What Makes Good Filtering?

[Jud]

Over at the "Are we fooling ourselves?" thread, we've had a lot of discussion about whether ultrasonic pre-ringing in filters affects the resulting analog sound quality. Many people say no, many say yes. What I have *not* seen, and am very interested to find out, is what people, especially but not exclusively filter designers, think are some other characteristics of filters that are important for resulting sound quality. (I'm not being totally accurate here - John Swenson did say he thought cascaded filters sounded worse than single pass designs.) So folks, as informatively as you can without giving away any secret sauce - what makes good filtering?

[manisandher]

Hey Jud, excellent idea.

 

As a long-term user of XXHighEnd and HQPlayer, both feeding a 24/768 capable DAC that does nothing to what its fed (i.e. only converting to analogue with no internal over-sampling or filtering), I can say without hesitation that the quality of the filter used in the software player to take 16/44.1 to 24/705.6 makes a very real and audible difference to sound quality.

 

Looking forward to hearing back from the guys who actually design and implement these filters.

 

Mani.

[acg]

Hey Jud, excellent idea.

 

As a long-term user of XXHighEnd and HQPlayer, both feeding a 24/768 capable DAC that does nothing to what its fed (i.e. only converting to analogue with no internal over-sampling or filtering), I can say without hesitation that the quality of the filter used in the software player to take 16/44.1 to 24/705.6 makes a very real and audible difference to sound quality.

 

Looking forward to hearing back from the guys who actually design and implement these filters.

 

Mani.

 

What Mani said ^^^^^. Very much interested in where this thread leads. Digital filters make quite a substantial difference, even between "good" ones in my experience.

 

Anthony

[PeterSt]

John Swenson did say he thought cascaded filters sounded worse than single pass designs.

 

Hi Jud,

 

Then John maybe can tell the why of this, because to me this makes no sense (at all).

Of course, one should never randomly cascade two filters hence the both must anticipate each other (must be made for each other).

Generally this will be about two (or more) types of filters which can't be integrated.

 

Regards,

Peter

[PeterSt]

think are some other characteristics of filters that are important for resulting sound quality.

 

I'm afraid that not many answers exist because it is all too obvious.

But maybe this is a not so obvious one :

 

Filter out as much high frequency as possible (so I am talking (multi) MHz now) and stay away of the capacitors as long as possible.

Maybe it's a hobby horse only.

 

Peter

[Jay-dub]

It is, of course, only possible to speak of the sound quality of the net result of the filters in the ADC, cascaded with any filters subsequently used in production and those in playback. Having no cascaded filters at all would only be possible with DSD or some similar low-bit format, which is certainly less practical, and I have nothing to say on the matter. Once you're in the PCM domain, I trust the mathematics: linear filters can be combined, or factored and cascaded in any order, with no effect.

 

The digital chain should have as its net result a low-pass filter, with no detectable aliasing either above or below the Nyquist frequency, and the addition of quantization noise that has no correlation with the signal and has a power spectral density that is dominated by other sources of noise throughout the audio band. For the transition band response of said filter, I prefer phase-linear. This is because my subjective listening of different phase-linear filters with 10kHz or more passband reveals that they do not affect tone color. The only differences among them is in how clean the transients are. In contrast, minimum-phase filters and others that are designed to reduce pre-ringing by means of an asymmetrical impulse response all seem to color the music, and add different coloring depending on their cutoff frequency. They don't necessarily sound bad, but I have to get used to each one, whereas I am already used to all phase-linear filters.

 

This leaves the question of how much bandwidth is required for the result to sound "good", and how localized the impulse response needs to be, at a given transition band, for pre-ringing not to be objectionable. I recommend that you figure this out for yourself. For me, less than about 1ms of pre-ringing is the point at which it sounds very good with cutoffs around 20kHz. A bandwidth of 18kHz is sufficient that I do not feel any need to buy other recordings of the same music with better sound quality. At 21kHz it sounds really, really good. At this point the headphones are probably getting more high-frequency content into your ears, and more consistently, than if you had the instruments right in front of you. Somewhere between 23-25kHz bandwidth, and I no longer imagine I can hear any difference compared to the ~48 kHz bandwidth of a 24/96 recording.

 

On the subject of aliasing, the most insidious form of aliasing is between two frequencies in the audio band. Ultrasonic aliasing can always be filtered out subsequently, but this can't. It can occur when you switch between 44.1 and 48 kHz based sampling rates. It can be noticeable and objectionable even when its total power is less than that of the quantization noise. I have a number of CD's in which the sound quality is noticeably degraded due to this kind of aliasing in the conversion from a 24/96 master. There is no record company that I trust to do this conversion properly. In fact that is one of the major reasons why I buy hi-res downloads.

[beanbag]

I thought I was going to say "whatever it takes to make the output waveform match the Whittaker-Shannon interpolation formula, and how you achieve that is a minor implementation detail", but that may be a little bit too smart ass.

 

In the meantime, I found an application note explaining what the DAC output looks like without any filtering at all, and some of the techniques employed to make it less bad. In general, I find application notes written by nameless white collar electrical engineers to be more enlightening since they generally don't try to push an agenda or promote audiophile boogeymen.

 

Equalizing Techniques Flatten DAC Frequency Response - Application Note - Maxim

 

Looking at the datasheets for some DACs also gives you an idea what manufacturers think are important, namely stop band attenuation (no extraneous noises above fs/2), pass band ripple (no higher frequencies aliased down into the pass band), and pass band flatness. May as well get these basics right first before even talking about pre-ringing, transients, and etc.

[Miska]

Looking at the datasheets for some DACs also gives you an idea what manufacturers think are important, namely stop band attenuation (no extraneous noises above fs/2), pass band ripple (no higher frequencies aliased down into the pass band), and pass band flatness. May as well get these basics right first before even talking about pre-ringing, transients, and etc.

 

Too bad those are the areas where their results tend to be especially inadequate...

[Jud]

linear filters can be combined, or factored and cascaded in any order, with no effect.

 

In contrast, minimum-phase filters and others that are designed to reduce pre-ringing by means of an asymmetrical impulse response all seem to color the music, and add different coloring depending on their cutoff frequency.

 

This leaves the question of how much bandwidth is required for the result to sound "good", and how localized the impulse response needs to be, at a given transition band, for pre-ringing not to be objectionable. I recommend that you figure this out for yourself. For me, less than about 1ms of pre-ringing is the point at which it sounds very good with cutoffs around 20kHz. Somewhere between 23-25kHz bandwidth, and I no longer imagine I can hear any difference compared to the ~48 kHz bandwidth of a 24/96 recording.

 

I have a number of CD's in which the sound quality is noticeably degraded due to this kind of aliasing in the conversion from a 24/96 master. There is no record company that I trust to do this conversion properly. In fact that is one of the major reasons why I buy hi-res downloads.

 

Pardon me for having cut up your response, but the system I'm currently on doesn't allow use of the Return key in the composition window, so I have to do my questions as one paragraph, rather than interspersing them in your comment. (1) When you say "linear filters" can be combined in any order - do you mean linear phase, or something else? (2) When you say min-phase filters seem to "color" the music in different ways depending on cutoff frequency, do you mean color as a synonym for tone/pitch/correct frequency response, or something else; and what are your thoughts on the means by which this result is produced? (3) The amplitude of pre-ringing falls off pretty rapidly with time; when you say "1ms" of pre-ringing, is that until there is no detectable amplitude at all, or if there is still some detectable amplitude, what level? (4) When you talk about the sound of various bandwidths, including some uncommon figures like 23-25kHz, what are the circumstances under which you're comparing these? Actual bandwidths of various hi res downloads, or some other fashion? (5) Any examples you can provide of reasonably popular CDs with this type of sound quality degradation?

[Jay-dub]

"whatever it takes to make the output waveform match the Whittaker-Shannon interpolation formula, and how you achieve that is a minor implementation detail"

 

Well, the thing is, if you give me a DAC, I can give you a signal for which the output does not match the Whittaker-Shannon interpolation formula. In fact, for a general signal, the formula does not converge absolutely. But yes, my goal is always to make sure that for a given PCM signal as transmitted to the playback system, the interpolated signal is (1) well-defined and easy to compute, and (2) good-sounding. Then I can regard the question of how the interpolation is achieved as a minor inplementation detail.

 

 

I don't think the equalization technique described in that white paper is relevent to audio applications, although there's no harm in it. Typical audio DAC's oversample to 8x using FIR and then sigma-delta modulate to at least 64x the base sample rate. If you assume rolloff from sample-and-hold at 8x oversampling, the rolloff at 20kHz is (normalized output frequency (20/44.1)/8 = 0.057) about 0.04 dB according to Figure 6. Anything less than 1 dB in the audible range is hard to hear; that's inaudible.

 

 

By the way, passband ripple is just the deviation from passband flatness. Higher frequencies aliased into the passband occurs with downsampling, not in typical DAC's, and is associated with the the stopband attenuation of the antialiasing filter applied previously.

[Jud]

Jay-dub, I just wanted to make sure you didn't mistake me, because a friend sent me a message saying they thought I was being mean to you. I realize from the friend's note that it could seem as if I was trying to cross-examine you in my last post. That's not what I meant to do at all; I was just full of questions and very eager to see the answers. So please take my questions to you in the spirit of curiosity, as they were intended. Thanks!

[Jay-dub]

(1) When you say "linear filters" can be combined in any order - do you mean linear phase, or something else? (2) When you say min-phase filters seem to "color" the music in different ways depending on cutoff frequency, do you mean color as a synonym for tone/pitch/correct frequency response, or something else; and what are your thoughts on the means by which this result is produced? (3) The amplitude of pre-ringing falls off pretty rapidly with time; when you say "1ms" of pre-ringing, is that until there is no detectable amplitude at all, or if there is still some detectable amplitude, what level? (4) When you talk about the sound of various bandwidths, including some uncommon figures like 23-25kHz, what are the circumstances under which you're comparing these? Actual bandwidths of various hi res downloads, or some other fashion? (5) Any examples you can provide of reasonably popular CDs with this type of sound quality degradation?

 

Hey Jud, I don't mind your questions. I'm trying to be clear, but these are complex, technical matters, and I am not a really great writer. So here are the clarifications you asked for.

 

 

When I say "linear filters" I mean "linear, time independant systems" which includes all FIR filters and both analog and digital equalizers, but excludes peak limiters, dynamic range compression, and the like.

 

 

Color simply means that I hear a change in the tone-color of certain instruments. As an extreme case, when I put some spoken word content through a minimum-phase filter with less than 10kHz cutoff, my thoughts were: this sounds boxy, and it reminds me of AM radio. My feeling is that all musical notes are the result of a particular waveform (a sawtooth wave from a bow catching and slipping against a string, or puffs of air from the reed in the case of a wind instrument) put through a linear filter (the instrument, room, and listener's outer ear) whose characteristic frequencies are much less than 20kHz. When you apply filters with high-frequency phase-shifts, these change the shape of the waveform into something that my ear recognizes can't result from any natural process.

 

 

When I said 1ms, that was a very rough estimate. For more precise quantification, here is the impulse response for a 96 kHz test file converted to 44.1 kHz sampling by Sox with an 18.3 kHz lowpass that I consider good: sinc -a 60 -t 2400 -18300. The impulse peak is at sample 856776, at least 90% of preringing is after sample 856769, and nothing is perceptible before sample 856746. At 44.1 samples per millisecond, I would say that realistically, preringing is about 0.15 ms, and conservatively, less than 0.68 ms.

 

 

 

All my subjective impressions refer to direct, informal comparison (with Beyerdynamic headphones advertizing 30kHz bandwidth) between 24/96 or 24/88.2 hi-rez downloads and converted files of 48 or 64 kHz sample rate.

 

 

For examples of CD's that I suspect were converted from 24/96 by resamplers with insufficient stopband attenuation, I can name the ca. 1999 "Strauss/Solti" releases of Rosenkavalier and Elektra, or the Chandos Jenufa in English. But you can get the effect by taking any excellent 24/96 file, and converting it to 44.1 using Sox or Audacity with the default filters.

[Superdad]

...a friend sent me a message saying they thought I was being mean to you.

 

Jud, I don't think there is a mean bone in your body. And curiosity may kill the cat, but never the thoughtful audiophile.

 

John Swenson did say he thought cascaded filters sounded worse than single pass designs.

 

I was speaking to John later the other night and mentioned your quote above. I am afraid that you unintentionally took it out of context. Although I am not looking at the paragraph you quoted from, he meant it in the context of resource-contrained DAC chips. As most of you know, almost all S-D DAC chips apply a different filter (sometimes selectable) depending upon what rate is coming in (you can see the various curves in the spec sheets). And the manufacturers are so committed to showing competitive specs (stop band attenuation, ripple, flatness) that they go to great lengths combining different types--but still within the constraints of what they can do with a chip that will in the end sell for just a couple bucks. That's what he was saying sounds bad.

Now if they had the resources for a filter with more taps, they might be able to achieve the specs they want with less compromise. But it would cost much more.

 

--------

 

Where I would enjoy seeing this conversation go is into a discussion of:

a) Overall filter "envelope" parameters (cut-off point, steepness, final attenuation, phase, number of taps) and what balance sounds most musically realistic (transient attack, lack of aliases, group delay, high frequency extension, etc.);

 

b) A comparison of what filter methods and parameters are being used--both in quality SRC software (SoX, iZotope, XXHighEnd, HQPlayer, AuI ConverteR, etc.) and in DACs that are not using the filter's built into the chips (I'm thinking of the various FPGA-based and discrete FIR filter DACs--Chord, PSA's DS, Miska's DSC1).

 

I'd like to understand more about how the above are both different and similar to one another. Plus other filter related questions:

How does Peter's ARC-prediction work (somewhat secret I know);

What, other than early cut-off, really characterizes a filter as "apodizing?";

If one had infinite computing resources (h/w or s/w), how many filter taps would be enough--or too many--to make a really good sounding filter.

 

[Right now I just fine-tune iZotope advanced's 5 parameters in Audirvana as I upsample Redbook; I can hear them all, some down to the granularity limits of the numerical control iZotope offers. All to feed my NOS PCM1704K DAC with discrete op-amp output stage.]

 

Pretty much all of the above questions are in the context of interpolating the most difficult source material--Redbook--and going up to at least 352.8KHz.

 

A separate topic--which really should be a separate thread--includes a lot of my curiosity about sigma-delta modulators (order, design, optimal rates, number of levels) and THEIR filters. Since we (mostly) live in a post-R2R world, S-D modulation is a inextricable part of the process and we might as well embrace it by doing it well at very high rates. But again, I'm looking to learn more about what "doing it well" really entails. Separate topic, and for some like Miska, I'd be asking questions a little too close to his IP.

 

Cheers,

 

Alex C.

 

P.S. Jay-dub: I'm just reading you latest post. VERY interesting. Thanks!

[PeterSt]

Jay-dub,

 

I like your approach.

 

There is no record company that I trust to do this conversion properly. In fact that is one of the major reasons why I buy hi-res downloads.

 

For examples of CD's that I suspect were converted from 24/96 by resamplers with insufficient stopband attenuation

 

I obviously combined these both texts, possibly unjustified. But it almost looks like you deliberately listen to downsampled material ? I must be wrong here ...

 

Peter

[PeterSt]

Although I am not looking at the paragraph you quoted from, he meant it in the context of resource-contrained DAC chips. As most of you know, almost all S-D DAC chips apply a different filter (sometimes selectable) depending upon what rate is coming in (you can see the various curves in the spec sheets).

 

Maybe I am too fast with responding, but John (possibly somewhere else) also explicitly mentioned the virtue of being able to listen to a DAC (chip) that does not contain a filter at all. He said something like "and most of you don't have the opportunity to listen to that / compare".

I recall this because this is my always and ever story and it is crucial for observing your own filters.

 

Peter

[Miska]

sinc -a 60 -t 2400 -18300

 

Do you consider filter with 60 dB stop-band attenuation good!?

[Superdad]

Maybe I am too fast with responding, but John (possibly somewhere else) also explicitly mentioned the virtue of being able to listen to a DAC (chip) that does not contain a filter at all. He said something like "and most of you don't have the opportunity to listen to that / compare".

I recall this because this is my always and ever story and it is crucial for observing your own filters.

 

Well of course Peter. Although with a fair number of popular modern SD DAC chips, if you SRC in s/w up to 352.8/384, then you do get to hear the chip without its built-in filters--and can compare that to what can be done much better in s/w with computing power and good SRC s/s algorithms. BTW, how is that OS X version of XXHighEnd coming along?

 

As far as listening to DACs without ANY filter goes, my NOS PCM1704K (a Swenson/Hovland design prototype) is still my unmatched reference. And for a long time I listened to it without any s/w SRC--aliases and all--still darn good!

Now if only I could find an interface/software to allow me to feed it 705.6/768KHz… Then I might endure the learning curve and visual assault of XXHighEnd!

[Jud]

As most of you know, almost all S-D DAC chips apply a different filter (sometimes selectable) depending upon what rate is coming in (you can see the various curves in the spec sheets). And the manufacturers are so committed to showing competitive specs (stop band attenuation, ripple, flatness) that they go to great lengths combining different types--but still within the constraints of what they can do with a chip that will in the end sell for just a couple bucks. That's what he was saying sounds bad.

 

I thought the filtering was 0-3 "rounds" of pretty close to the same thing (except for halving the number of taps?), depending on the incoming rate: 3 rounds of 2x upsampling and accompanying interpolation filtering for 44.1/48kHz; 2 rounds for 88.2/96; 1 round for 176.4/192; 0 for 352.8/384. No? Each "round" is typically different over and above the difference in number of taps?

[acg]

 

Now if only I could find an interface/software to allow me to feed it 705.6/768KHz… Then I might endure the learning curve and visual assault of XXHighEnd!

 

The XXHE layout and visuals are completely customisable...you can make XXHE look just about any way you want.

[Superdad]

Each "round" is typically different over and above the difference in number of taps?

 

I believe so. I know for certain (at least believing John) that the chips implement a differently optimized filter depending upon if you feed it 44.1, 88.2, or 176.4 (and then no filter when you get to 352.8--at least for many). The distinction being if the 2 cascaded filters used for 88.2 are just using 2 of the 3 cascaded filters that get used at 44.1, or a different set. I am pretty sure John told me they were a different set--and that each round was different from one another as well. The graphs in the data sheets seem to bear this out.

John would have to chime in here about this.

 

But I hope my other questions don't get lost in this. I'd really like to read some of the ideas and philosophy of filter design by Peter, Miska, Alexey Lukin, and Yuri on the s/w side, and maybe from Hansen, Mallison, Loesch on the h/w side. I know that is unlikely that any but the first two will even see my questions, but at least I can put them out into the ether…

[Miska]

I believe so. I know for certain (at least believing John) that the chips implement a differently optimized filter depending upon if you feed it 44.1, 88.2, or 176.4 (and then no filter when you get to 352.8--at least for many). The distinction being if the 2 cascaded filters used for 88.2 are just using 2 of the 3 cascaded filters that get used at 44.1, or a different set. I am pretty sure John told me they were a different set--and that each round was different from one another as well. The graphs in the data sheets seem to bear this out.

John would have to chime in here about this.

 

No, usually there's just one set of filters and you just get filters dropped off starting from the first as rate increases. So the front blocks are bypassed.

 

44.1/48 input: (2x filter for 44.1/48) -> (2x filter for 88.2/96) -> (2x filter for 176.4/192) -> (S/H) -> (modulator)

88.2/96 input: (2x filter for 88.2/96) -> (2x filter for 176.4/192) -> (S/H) -> (modulator)

176.4/192 input: (2x filter for 176.4/192) -> (S/H) -> (modulator)

 

This way the computational load stays constant as input sampling rate increases but MCLK stays the same.

 

When there is second or more sets, those are for example the "slow roll-off" set, or "minimum phase set" or similar, but they are also constructed in the same way, but just the entire filter triple is different.

[Miska]

I thought the filtering was 0-3 "rounds" of pretty close to the same thing (except for halving the number of taps?), depending on the incoming rate: 3 rounds of 2x upsampling and accompanying interpolation filtering for 44.1/48kHz; 2 rounds for 88.2/96; 1 round for 176.4/192; 0 for 352.8/384. No? Each "round" is typically different over and above the difference in number of taps?

 

All three are distinct filters, typically the next one about half shorter than previous. It is constructed as a pipeline, where higher rates get short-cut to a later step. So it works like a factory assembly line.

 

If you dig out datasheet of the old Burr-Brown DF1700 digital filter, there's a description in "Theory of operation" part. First filter is 153 taps, second is 29 taps and third is 17 taps. So not exactly half, but you get the idea.

 

The NPC's SM5847A digital filter uses 169, 29 and 17 taps, explained in similar way on the datasheet.

[Jay-dub]

Do you consider filter with 60 dB stop-band attenuation good!?

 

When the purpose is to remove objectionable content between 18-22 kHz, 60 dB attenuation is more than adequate. The complete filter chain was rate -v -s 44100 sinc -a 60 -t 2400 -18300. For the sample-rate conversion, I consider 175 dB stop-band attenuation good.

[Jay-dub]

Jay-dub,

 

But it almost looks like you deliberately listen to downsampled material ? I must be wrong here ...

 

Peter

 

I have a bunch of stuff on my iPod that I downloaded as 24/96 and converted to a format that it can read. What's unusual about that? I also have purchased CD's of recordings that were produced in 24/96 but never released as hi-rez downloads. Listening to downsampled content under those circumstances is unavoidable.

[PeterSt]

44.1/48 input: (2x filter for 44.1/48) -> (2x filter for 88.2/96) -> (2x filter for 176.4/192) -> (S/H) -> (modulator)

88.2/96 input: (2x filter for 88.2/96) -> (2x filter for 176.4/192) -> (S/H) -> (modulator)

176.4/192 input: (2x filter for 176.4/192) -> (S/H) -> (modulator)

 

This way the computational load stays constant as input sampling rate increases but MCLK stays the same.

 

I wouldn't know of another way when the output rate (to the modulator in your case) stays the same ? IOW this is not related to the way filters are cascaded.

 

This is different from working explicitly with the number of times of upsampling like "always 2x" or "always 4x" (the fx button in XXHighEnd). The use case of this is a bit beyond myself at this moment although I made it myself. Anyway, now the input rate determines the output rate (and now the MCLK (Master Clock) doesn't stay the same.

Notice : I talk in-PC-software regarding input rate and output rate (thus output rate is input for the DAC).