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192 khz vs 48 khz poll


esldude

192 khz sampled digital audio will record and reproduce analog musical signals below 20 khz more acc  

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Now on the other hand, would you please start a thread on digital filters. Please, pretty please with a cherry on top. Or discuss it here in my thread.

 

I don't have the knowledge to decide on some of the stuff Miska says. One thing Miska is talking about impulse response or response to above band signals. I just don't see anything to 'ring' the filter in music. I also don't measure those sorts of effects with equipment except single sample pulses. It therefore seems unlikely to me music has any transients or other pulses to ring the filter with the input filtering in place. Am I wrong about this?

 

So if you have knowledge of the filtering which you seem to have, discuss it, inform us, deign to answer our foolish questions please. And if I may put in a plug for Miska, he is most generous in deigning to respond to us. Or at least I have found him to be so. And Miska, if you read this, it isn't that I don't believe you, more I don't understand you (my fault I am sure not yours) so any further comments you could make would be welcome also.

 

And if I may be somewhat presumptuous. At least for myself and a few others, we seem to agree that if there is a difference in low vs high sample rate accuracy for sub 20khz signals, it is to be found in effects of filtering to achieve Nyquist conditions.

 

That is the point of this thread. To illuminate the idea that high rates are just better because there are more points of sampling to work with being the wrong picture in people's minds about how this works.

 

I would love to discuss digital filters if I can find the time. It is, however, very difficult to discuss digital filters in an accessible way with an audience having limited cursory background knowledge of such things as convolution and recursion...but let's give it a shot anyway.

 

I want to start with what Miska said, namely, about time domain and frequency domain dependence. Miska mentioned the notion of an impulse response. Every linear filter has three things: an impulse response, a step response, and a frequency response. They are in fact completely related to one another such that having just one you are able to determine the other two. This is because the step response is the discrete integration of the impulse response and the frequency response is the result of applying the FFT to the impulse response. Therefore, any change to any one, of course, affects the others.

 

Now, why does the improvement of performance in one domain cause the decline of performance in another (with respect to time and frequency domains)? This requires a knowledge of Fourier transforms properties that are difficult to word and easier to show using mathematical proofs. But suffice it to say that a narrowing in one domain manifests itself as a widening in the other because this is what the universe does.

 

About the shapes of some of the curves we see posted: The Fourier transform of a rectangular function is a sinc function and the Fourier transform of a sinc function is a rectangular function. So let's say I want to create a brick wall filter. Well, that looks like a rectangular function in the frequency domain, right? And I know that a sinc function in the time domain will Fourier transform to a rectangular function in the frequency domain (note: Fourier transforms map from the time domain to the frequency domain; the reverse direction is called the inverse Fourier transform). Now I now what kind of function I can convolve with my input to achieve the desired shape in the frequency domain. I also know that I can set the cutoff frequency of my brick wall by my choice of "width" in the sinc function keeping in mind that narrowing in the time domain causes a widening of the rectangular function in the frequency domain.

 

The example above is not the only way to do a digital filter but is a good example to give insight into the motivation behind digital filters. Incidentally, the above described filter takes the filter's impulse response and convolves it with the input signal. A mathematician would then call the impulse response of the filter the filter kernel. But note that the sinc function has infinite length from negative infinity to positive infinity along the time axis. In this case, we compose the sinc function with what is called a window function such that the resultant composed function has finite length and is near identical to the sinc function around its center of symmetry. This is an approximation. And since the resultant function is finite these filters are called finite impulse response (FIR) filters.

 

The other way to create a digital filter is to use recursion. Instead of dealing with a filter kernel, recursion coefficients are used. In the filter kernel method above each sample in the input is weighted by the kernel and then added together to arrive at an output (this is what convolution is). The recursive method actually involves not only weighting in the form of coefficients applied to input samples (like the filter kernel) but also coefficients applied to previously calculated output points to determine the output of the filter. When implemented correctly, this results in a slowly decaying sinusoid output for a simple impulse input (baseline to some value and immediately back to baseline). Because a decaying sinusoid mathematically never reaches zero and is therefore infinitely long these type filters are called infinite impulse response (IIR) filters. In practicality, however, the amplitude eventually falls below the round-off error of the system (the quantization noise floor) and can be ignored.

 

Just keep in mind that the step response and the frequency response are what are considered when talking about performance of a filter. The step response reveals performance in the time domain and the frequency response reveals performance in the frequency domain. Optimization in one domain adversely affects the other domain as Miska said. Again, it is not possible to optimize both at the same time, so it is the function or purpose of the filter that determines which domain will be optimized for.

 

See, probably better to start a blog or something like that.

Rob C

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I would love to discuss digital filters if I can find the time. It is, however, very difficult to discuss digital filters in an accessible way with an audience having limited cursory background knowledge of such things as convolution and recursion...but let's give it a shot anyway.

 

I want to start with what Miska said, namely, about time domain and frequency domain dependence. Miska mentioned the notion of an impulse response. Every linear filter has three things: an impulse response, a step response, and a frequency response. They are in fact completely related to one another such that having just one you are able to determine the other two. This is because the step response is the discrete integration of the impulse response and the frequency response is the result of applying the FFT to the impulse response. Therefore, any change to any one, of course, affects the others.

 

Now, why does the improvement of performance in one domain cause the decline of performance in another (with respect to time and frequency domains)? This requires a knowledge of Fourier transforms properties that are difficult to word and easier to show using mathematical proofs. But suffice it to say that a narrowing in one domain manifests itself as a widening in the other because this is what the universe does.

 

About the shapes of some of the curves we see posted: The Fourier transform of a rectangular function is a sinc function and the Fourier transform of a sinc function is a rectangular function. So let's say I want to create a brick wall filter. Well, that looks like a rectangular function in the frequency domain, right? And I know that a sinc function in the time domain will Fourier transform to a rectangular function in the frequency domain (note: Fourier transforms map from the time domain to the frequency domain; the reverse direction is called the inverse Fourier transform). Now I now what kind of function I can convolve with my input to achieve the desired shape in the frequency domain. I also know that I can set the cutoff frequency of my brick wall by my choice of "width" in the sinc function keeping in mind that narrowing in the time domain causes a widening of the rectangular function in the frequency domain.

 

The example above is not the only way to do a digital filter but is a good example to give insight into the motivation behind digital filters. Incidentally, the above described filter takes the filter's impulse response and convolves it with the input signal. A mathematician would then call the impulse response of the filter the filter kernel. But note that the sinc function has infinite length from negative infinity to positive infinity along the time axis. In this case, we compose the sinc function with what is called a window function such that the resultant composed function has finite length and is near identical to the sinc function around its center of symmetry. This is an approximation. And since the resultant function is finite these filters are called finite impulse response (FIR) filters.

 

The other way to create a digital filter is to use recursion. Instead of dealing with a filter kernel, recursion coefficients are used. In the filter kernel method above each sample in the input is weighted by the kernel and then added together to arrive at an output (this is what convolution is). The recursive method actually involves not only weighting in the form of coefficients applied to input samples (like the filter kernel) but also coefficients applied to previously calculated output points to determine the output of the filter. When implemented correctly, this results in a slowly decaying sinusoid output for a simple impulse input (baseline to some value and immediately back to baseline). Because a decaying sinusoid mathematically never reaches zero and is therefore infinitely long these type filters are called infinite impulse response (IIR) filters. In practicality, however, the amplitude eventually falls below the round-off error of the system (the quantization noise floor) and can be ignored.

 

Just keep in mind that the step response and the frequency response are what are considered when talking about performance of a filter. The step response reveals performance in the time domain and the frequency response reveals performance in the frequency domain. Optimization in one domain adversely affects the other domain as Miska said. Again, it is not possible to optimize both at the same time, so it is the function or purpose of the filter that determines which domain will be optimized for.

 

See, probably better to start a blog or something like that.

 

 

So, basically, we are all screwed.

In any dispute the intensity of feeling is inversely proportional to the value of the issues at stake ~ Sayre's Law

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I've done a lot of experimentation on this question, and I have to say that nobody I have ever played both a 24-bit, 48 KHz and a 24-bit, 96 KHz version of the same performance for has ever been able to detect any audible difference, and that includes me. OTOH, there is a clear difference between 44.1 and 48 KHz that most people can readily hear and most people seem to be able to hear a difference between 16-bit and 24-bit, but most can't put their finger on what it is they're hearing that is different. I've had responses like, "24-bit sounds cleaner," or "24-bit sounds smoother" and other nebulous responses like that. I generally record at 24-bit/96 KHz (when recording LPCM) because 24-bit gives the recordist more latitude. I have to say, that 16-bit/44.1 KHz audio CAN sound excellent, and I'm still convinced that with commercial recordings, the care taken in capturing and producing the finished product is far more important in terms of sound quality, than is either it's bit-depth or it's sampling rate (as long as we're taking 16/44.1 as a minimum, of course).

George

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Again, it is not possible to optimize both at the same time, so it is the function or purpose of the filter that determines which domain will be optimized for.

 

Of course you can try to balance to the extent possible. That's what I've been spending most of my effort on, to design a design method that gives as good and balanced performance as possible in both domains, with the requirements I've had in mind. Details of the design method determine how tight you can squeeze the two towards each other.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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I have to say, that 16-bit/44.1 KHz audio CAN sound excellent, and I'm still convinced that with commercial recordings, the care taken in capturing and producing the finished product is far more important in terms of sound quality, than is either it's bit-depth or it's sampling rate (as long as we're taking 16/44.1 as a minimum, of course).

 

I agree George.

 

I don't think bit depth or sample rate mean anything by themselves when it comes to sound quality or accuracy of reproduction.

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So, basically, we are all screwed.

 

Luckily not, increasing sampling rate helps relaxing the filter. We gain more frequency domain bandwidth to let the filter roll-off slower so we can afford it becoming shorter in time domain.

 

DSD is one extreme of this, it has Nyquist frequency of 1.4 MHz, so it won't have aliasing until that point. Simple fourth order analog filter is enough to eliminate aliasing in ADC and in practice you don't need even that much.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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I agree George.

 

I don't think bit depth or sample rate mean anything by themselves when it comes to sound quality or accuracy of reproduction.

 

The same is true regarding Dynamic Range analysis, by itself, and sound quality.

"Relax, it's only hi-fi. There's never been a hi-fi emergency." - Roy Hall

"Not everything that can be counted counts, and not everything that counts can be counted." - William Bruce Cameron

 

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Yep- when I do hear a difference it is most often between 16/44.1 and 24/96 or 16/44.1 and 24/192. I was under the impression that I heard little or no difference between 16/44.1 and 16/48, and that may or may not be true. I just don't remember ever comparing 16/44.1 and 16/48 directly to each other. DVD and Bluray playback at 16/48 in most cases, and sounds wonderful when watching operas and ballets. I sometimes think that the video of some of my favorites sound better in video than in CD, but I assumed that was some kind of video vs. audio thing. Might be a real phenomena though.

 

On the other hand, up sampling audio from 16/44.1 to 24/88.2 or above does make a very audible difference to me. Transcoding PCM audio to to DSD makes an even bigger difference. I don't know if that will prove out to be a special case or a general rule, but that is pretty consistent for us.

 

-Paul

 

I've done a lot of experimentation on this question, and I have to say that nobody I have ever played both a 24-bit, 48 KHz and a 24-bit, 96 KHz version of the same performance for has ever been able to detect any audible difference, and that includes me. OTOH, there is a clear difference between 44.1 and 48 KHz that most people can readily hear and most people seem to be able to hear a difference between 16-bit and 24-bit, but most can't put their finger on what it is they're hearing that is different. I've had responses like, "24-bit sounds cleaner," or "24-bit sounds smoother" and other nebulous responses like that. I generally record at 24-bit/96 KHz (when recording LPCM) because 24-bit gives the recordist more latitude. I have to say, that 16-bit/44.1 KHz audio CAN sound excellent, and I'm still convinced that with commercial recordings, the care taken in capturing and producing the finished product is far more important in terms of sound quality, than is either it's bit-depth or it's sampling rate (as long as we're taking 16/44.1 as a minimum, of course).

Anyone who considers protocol unimportant has never dealt with a cat DAC.

Robert A. Heinlein

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Transcoding PCM audio to to DSD makes an even bigger difference. I don't know if that will prove out to be a special case or a general rule, but that is pretty consistent for us.

 

I would think that may be true of particular DACs but, generally, wouldn't you expect playback of a recording in its native format to sound best?

"Relax, it's only hi-fi. There's never been a hi-fi emergency." - Roy Hall

"Not everything that can be counted counts, and not everything that counts can be counted." - William Bruce Cameron

 

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Luckily not, increasing sampling rate helps relaxing the filter. We gain more frequency domain bandwidth to let the filter roll-off slower so we can afford it becoming shorter in time domain.

 

DSD is one extreme of this, it has Nyquist frequency of 1.4 MHz, so it won't have aliasing until that point. Simple fourth order analog filter is enough to eliminate aliasing in ADC and in practice you don't need even that much.

 

 

Gott sie dank!

 

Thank you.

In any dispute the intensity of feeling is inversely proportional to the value of the issues at stake ~ Sayre's Law

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I don't think it's reason not to improve on other parts. And IMO headphones are not bad at all, especially Sennheiser HD800 and AKG K812.

 

For analyzing loudspeaker element behavior, I would probably use LDV. We successfully used it for rotating machinery bearing fault analysis together with acoustic analysis.

Laser Doppler Vibrometer (LDV) for Vibration measurement: Optomet GmbH

 

Neither do I......but a better DAC filter is not a fix for poor speakers or bad acoustics either.

I find quite a few audiophiles use their speaker system as a reference and then work towards improving upon that, 'assuming' that their speaker system is a suitable benchmark. Do you find that's a fairly accurate assesment of our community....at least here on CA where the focus is primarily digital?

 

Is this the best way to go about things in building or improving on a system?....I can't answer empirically but there's plenty of system signatures I've viewed here that in my experience are quite a bit off balance. There's also the reluctance for people here to talk acoustics......like it's a dirty word or something. Wanna shit down a discussion? Mention polar response or directivity....see what happens! Lol

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...increasing sampling rate helps relaxing the filter. We gain more frequency domain bandwidth to let the filter roll-off slower so we can afford it becoming shorter in time domain.

 

DSD is one extreme of this, it has Nyquist frequency of 1.4 MHz, so it won't have aliasing until that point. Simple fourth order analog filter is enough to eliminate aliasing in ADC and in practice you don't need even that much.

 

This is exactly the point I wanted to arrive at. This is why higher sampling rates afford us more latitude. As you said Miska, striking a balance between performance in the time domain and performance the frequency domain is certainly a possibility.

 

Oftentimes, however, one or the other is typically optimized according to the demands of the application. I would argue that digital audio is no different and what we tend to want in digital audio is better time domain performance. This statement is evidenced by the preference by most of increased sample rates so that we can have gentler filters (meaning less steep which absolutely means better time domain performance compared to one more steep).

 

I never answered esldude's original question: I do think the higher sample rate is going to be more accurate for the reason above about filter cutoff steepness. If you want to say that no other thing is changed but the sample rate (meaning the exact same AA filter and exact same reconstruction filter is used), how do you propose to do that since you can't use the same coefficients for different rates unless you do something like skip samples in the weighting? The AA filter is analog so no problem there.

Rob C

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This is exactly the point I wanted to arrive at. This is why higher sampling rates afford us more latitude. As you said Miska, striking a balance between performance in the time domain and performance the frequency domain is certainly a possibility.

 

Oftentimes, however, one or the other is typically optimized according to the demands of the application. I would argue that digital audio is no different and what we tend to want in digital audio is better time domain performance. This statement is evidenced by the preference by most of increased sample rates so that we can have gentler filters (meaning less steep which absolutely means better time domain performance compared to one more steep).

 

I never answered esldude's original question: I do think the higher sample rate is going to be more accurate for the reason above about filter cutoff steepness. If you want to say that no other thing is changed but the sample rate (meaning the exact same AA filter and exact same reconstruction filter is used), how do you propose to do that since you can't use the same coefficients for different rates unless you do something like skip samples in the weighting? The AA filter is analog so no problem there.

 

Ignore my last. On second thought, it is possible to avoid the use of digital filters altogether. If no upsampling is ever employed in the chain (say, if the DAC used supports the two sample rates natively meaning without upsampling) and the reconstruction filter is made analog like the AA then no digital filters are even needed. The only problem is we now need to make the assumption that the DAC handles both rates equally well performance-wise. I have no problem with that to further the converstion. And we also need to make the assumption that the ADC performs equally well at both rates. I have no problem making that assumption either for the purpose of this exercise.

 

In this case, no, there would not be a meaningful difference in accuracy for content below 20 kHz. But those are pretty tough assumptions to believe/achieve in the real world so this remains an exercise in the theoretical.

 

Edited for grammar

Rob C

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So about these digital filtering requirements and the ringing. Miska said any signal above the filter cut-off would ring the filter. How much ringing amplitude are we talking?

 

I just played a 30 khz full level tone at 96 khz sample rate into a sound card recording at 48 khz sample rate. One channel with the tone and the other without. Nothing showed up I could find. Admittedly the soundcard I used isn't super quiet. But sample levels were bouncing around the -80 db level and lower. About the same as the silence just before and after the tone was playing. I would have thought the tone hitting the filter would cause continuous ringing. I also put a single sample impulse through and that caused ringing at least a couple hundred samples either side of the impulse.

 

So would a steady signal above the filter corner not cause continuous ringing or is the ringing quite low in level?

And always keep in mind: Cognitive biases, like seeing optical illusions are a sign of a normally functioning brain. We all have them, it’s nothing to be ashamed about, but it is something that affects our objective evaluation of reality. 

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I sometimes think that the video of some of my favorites sound better in video than in CD, but I assumed that was some kind of video vs. audio thing. Might be a real phenomena though.

Yes they do. Your observation is correct, although the released CD often appears to have suffered more compression.

I wonder how many people after viewing a record company Music Video Promo have been slightly disappointed by the CD ?

 

How a Digital Audio file sounds, or a Digital Video file looks, is governed to a large extent by the Power Supply area. All that Identical Checksums gives is the possibility of REGENERATING the file to close to that of the original file.

PROFILE UPDATED 13-11-2020

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I just played a 30 khz full level tone at 96 khz sample rate into a sound card recording at 48 khz sample rate.

 

You should use some signal that contains harmonics extending over the cut-off frequency. Easiest way is to use for example 1 kHz square wave, even better if you can produce it from a non-bandlimited function generator so that it doesn't have ringing when going in.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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Ignore my last. On second thought, it is possible to avoid the use of digital filters altogether.

 

That is not very practical for 48 kHz sampling rate, because you have just 8 kHz transition band available where you'd need to get at least 96 dB attenuation to properly reconstruct up to 20 kHz frequencies.

 

the reconstruction filter is made analog like the AA then no digital filters are even needed. The only problem is we now need to make the assumption that the DAC handles both rates equally well performance-wise. I have no problem with that to further the converstion. And we also need to make the assumption that the ADC performs equally well at both rates. I have no problem making that assumption either for the purpose of this exercise.

 

I was mostly talking about ADC in this context. Practically nobody really runs ADC at 48 kHz with plain analog AA-filters.

 

1) Having steep enough analog AA-filter to avoid aliasing while preserving 20 kHz pass-band is not practical.

2) Even if such analog filter would be practical (elliptical) it would have horrible phase response across upper audio band.

 

So practically all ADCs are oversampling ones with digital decimation filters to produce lower PCM output rates. This way the analog AA-filter can be low-order with reasonably high corner frequency. I've been using second or third order filter with fc=100kHz

 

In practice, all modern ADC and DAC chips are delta-sigma typically running at 5.6/6.1 MHz speed with digital decimation and oversampling filters to deal with PCM.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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Yep- when I do hear a difference it is most often between 16/44.1 and 24/96 or 16/44.1 and 24/192. I was under the impression that I heard little or no difference between 16/44.1 and 16/48, and that may or may not be true. I just don't remember ever comparing 16/44.1 and 16/48 directly to each other. DVD and Bluray playback at 16/48 in most cases, and sounds wonderful when watching operas and ballets. I sometimes think that the video of some of my favorites sound better in video than in CD, but I assumed that was some kind of video vs. audio thing. Might be a real phenomena though.

 

I find that unless I have the same performance recorded at two different quality levels by me (so I know that it hasn't been manipulated post-capture), hearing differences between sample rates and/or bit depths is a pretty iffy proposition. IOW, the differences that I hear might be a product of the different bit rates/bit depths involved, and then again, they might be due to something else that has been done to one or the other, of which I, as a listener, am not aware.

 

They say (and we all know who "they" are!) that in humans, sight is the most dominant sense, and in any phenomena involving sight and sound (like a video presentation), the visual images take precedence over the audio. Whether or not this holds true for audiophiles whose dominant interest is how something sounds, is unclear to me. But generally, your experience tells me that the pleasant pictures accompanying the sound is making the sound seem more pleasurable to you than it would be if you were just listening. Just a thought...

 

On the other hand, up sampling audio from 16/44.1 to 24/88.2 or above does make a very audible difference to me. Transcoding PCM audio to to DSD makes an even bigger difference. I don't know if that will prove out to be a special case or a general rule, but that is pretty consistent for us.

 

-Paul

 

Uh-huh. I have a an upsampling "engine" called a 'D2D' from a now defunct Canadian company called "Assembledge" that will convert 16/44.1 material to 24/96. It then outputs that unconverted audio as SPDIF to my DAC. I use the thing (due to its myriad of selectable inputs) mostly as a digital port multiplier for my DAC (The D2D allows you to bypass the up-conversion and just use the device as a switch), but I do use the up conversion for my Logitech Squeezebox Touch for Internet radio. The decompressed 16/44.1 stream is fed to the D2D and then the outputted 24/96 stream is fed to my DAC. I certainly can hear the difference between the straight decompressed MP3 radio stream and the up-sampled one. I find the up-sampled version much better and very much less "MP3-like".

George

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Yes they do. Your observation is correct, although the released CD often appears to have suffered more compression.

I wonder how many people after viewing a record company Music Video Promo have been slightly disappointed by the CD ?

 

Since Paul was talking about ballets and operas, I don't think that compression on the CDs is the answer here. Yes, pop music is terribly compressed and limited in it's commercial release form. I see people complaining about how terrible some recent reissue of a pop "classic" sounds compare to the original release all the time. Articles in various recording magazines say that it is done on purpose to catch the casual listener's ear on the radio. I am not aware of any instances where this has been done on classical CDs - that said, I guess it is possible, though!

George

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So about these digital filtering requirements and the ringing. Miska said any signal above the filter cut-off would ring the filter. How much ringing amplitude are we talking?

 

I just played a 30 khz full level tone at 96 khz sample rate into a sound card recording at 48 khz sample rate. One channel with the tone and the other without. Nothing showed up I could find. Admittedly the soundcard I used isn't super quiet. But sample levels were bouncing around the -80 db level and lower. About the same as the silence just before and after the tone was playing. I would have thought the tone hitting the filter would cause continuous ringing. I also put a single sample impulse through and that caused ringing at least a couple hundred samples either side of the impulse.

 

So would a steady signal above the filter corner not cause continuous ringing or is the ringing quite low in level?

 

It depends. A filter can have high overall amplitudes of ringing (relative to the signal) or low levels depending on its design. That said, in general as it pertains to audio the ringing is at very low amplitude because most of the content is actually far away from jump discontinuities and the number of terms used high. Let me explain:

 

The cause of the ringing has to do with a phenomenon in mathematics from the field of partial differential equations. It is called the Gibbs phenomenon and is what happens to the Fourier series at jump discontinuities. Gibbs, the mathematician, showed that partial sums of the Fourier series of a function always differ from the actual function near the jump by an "overshoot" of about 9 percent. Now the width (or duration) of the overshoot goes to zero as the number of terms in the partial sum of the series goes to infinity while the overshoot remains at 9 percent. The terms of the partial sums, btw, are from the Dirichlet kernel. If all the terms of the Dirichlet kernel were to be used (an infinite set) then this phenomenon would disappear. Because we are using a finite number of sample points the phenomenon is here to stay. In fact, since we are never using an infinite number of terms in our partial sums, the max of the absolute value of the difference of the partial sum of the series from the actual function will not be zero (although it tends to zero for each x where f(x) does not jump) even at the limit as the number of terms approaches infinity. There is a difference between infinite and approaching infinity.

 

When a filter is designed (let's take the case of an FIR filter, the one that makes use of the filter kernel) the number of coefficients (or terms) are determined based on design parameters. (Assume using a sinc filter for the remainder of this discussion.) In most cases the number of terms is such that the "width" or duration of the ringing is minimized. Ringing is manifested in the time domain and can be readily identified in the step response. Again, the step response is the discrete integration of the impulse response, which implies that the impulse response influences ringing, with narrowing the impulse response "width" equivalent to increasing the number of terms from the Dirichlet kernel of the function (or signal in this case). The overshoot near each sample point will remain about the same but the tails will decay much more quickly toward zero (though never going to absolute value of the max of the difference equal to zero) with narrowing impulse response such that perhaps the ringing reaches less than 1 % of the signal in a very, very short period of time. All of it is calculable.

 

Hope that made sense.

Rob C

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That is not very practical for 48 kHz sampling rate, because you have just 8 kHz transition band available where you'd need to get at least 96 dB attenuation to properly reconstruct up to 20 kHz frequencies.

 

 

 

I was mostly talking about ADC in this context. Practically nobody really runs ADC at 48 kHz with plain analog AA-filters.

 

1) Having steep enough analog AA-filter to avoid aliasing while preserving 20 kHz pass-band is not practical.

2) Even if such analog filter would be practical (elliptical) it would have horrible phase response across upper audio band.

 

So practically all ADCs are oversampling ones with digital decimation filters to produce lower PCM output rates. This way the analog AA-filter can be low-order with reasonably high corner frequency. I've been using second or third order filter with fc=100kHz

 

In practice, all modern ADC and DAC chips are delta-sigma typically running at 5.6/6.1 MHz speed with digital decimation and oversampling filters to deal with PCM.

 

The part you are addressing was meant for esldude. I was trying to find a way to at least theoretically work within the confines of the scenario in his first post. It was theoretical not practical. I do agree with you about the impracticalities and stated as much. I'm sure esldude wanted to discuss the one point he made isolated from any other influence.

 

But you do bring up SDM. Now that is a subject I could see myself writing about at length. I am fascinated by the limitations of SDM such as instability, limit cycles, idle tones, and noise.

Rob C

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It depends. A filter can have high overall amplitudes of ringing (relative to the signal) or low levels depending on its design. That said, in general as it pertains to audio the ringing is at very low amplitude because most of the content is actually far away from jump discontinuities and the number of terms used high. Let me explain:

 

The cause of the ringing has to do with a phenomenon in mathematics from the field of partial differential equations. It is called the Gibbs phenomenon and is what happens to the Fourier series at jump discontinuities. Gibbs, the mathematician, showed that partial sums of the Fourier series of a function always differ from the actual function near the jump by an "overshoot" of about 9 percent. Now the width (or duration) of the overshoot goes to zero as the number of terms in the partial sum of the series goes to infinity while the overshoot remains at 9 percent. The terms of the partial sums, btw, are from the Dirichlet kernel. If all the terms of the Dirichlet kernel were to be used (an infinite set) then this phenomenon would disappear. Because we are using a finite number of sample points the phenomenon is here to stay. In fact, since we are never using an infinite number of terms in our partial sums, the max of the absolute value of the difference of the partial sum of the series from the actual function will not be zero (although it tends to zero for each x where f(x) does not jump) even at the limit as the number of terms approaches infinity. There is a difference between infinite and approaching infinity.

 

When a filter is designed (let's take the case of an FIR filter, the one that makes use of the filter kernel) the number of coefficients (or terms) are determined based on design parameters. (Assume using a sinc filter for the remainder of this discussion.) In most cases the number of terms is such that the "width" or duration of the ringing is minimized. Ringing is manifested in the time domain and can be readily identified in the step response. Again, the step response is the discrete integration of the impulse response, which implies that the impulse response influences ringing, with narrowing the impulse response "width" equivalent to increasing the number of terms from the Dirichlet kernel of the function (or signal in this case). The overshoot near each sample point will remain about the same but the tails will decay much more quickly toward zero (though never going to absolute value of the max of the difference equal to zero) with narrowing impulse response such that perhaps the ringing reaches less than 1 % of the signal in a very, very short period of time. All of it is calculable.

 

Hope that made sense.

 

Yes, it made sense to me in large measure.

 

Now my question I suppose it back to what it was. I don't see these jumps or discontinuities in music for the most part. It appears such discontinuities and the wide bandwidth related to them is what causes the ringing more than just the frequency. That was how I thought it worked until Miska said frequencies over the filter caused ringing. Which is why I have been thinking ringing filters are not a common audible issue.

And always keep in mind: Cognitive biases, like seeing optical illusions are a sign of a normally functioning brain. We all have them, it’s nothing to be ashamed about, but it is something that affects our objective evaluation of reality. 

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But you do bring up SDM. Now that is a subject I could see myself writing about at length. I am fascinated by the limitations of SDM such as instability, limit cycles, idle tones, and noise.

 

Those can be fixed, apart from noise that falls into Nyquist band, but it is a "non-Nyquist" sampling system, so Nyquist frequency can be largely ignored in this context.

 

But especially since doing SDM properly takes a lot of resources, I prefer running in it software instead of using resource constrained hardware implementation.

 

At DSD512 I can get pretty good performance already:

temp2.png

 

Here's another a bit wider view with my crazy multi-tone test signal:

temp3.png

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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