Why reconstruction filters? Just intermodulation distortion?

[33AndAThird]

Hi ASR,
I watched Amir's video on clipping which was very interesting. There was a penny-drop moment when Amir described how a 12KHz square wave is effectively a 12KHz sine wave with odd harmonics added at decreasing amplitudes, and that if you apply a low-pass filter you get a pure sine wave. I recognised that this is effectively what a reconstruction filter does to a DAC's stepped output to smooth it back into the original signal.

I later read this article by Archimago on DAC filters comparing filtered vs non-filtered DACs.

NOS vs. Digital Filtering DACs: Exploring filtering turned off, implications, fidelity and subjective audibility. (Recent BorderPatrol DAC chatter...)

A blog for audiophiles about more objective topics. Measurements of audio gear. Reasonable, realistic, no snakeoil assessment of sound, and equipment.

archimago.blogspot.com

Archimago shows the stepped output of a DAC without a reconstruction filter and asks how that signal could be considered to be anything but artificial.
"Since when did jagged edged reproduction of digital become anything but "artificial"!? "
Is this not a bit disingenuous? In practice do we still not hear the smoothed waveform? I have the following questions:

• Given our audio reproduction chain beyond the DAC (amp, speakers) likely can't reproduce anything above 20-30KHz, does this not provide filtering by default, largely restoring that waveform to its more recognisable smoothed representation? Put another way, if we play Amir's 12KHz square wave would the physical wave reproduced by the amp & speakers not be a 12KHz sine wave?
• Even if we had an a reproduction chain capable of 1000KHz, wouldn't our ears not also provide a natural filter to the sound at 20KHz? Ie. would we not perceive the 12KHz sine wave rather than the square wave?

This brings me to a third point. Archimago references that a non-filtered DAC signal will be 3db down at 20KHz because the sampling rate is too small to hit the peaks of the waveform.

• Is it not the ultrasonic harmonics that effectively reduce the ampliture of that 20KHz signal? If so and assuming the above two propositions are true, then our reproduction equipment and our ears provide filters to the sound and the ultra harmonics will be filtered out, effectively restoring the signal to its full amplitude. Put another way; is it true that our perception of that sound would not be 3db down at all as the ultrasonics are filtered by our equipment/ears anyway?

Finally - if all my propositions are correct, it would seem to me that the only reason we bother with a reconstruction filter is to counter intermodulation distortion produced by our equipment when we put ultrasonic signals through it - as described in this paper: https://people.xiph.org/~xiphmont/demo/neil-young.html (Scroll to 192kHz considered harmful). Is this true, or do we want a reconstruction filter for other reasons?

Thanks

 

[kemmler3D]

Hi ASR,
I watched Amir's video on clipping which was very interesting. There was a penny-drop moment when Amir described how a 12KHz square wave is effectively a 12KHz sine wave with odd harmonics added at decreasing amplitudes, and that if you apply a low-pass filter you get a pure sine wave. I recognised that this is effectively what a reconstruction filter does to a DAC's stepped output to smooth it back into the original signal.

I later read this article by Archimago on DAC filters comparing filtered vs non-filtered DACs.

NOS vs. Digital Filtering DACs: Exploring filtering turned off, implications, fidelity and subjective audibility. (Recent BorderPatrol DAC chatter...)

A blog for audiophiles about more objective topics. Measurements of audio gear. Reasonable, realistic, no snakeoil assessment of sound, and equipment.

archimago.blogspot.com

Archimago shows the stepped output of a DAC without a reconstruction filter and asks how that signal could be considered to be anything but artificial.
"Since when did jagged edged reproduction of digital become anything but "artificial"!? "
Is this not a bit disingenuous? In practice do we still not hear the smoothed waveform? I have the following questions:

• Given our audio reproduction chain beyond the DAC (amp, speakers) likely can't reproduce anything above 20-30KHz, does this not provide filtering by default, largely restoring that waveform to its more recognisable smoothed representation? Put another way, if we play Amir's 12KHz square wave would the physical wave reproduced by the amp & speakers not be a 12KHz sine wave?
• Even if we had an a reproduction chain capable of 1000KHz, wouldn't our ears not also provide a natural filter to the sound at 20KHz? Ie. would we not perceive the 12KHz sine wave rather than the square wave?

This brings me to a third point. Archimago references that a non-filtered DAC signal will be 3db down at 20KHz because the sampling rate is too small to hit the peaks of the waveform.

• Is it not the ultrasonic harmonics that effectively reduce the ampliture of that 20KHz signal? If so and assuming the above two propositions are true, then our reproduction equipment and our ears provide filters to the sound and the ultra harmonics will be filtered out, effectively restoring the signal to its full amplitude. Put another way; is it true that our perception of that sound would not be 3db down at all as the ultrasonics are filtered by our equipment/ears anyway?

Finally - if all my propositions are correct, it would seem to me that the only reason we bother with a reconstruction filter is to counter intermodulation distortion produced by our equipment when we put ultrasonic signals through it - as described in this paper: https://people.xiph.org/~xiphmont/demo/neil-young.html (Scroll to 192kHz considered harmful). Is this true, or do we want a reconstruction filter for other reasons?

Thanks

I guess a very minor additional reason is not to send too much power to tweeters, or waste amp power on ultrasonics, but those would tend to be very low in level.

 

[MRC01]

An aspect to consider is that the digital sampling points are inherently ambiguous unless you limit the bandwidth to half the sampling rate. For example, suppose you sample a simple 12 kHz sin wave at a CD quality 44,100 Hz. The DAC doesn't know what you sampled, it only sees the sample points. And there are an infinite number of different waves that all pass through those same points. For example, the first "alias" of this 12 Khz wave is 22,050 + (22,050 - 12,000) = 32,100 Hz. There are infinitely many more.

So without a filter, the DAC is free to construct a 32,100 Hz wave instead of a 12,000 Hz wave. It is "correct" in that passes perfectly through every sample point just like a 12,000 Hz wave would. Or, the DAC could construct multiple waves together, and their superposition might also pass through every sample point. Of course all but one of these many different waves are above 22,050 Hz, so after you apply the filter there is only 1 and the sampling points are no longer ambiguous.

 

[DonH56]

It's an anti-imaging filter. See e.g. https://www.audiosciencereview.com/...ital-audio-converters-dacs-fundamentals.1927/

There are a few other articles on here describing sampling and such, as well as plenty of other material around, that would help clear up some of your questions and misconceptions.

 

[NTK]

This brings me to a third point. Archimago references that a non-filtered DAC signal will be 3db down at 20KHz because the sampling rate is too small to hit the peaks of the waveform.

• Is it not the ultrasonic harmonics that effectively reduce the ampliture of that 20KHz signal? If so and assuming the above two propositions are true, then our reproduction equipment and our ears provide filters to the sound and the ultra harmonics will be filtered out, effectively restoring the signal to its full amplitude. Put another way; is it true that our perception of that sound would not be 3db down at all as the ultrasonics are filtered by our equipment/ears anyway?

The 3 dB roll off is from the stairstep reconstruction. Mathematically, the stairsteps as created by the zeroth-order hold process (i.e. sample and hold), is the result from convolving the discrete signal samples as represented by an impulse train (a series of impulses scaled to the amplitudes of the discrete samples) with a unit step function. The convolution with the unit step function is equivalent to filtering the impulse train using a filter with a frequency response of a sinc function. As the sinc function rolls down to about -3 dB at 0.9 Nyquist frequency, that's where the 3 dB drop came from.

Reference: https://www.dspguide.com/ch3/3.htm

 

[DVDdoug]

I had a soundcard once with no filtering. I didn't use this setup for "critical listening but I'd never heard anything wrong! I was doing some experiments with an oscilloscope and I was shocked to see a stair-stepped waveform!

Then I thought about it... The harmonics are above the audible range (I think the sample rate was 44.1kHz), the amplifier (built-into the "computer speakers") might have limited bandwidth, and the speakers would certainly filter mechanically.

 

[MRC01]

I had a soundcard once with no filtering. I didn't use this setup for "critical listening but I'd never heard anything wrong! I was doing some experiments with an oscilloscope and I was shocked to see a stair-stepped waveform!

Then I thought about it... The harmonics are above the audible range (I think the sample rate was 44.1kHz), the amplifier (built-into the "computer speakers") might have limited bandwidth, and the speakers would certainly filter mechanically.

Sure, but this relates to the intermodulation issue that @33AndAThird mentioned. Many of the HF images are typically spaced a few hundred or thousand Hertz apart, which puts the IM distortion smack-dab into the frequency range most sensitive to human hearing. That doesn't necessarily make it audible (though it may be), but it is definitely passband distortion which we strive to avoid.

 

[DonH56]

The 3 dB roll off is from the stairstep reconstruction. Mathematically, the stairsteps as created by the zeroth-order hold process (i.e. sample and hold), is the result from convolving the discrete signal samples as represented by an impulse train (a series of impulses scaled to the amplitudes of the discrete samples) with a unit step function. The convolution with the unit step function is equivalent to filtering the impulse train using a filter with a frequency response of a sinc function. As the sinc function rolls down to about -3 dB at 0.9 Nyquist frequency, that's where the 3 dB drop came from.

Reference: https://www.dspguide.com/ch3/3.htm

Exactly. In fact, -3.54 dB at Nyquist, as stated in the article I linked:

"Note that the amplitude rolls off in the images, and there are notches (nulls, zero inflection points) at each multiple of the sampling frequency (44.1 kHz). It’s in the math which I’m trying to minimize, so trust me – it’s correct. Technically, it follows a sinc (sinX/X) envelope. Furthermore, it’s easy to show that at the Nyquist frequency (Fs/2) the output is actually down -3.54 dB. We don’t measure this roll-off in commercial audio DACs because peaking filters (or other techniques not discussed here) are used to flatten the response. Analog output filters are used to roll off any signals and noise above about 20 kHz so you will not see these images at the output of a commercial audio DAC. Not without some serious test equipment, anyway…"

 

[MaxwellsEq]

I don't need to add anything further on how anti-imaging filters work - this is already clear from the contribution from experts.

But to pick up on your title:

Just intermodulation distortion?

You may not have intended it, but I feel there's an implication here that you consider intermodulation distortion is not important: i.e. "just". I think IMD is sometimes more important than harmonic distortion. Of course, it's questionable whether you can hear it, but it makes no sense it introduce it if you can avoid doing so.

Another thing worth considering is how your system actually behaves above 20kHz. You are correct in thinking that many audio system naturally have a built in analogue roll-off above 20kHz. But that's not an iron rule. It's not difficult to build preamplifiers and power amplifiers with a flat frequency response to 100kHz. Some tweeters have uncontrolled resonances close to or above 20kHz. So although your hearing may be rolling off by 16kHz, feeding unnecessary, inaccurate HF into your amplifier and speakers is a mistake.

 

[solderdude]

Some headphones and speakers can easily do 40kHz.
You really want them, aside from the intended signal, to also have to produce images (which are not harmonically related) with all the non desirable non linearities those drivers may have ?
Do you want a driver to have try to reproduce the signal on the left (or right) or want the driver to reproduce the signal in the middle ?

Do you think drivers turn the signal on the left/right into the signal in the middle ?
Why settle for such low quality signal when you can have a near-perfect copy of the original input signal ?

Filter everything above half the sample frequency and you end up with a signal that looks exactly like what went in the ADC. Fail to do so and you get signals in there that may not be audible as such but should not be in there and could, potentially cause 'harm' to the original signal in some form.

That's why one wants the reconstruction or anti-imaging filter.

A way around this, but of course makes little sense, is to upsample to say 4x the original sample rate (44.1/48kHz) while using a 'near perfect' filter and then use the 'crappy' DAC.
In such case the images are so far above the audible range it does not matter and there is no audible roll-off either.
Or... just use such DACs with 192kHz and higher bitrates. In that case the chances that images may bite the audible audio in its a$$ are extremely small.

 

[DonH56]

To follow up on IMD, as @MaxwellsEq said, IMD can actually be worse than HD to listeners. The basic reasons are two-fold:

1. For given peak signal levels, IMD is actually higher than HD, by e.g. 9.5 dB for third-order and 6 dB for second-order products. That is, third-order IMD terms are 9.4 dB higher than third-order HD terms of the same two signals (it takes two or more to generate IMD) for given nonlinearity (distortion).

2. IMD creates tones that are not harmonically related to the fundamental frequencies of the two (or more) signals. IMD terms, instead of being multiples (though there are some of those too), include sum and difference terms both close to and far away from the input signals. These terms may stand out more since they are not simple harmonics of the input but new "unrelated" terms.

HD/IMD article: https://www.audiosciencereview.com/...armonic-and-intermodulation-distortion.25436/

 

[33AndAThird]

Evening all. Firstly apologies for delayed reply, my wife and young daughter became ill and after looking after them inevitebly caught the bug myself so have been distracted from audio fun and learning for a little while.

It's an anti-imaging filter. See e.g. https://www.audiosciencereview.com/...ital-audio-converters-dacs-fundamentals.1927/

There are a few other articles on here describing sampling and such, as well as plenty of other material around, that would help clear up some of your questions and misconceptions.

Thanks for the link Don - I've now read that and the other two of your articles on DACs which have certainly helped clear things up for me. You mention my misconceptions, would I be correct in thinking that the misconception is that other than intermodulation distortion, we might otherwise also want to save our tweeters? ie. Amps may well amplify the image above 20KHz and pass that on to our speakers which may not be designed to reproduce that frequency band, and rather than simply not reproduce the frequency (hence providing a filter by default) instead cause them to fail? Also kemmler3Ds reference to wasting power amplifying ultrasonics (even if only at small levels).

An aspect to consider is that the digital sampling points are inherently ambiguous unless you limit the bandwidth to half the sampling rate. For example, suppose you sample a simple 12 kHz sin wave at a CD quality 44,100 Hz. The DAC doesn't know what you sampled, it only sees the sample points. And there are an infinite number of different waves that all pass through those same points. For example, the first "alias" of this 12 Khz wave is 22,050 + (22,050 - 12,000) = 32,100 Hz. There are infinitely many more.

So without a filter, the DAC is free to construct a 32,100 Hz wave instead of a 12,000 Hz wave. It is "correct" in that passes perfectly through every sample point just like a 12,000 Hz wave would. Or, the DAC could construct multiple waves together, and their superposition might also pass through every sample point. Of course all but one of these many different waves are above 22,050 Hz, so after you apply the filter there is only 1 and the sampling points are no longer ambiguous.

Thanks, I get this, but my point is that given we don't hear anything above 20KHz we in effect have a natural filter, so why else would we care that higher frequencies were reproduced even if incorrect? Though I think I have the answer as above.

The 3 dB roll off is from the stairstep reconstruction. Mathematically, the stairsteps as created by the zeroth-order hold process (i.e. sample and hold), is the result from convolving the discrete signal samples as represented by an impulse train (a series of impulses scaled to the amplitudes of the discrete samples) with a unit step function. The convolution with the unit step function is equivalent to filtering the impulse train using a filter with a frequency response of a sinc function. As the sinc function rolls down to about -3 dB at 0.9 Nyquist frequency, that's where the 3 dB drop came from.

Reference: https://www.dspguide.com/ch3/3.htm

It took a reading this a few times to get it, but that explains it thank you!
This implies to me that Archimago's explanation as follows is incorrect?

Something else to notice is that as the frequency increases, with fewer samples to define the sinusoidal wave (since we only have 44.1kHz sample points), notice that many of the frequency peaks do not reach the full amplitude of the sine wave with the NOS output. This correlates with the dip in high frequency amplitude response which we can easily measure:

That is, the roll-off is not actually caused by fewer samples per wavelength at higher frequences reaching full amplitude, but the fact that a sinc function rolls down -3db at Nyquist? Or are these two different ways of describing the same phenominon?

I don't need to add anything further on how anti-imaging filters work - this is already clear from the contribution from experts.

But to pick up on your title:

You may not have intended it, but I feel there's an implication here that you consider intermodulation distortion is not important: i.e. "just". I think IMD is sometimes more important than harmonic distortion. Of course, it's questionable whether you can hear it, but it makes no sense it introduce it if you can avoid doing so.

Another thing worth considering is how your system actually behaves above 20kHz. You are correct in thinking that many audio system naturally have a built in analogue roll-off above 20kHz. But that's not an iron rule. It's not difficult to build preamplifiers and power amplifiers with a flat frequency response to 100kHz. Some tweeters have uncontrolled resonances close to or above 20kHz. So although your hearing may be rolling off by 16kHz, feeding unnecessary, inaccurate HF into your amplifier and speakers is a mistake.

I hadn't meant to diminish intermodulation distortion though I can see how that came across, 'solely' would prehaps have been a better choice of word. That said, your description as to why it might be more important not to feed unnecessary, innacurate HF into one's speakers certainly has impresed on me why we filter these things out.

Thanks to all who replied and helped improve my understanding. Special thanks to @DonH56 for your articles in the reference library that have been enlightening!

 

[DonH56]

Evening all. Firstly apologies for delayed reply, my wife and young daughter became ill and after looking after them inevitebly caught the bug myself so have been distracted from audio fun and learning for a little while.

That is painful (literally); glad everyone is OK.

Thanks for the link Don - I've now read that and the other two of your articles on DACs which have certainly helped clear things up for me. You mention my misconceptions, would I be correct in thinking that the misconception is that other than intermodulation distortion, we might otherwise also want to save our tweeters? ie. Amps may well amplify the image above 20KHz and pass that on to our speakers which may not be designed to reproduce that frequency band, and rather than simply not reproduce the frequency (hence providing a filter by default) instead cause them to fail? Also kemmler3Ds reference to wasting power amplifying ultrasonics (even if only at small levels).

It's been long enough that I don't remember what I had in mind at the time and am too lazy to wade back through the posts. I would certainly want to avoid sending HF energy through the tweeters, but in the real world conventional tweeters with voice coils tend to intrinsically block very high-frequency signals all by themselves. Technically the voice coil is an inductor and that blocks HF signals, though stray (parasitic) capacitance will allow some signal to leak around the coil (not necessarily through the tweeter itself). However, signals above the audio band but within the tweeter's passband could conceivably cause damage, so I prefer to be cautious.

Not wanting to waste amplifier power is reasonable, though again in reality the very HF energy tends to be small compared to the bass and midrange, so chances are not much is wasted. Always assuming there is a proper image filter at the DAC's output.

Not using an image filter could send very HF signals to the speaker so I would not want to use a DAC that did not have one. There are "filterless" DACs and that always struck me as a bad idea. For example, a 100 Hz tone sampled at 44 kHz will generate a 43.9 kHz signal that is likely to be large if there is no (anti-)image filter, and I could see that damaging a teeter. Ditto a 1 kHz tone that produces an image at 43 kHz, and so forth.

 

[33AndAThird]

That is painful (literally); glad everyone is OK.

Indeed we are, thanks

It's been long enough that I don't remember what I had in mind at the time and am too lazy to wade back through the posts. I would certainly want to avoid sending HF energy through the tweeters, but in the real world conventional tweeters with voice coils tend to intrinsically block very high-frequency signals all by themselves. Technically the voice coil is an inductor and that blocks HF signals, though stray (parasitic) capacitance will allow some signal to leak around the coil (not necessarily through the tweeter itself). However, signals above the audio band but within the tweeter's passband could conceivably cause damage, so I prefer to be cautious.

Not wanting to waste amplifier power is reasonable, though again in reality the very HF energy tends to be small compared to the bass and midrange, so chances are not much is wasted. Always assuming there is a proper image filter at the DAC's output.

Not using an image filter could send very HF signals to the speaker so I would not want to use a DAC that did not have one. There are "filterless" DACs and that always struck me as a bad idea. For example, a 100 Hz tone sampled at 44 kHz will generate a 43.9 kHz signal that is likely to be large if there is no (anti-)image filter, and I could see that damaging a teeter. Ditto a 1 kHz tone that produces an image at 43 kHz, and so forth.

Thanks for the rapid response, the large amplitude 100Hz signal imaged at 43.9KHz brings the point home, thank you!

 

[MRC01]

... Thanks, I get this, but my point is that given we don't hear anything above 20KHz we in effect have a natural filter, so why else would we care that higher frequencies were reproduced even if incorrect? Though I think I have the answer as above.

As I mentioned above, if the DAC doesn't have a filter, it can generate a 32,100 Hz wave instead of a 12,000 Hz wave, or a 43,100 Hz wave instead of a 1,000 Hz wave, because both perfectly fit the same sampling points. If it did that you would hear nothing; the 12,000 or 1,000 Hz waves that were encoded, would not be reproduced at all. Not that the DAC would do this, but it could. The filter is mathematically/theoretically necessary; without it the sampling points have no unique solution.

While my answer is from the math/theory side, @DonH56 answer gives a more practical side of this same point.

 

[DonH56]

As I mentioned above, if the DAC doesn't have a filter, it can generate a 32,100 Hz wave instead of a 12,000 Hz wave, or a 43,100 Hz wave instead of a 1,000 Hz wave, because both perfectly fit the same sampling points. If it did that you would hear nothing; the 12,000 or 1,000 Hz waves that were encoded, would not be reproduced at all. Not that the DAC would do this, but it could. The filter is mathematically/theoretically necessary; without it the sampling points have no unique solution.

While my answer is from the math/theory side, @DonH56 answer gives a more practical side of this same point.

Apart from internal processing to eliminate the baseband signal (as is done in some RF systems), how would an audio DAC generate the image without the fundamental? I admit I have not thought about this, just caught me off guard, curious. Does not fit my little pea brain's one-second grasp of the theory.

Thanks - Don

 

[MRC01]

Apart from internal processing to eliminate the baseband signal (as is done in some RF systems), how would an audio DAC generate the image without the fundamental? I admit I have not thought about this, just caught me off guard, curious. Does not fit my little pea brain's one-second grasp of the theory. ...

My response is not about "how" but about "what". From a theoretical perspective, you have a set of sampled points and you must generate a wave that passes through those points. Call each such wave a solution. Without limiting the bandwidth, there are an infinite number of different solutions. Once you limit the bandwidth to half the sampling frequency, there is only one solution.

One way to generate the mathematically perfect solution is the Whittaker-Shannon interpolation formula. The problem is, it's not practical, requiring computing an infinite series for every sample point (well, not exactly infinite but all sample points). Sure, you could truncate the series when the additional terms fall below the noise floor, but it's still computationally infeasible. Methods like Delta-Sigma are more efficient and get very close to the same solution.

 

[danadam]

if the DAC doesn't have a filter, it can generate a 32,100 Hz wave instead of a 12,000 Hz wave

Without limiting the bandwidth, there are an infinite number of different solutions.

In order to generate 32,100 Hz instead of 12,000 Hz you also need to limit the bandwidth, therefore you need a filter. The only difference is that in that case you need a band-pass filter instead of low-pass one.

 

[MRC01]

In order to generate 32,100 Hz instead of 12,000 Hz you also need to limit the bandwidth, therefore you need a filter. The only difference is that in that case you need a band-pass filter instead of low-pass one.

Sure. My point is that without a bandwidth filter the sampling points are inherently ambiguous, as infinitely many different waveforms all pass through them. Bandwidth filtering is not only good engineering practice but theoretically/mathematically necessary. This is in response to the OP's question, "why reconstruction filters?" Without them, the DAC is free to reconstruct a wave entirely different from the wave that was encoded. Not just a wave with spurious high frequency tones, but one that is entirely different, lacking even the passband frequencies.

 

[DonH56]

My response is not about "how" but about "what". From a theoretical perspective, you have a set of sampled points and you must generate a wave that passes through those points. Call each such wave a solution. Without limiting the bandwidth, there are an infinite number of different solutions. Once you limit the bandwidth to half the sampling frequency, there is only one solution.

One way to generate the mathematically perfect solution is the Whittaker-Shannon interpolation formula. The problem is, it's not practical, requiring computing an infinite series for every sample point (well, not exactly infinite but all sample points). Sure, you could truncate the series when the additional terms fall below the noise floor, but it's still computationally infeasible. Methods like Delta-Sigma are more efficient and get very close to the same solution.

OK, but to generate 32.1 kHz instead of 12 kHz, you'd need to either suppress (filter) the fundamental so only the image is present, or up sample using a scheme that also suppresses the fundamental. Both are do-able, using W-S or one of many other schemes, but AFAIK that is not what a conventional (delta-sigma or not) audio DAC would implement. The problem of whether or not the signal is baseband or one of the higher replicas (images) is huge on the ADC side, but for the DAC side the input signal is usually known and it takes extra work (filtering, interpolation, mixing, whatever) to generate only the image tone without the baseband tone. At least as I understand them. I have designed DACs to intentionally generate and use an image band, but that required special digital processing (and analog output filters) I have not seen in a baseband (e.g. audio) DAC. Without an output filter, which tone (which image band) is correct is ambiguous, true, but in general you get all the images unless you explicitly do something to suppress certain ones. I once worked on a DAC design using Hadamard sequences and multipliers that did exactly that, but while the theory was sound, implementation was impractical.

I think I'm lost, sorry... The theory is sound, but I do not see it happening in an audio DAC. That is, images will be present if not filtered, but the baseband signals will still be there.