time-limited) ?

See above.

Quote:

And does it mean that if I manage to perfectly bandlimit that piece, that it will ring on forever ?

YES!!  Exactly!  But only if you use an analog filter on the output!

Quote:

So, as I cannot truly bandlimit it, if I do not want it to go on forever, ...

Why not!?

Quote:

And if I am able to bandlimit it 100% the music is gone, as I have built an oscillator. So how can we make use of Shannons theorem with music?   Wow. I was not that wrong. I think I am really in the sweet spot of it...

Yes, you are just on the cusp of some serious learning.

Nika.

[Nika Aldrich]

Chuck wrote on Wed, 16 June 2004 14:25

And if you get a DAC doing something like a perfect 21kHz sine at 44.1 sample-rate, it will sound awful, as it will ring very very long.

NO!   The ringing in the filter contains frequencies that are the iinverse of its transition band.  If the transition band is relegated to the range of 20kHz to 22kHz then the ringing contains only those frequencies as well and is entirely inaudible.  Try it.  

Quote:

As I posted earlier, a result of Shannon's theory is, that the more perfect you are able to limit the bandwidth, the less time-limited (ringing) your signal becomes.

Right!  The ringing is GOOD!  

Quote:

Any kind of oversampling is an attempt to reduce one kind of distortion (beating) at the expense of another kind of distortion (ringing). So you can choose what kind of distortion you would like more.

NO!  Any kind of FILTER is an attempt to remove the frequencies that are inherently "illegal" with regards to Shannon.  Yes, the system will have ringing, as it takes that long to dissipate out the frequency content in the waveform after any last transiental material.  This ringing is essentially prescribed by Nyquist and is not any form of distortion.  It is the inherent nature of a band-limited waveform.  The advantage of OVERSAMPLING is just to be able to use digital filters that help reduce phase distortion and keep the filtering stable without the distortion and noise of analog components required to filter that steeply.

Quote:

You can eliminate both kinds of distortion if you record with a high enough sample-rate (4..5 x 44.1kHz) and don't use any bandlimiting during recording and also no oversampling during playback. The "reconstruction" filter will be of low order, as you only have to filter the odd order square products. In this case you would not even call it "reconstruction filter" as reconstruction is not necessary because you have enough samples per wave. This way your beat products (amplitude modulation) will be much smaller than with 44.1 plus oversampling AND you will have extremely short ringing. This is what is called a time-correct reproduction.

Nope.  As you indicated above, a "time correct" reproduction inherently cannot be time-limited.  Unless your system has long filters it is not "time correct."  Further, if you filter properly there IS NO AMPLITUDE MODULATION.  You must get away from the idea that there IS amplitude modulation somehow.  That is ONLY the result of a lack of filtering.  So we don't need to talk about ways to "get rid of it."  "IT" is not an inherent part of the sampling process.  "IT" is only a part of a broken sampling system.

Quote:

Of course, you cannot get to that high level of sound quality with sigma-delta converters, as they all use oversampling.

This is also incorrect, but we'll save DSMs until after we're sure you have traditional sampling down.

Nika.

[Chuck]

Good morning Nika,,

you still do not get the point.

As Shannon's proof postulates that a bandlimited function cannot time-limited, and it is a prerequisite to feed the sampler with a bandlimited function, then it must be infinite for the sampling theorem to work.

As music is not infinite, it cannot be perfectly bandlimited and therefore does not apply to the prerequisite of the sampling theorem.

If you make music bandlimited it is not music anymore, as you made it oscillate into infinity.

You can put it this or that way. Either you get amplitude modulation if you sample too slow (and Fs/2 is much too slow) OR you treat the signal as if it was (suppose the original was) time-unlimited, and then you distort it with the ringing of your oversampling filter.

As I said earlier, when you sample so slow, you have to chose which distortion you want to have. You cannot eliminate both.

I totally sympathize with you in that you try to defend something that we have believed in for so long. But our believe was because we had no deeper insight into this area of mathematics.

It is perfectly obvious that Shannon's sampling theorem works for a infinite signal, like one or thousand sines you put together, okay, only if you have much time to look at that signal as his interpolation formula is an infinite sum.

But it is also intuitively obvious AND and outcome of his mathematical proof, that you cannot apply it to music, as the very time-limitness of a musical or speech signal violates the required bandlimit.

What more can I say ?

Charles

[Nika Aldrich]

Chuck wrote on Wed, 16 June 2004 16:25

Good morning Nika,, you still do not get the point. As Shannon's proof postulates that a bandlimited function cannot time-limited, and it is a prerequisite to feed the sampler with a bandlimited function, then it must be infinite for the sampling theorem to work.

I agree.

Quote:

As music is not infinite, it cannot be perfectly bandlimited and therefore does not apply to the prerequisite of the sampling theorem.

Music is infinite if you put an IIR filter on it.

Quote:

If you make music bandlimited it is not music anymore, as you made it oscillate into infinity.

You are extrapolating unncessarily.  The fact that it oscillates into infinity does not make it no longer music.  Do you not agree that ANY IIR filter is an infinite function?  Does that mean we can NEVER use IIR filters in music?

Quote:

I totally sympathize with you in that you try to defend something that we have believed in for so long. But our believe was because we had no deeper insight into this area of mathematics.

Chuck, I don't know a nice way to say that you are using the math incompletely and you simply do not understand the details of WHY it works and are insisting that it doesn't, and until you are willing and ready to open your mind and listen to what the rest of us are telling you, and put down your confidence that you have somehow defeated the basis of the digital foundations of our world, then this is going to be an annoyingly long conversation.  You are simply not correct, and the first step is to get you to understand that and recognize that there is an opportunity for this to be the case.  Once you get to that point you will start asking questions that will allow us to help clarify these matters for you.  

Quote:

It is perfectly obvious that Shannon's sampling theorem works for a infinite signal, like one or thousand sines you put together, okay, only if you have much time to look at that signal as his interpolation formula is an infinite sum.

Tell me this.  Let's say that we DO time-limit the signal.  Let's say that we put a really long ringing on it, but not an infinite ringing.  Let's say that the ringing goes on for, say, 1 second, and is properly windowed to allow it to fade into oblivion within that 1 second.  While this is indeed time-limited, and this relegates the frequency content to be infinite, do you agree that we can control the amplitude of that frequency content - that we can, say, filter it so that none of it exists above, say, -120dBFS?  

Quote:

But it is also intuitively obvious AND and outcome of his mathematical proof, that you cannot apply it to music, as the very time-limitness of a musical or speech signal violates the required bandlimit.

Just because I stop speaking does not mean that the waveform stops.  

Again, is an IIR filter not infinite?

Nika.

[Chuck]

Nika Aldrich wrote on Wed, 16 June 2004 17:37

Does that mean we can NEVER use IIR filters in music? Nika.

Yes, it means exactly this.

Charles

[Nika Aldrich]

Quote:

Nika: Does this mean we can never use IIR filters in music?

Quote:

Chuck: Yes, it means exactly this.

Tell me, does that mean we can not use speakers?  A speaker is an IIR filter, no?  It rings infinitely after stimulated.

For that matter, any transducer is an IIR filter, including guitar strings, the brass on a trumpet, the lid on a violin, the soundboard on a piano, a microphone, the vocal chords, etc.  

Are these IIR filters to be eliminated completely from music?

Nika.

[Chuck]

Nika Aldrich wrote on Wed, 16 June 2004 17:56

Tell me, does that mean we can not use speakers?  A speaker is an IIR filter, no?  It rings infinitely after stimulated. Nika.

A string and  a speaker rings after the impact (impulse). An oversampling filter also rings in front of the impulse.

Sounds in music don't do this.  If I hit a key, string or drum there will be no lookahead ringing in my ears, before I have hit it.

But because a oversampling filter treats any input as stationary and repetitive, it introduces a ring before the real thing happens.

But all those things can also be experienced by listening to different filter responses, which are selectable with many of todays DA  chips.

You seem to have very few listening experience.

Well, if listening is no fun for you, maybe now you know why

Charles

[Nika Aldrich]

Chuck wrote on Wed, 16 June 2004 17:22

Nika Aldrich wrote on Wed, 16 June 2004 17:56 Tell me, does that mean we can not use speakers?  A speaker is an IIR filter, no?  It rings infinitely after stimulated. Nika. A string and  a speaker rings after the impact (impulse). An oversampling filter also rings in front of the impulse.

That's an FIR filter, not an IIR filter.  Let's get back to IIR filters.  You said that you can't use IIR filters with music.  Are you still in agreement with this?

Quote:

Sounds in music don't do this.  If I hit a key, string or drum there will be no lookahead ringing in my ears, before I have hit it.

Believe me, we'll get back to FIRs.  First, however, we need to get some fundamentals taken care of.

Nika.

[Paul Frindle]

Chuck wrote on Wed, 16 June 2004 17:22

Nika Aldrich wrote on Wed, 16 June 2004 17:56 Tell me, does that mean we can not use speakers?  A speaker is an IIR filter, no?  It rings infinitely after stimulated. Nika. A string and  a speaker rings after the impact (impulse). An oversampling filter also rings in front of the impulse. Sounds in music don't do this.  If I hit a key, string or drum there will be no lookahead ringing in my ears, before I have hit it. But because a oversampling filter treats any input as stationary and repetitive, it introduces a ring before the real thing happens. But all those things can also be experienced by listening to different filter responses, which are selectable with many of todays DA  chips. You seem to have very few listening experience. Well, if listening is no fun for you, maybe now you know why Charles

Oh jeez!! Time to hit the bottle I think  

[Chuck]

Nika Aldrich wrote on Wed, 16 June 2004 18:27

Believe me, we'll get back to FIRs.  First, however, we need to get some fundamentals taken care of. Nika.

Hi Nika,,

before I jump into another trap of yours, let me finish my work. I may come back to you tomorrow. Use that time for contemplation.

Have a great day.

Charles

[Corey Bowers]

thermionic wrote on Tue, 15 June 2004 13:47

Charles's site is an intriguing source of information, check this link and see what you think: http://www.altmann.haan.de/tubeolator/default.htm The BYOB amp, is it really 700 Euros?? Justin

[sfdennis]

Chuck,

Thanks for the reply.

You didn’t tell us the corner frequency for your filter. I’m now also curious about the word lengths going into and out of the DF1704 during your tests. It is probably not important, but I’m curious just the same.

-Dennis

[Nika Aldrich]

It can only possibly be a trap if your understanding has some holes that aren't addressed yet.


Just to recap - we agree that you can't have both a time-limited and band-limited waveform.  It has to be one or the other.

We also agree that IIR filters inherently make waveforms not time-limited because they ring infinitely.  

We also agree that speakers, transducers, etc. are all IIR filters (including your eardrum) and that those things are used in music all the time.

So why, exactly, should we not use an IIR filter on the output of our D/A converters?  It will make it band-limited and not time-limited, just like a speaker does.

The problem with your converters is that they ARE time limited, which means that they AREN'T band limited, which means that you have excess frequency content (above Nyquist) in them which manifests itself as amplitude modulation and means that the waveforms don't conform to Nyquist.  Put an approrpriate IIR filter on the output and it will make it a time-unlimited waveform with band-limited content, the AM will go away without the need for higher sample rates, and you'll end up with a waveform that conforms to Shannon/Nyquist.

Try the experiment.  The converters will sound better also.   Fortunately, your ears are a LP IIR filter and are doing the filtering for you so aren't hearing the AM anyway, but relying on the ears to do the reconstruction causes problems of its own and you may indeed hear some forms of distortion with your current design.  Best to do the filtering linearly - which the ear is not.  I know you're concerned about that ringing after the event.  The ringing, however, again only contains frequency content in the transition band.  Since the IIR LPF you use will have a transition band entirely contained above the audible range you won't hear the ringing - just like you don't hear the ringing with other IIF LPFs, like speakers, your eardrums, etc.

Ask if you have questions.

Nika.

[Zoesch]

Nika Aldrich wrote on Thu, 17 June 2004 01:56

Tell me, does that mean we can not use speakers?  A speaker is an IIR filter, no?  It rings infinitely after stimulated.

No, and I think you're getting the speaker construction mixed up with the characteristics of the transducer itself.

If what you are referring to is "infinite baffle" cabinets, then the answer is... not quite.

I still haven't seen a speaker cabinet that will oscilate infinitely after an exitation... again, the second law of thermodynamics prevents things in real life from exhibiting that behavior (Or else they would rattle and fall apart as the materials would behave in accordance with tension and stress)

Quote:

For that matter, any transducer is an IIR filter, including guitar strings, the brass on a trumpet, the lid on a violin, the soundboard on a piano, a microphone, the vocal chords, etc.

Actually, there's no feedback loop in acoustic instruments (Or in normal transducers) so their behaviour is completely different from that of an IIR filter... they can resonate of course, but they don't exhibit infinite resonance and where they do, they fall apart.