Are Reconstruction Filters Audible?

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(Mytek's Brooklyn DAC+)

Based on what we currently know about how the ear works, they shouldn't be.

But they are. What the heck?

This is a contentious topic. Audio -- and we're usually talking about music played through headphones or a home stereo -- is very subjective and tends to attract very strong opinions about what does and does not matter.

Amplifier topology (Class A, A/B, D), tubes vs transistors, analog vs digital, expensive vs cheap cables, etc. have always divided enthusiasts about what's important for good sound.

Digital reconstruction filters have recently (especially within the last decade or so) come into focus as well. Since the beginnings of digital audio, linear phase reconstruction filters have been used due to their favorable phase and frequency-domain behavior.

But when CD players hit the market, a number of people said something was wrong with them.

A lot of explanations where passed around, from mastering engineers being stuck in "analog mode" to the "staircase-like" quantization of digital signals.

Despite the industry adapting to digital and the technology itself improving over time, there has persisted a "wrongness" of digital audio that's still around today.

A small number of people in the industry started to theorize that linear phase filters might be the culprit, even though their effects should not be audible.

A little theory

When we convert a digital signal (a FLAC file, a CD, etc.) to analog, we're converting a discrete signal (discrete in both time and amplitude) to a continuously varying one.

digi_vs_analog

Despite what people tend to think, the discrete, staircase-like version is not missing any information that is necessary to reconstruct the original signal.

The staircase pattern has been the target of pro-analog people since digital audio was first introduced, but the reality is a digital signal can perfectly reconstruct an analog signal up to a certain frequency (which happens to be 1/2 the sampling frequency).

But -- and this is a big but -- the staircase pattern does introduce other complications. While the values of the steps are an accurate representation of the original signal, the fact that we're jumping between these discrete steps introduces additional high frequency information. This is called aliasing.

In order to recover (or reconstruct) our original signal, we have to filter out these additional high frequencies.

Enter the ubiquitous filter

So, to make this work, we have to keep all of our original signal and filter out all of the aliasing. We could do this in the analog realm (after the signal has left the DAC chip) but it would require a very steep filter, which is both impractical and can introduce other problems.

The solution is to use a digital filter that pushes the aliasing higher up in frequency where an analog filter can get rid of it more effectively.

This filter has traditionally been a linear phase filter, which is ideal for this application. Linear phase filters tend to have two desirable properties -- they don't affect the sounds we want and very aggressively filter out the sounds we don't.

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(Courtesy ccrma.stanford.edu)

When we look at the time-domain behavior of this filter, we see another story. Linear phase filters (in this image called zero phase) delay the audio signal. We can see that here because the peak of that graph is shifted to the right.

That delay by itself isn't audible. But something else in that graph may be. There are also small oscillations arranged symmetrically around the peak. The oscillation on the left side of the peak are called pre-ringing. That's because they're happening before the main signal arrives.

So why are these time traveling artifacts a problem?

The truth is no one knows. They should not be, since in most audio equipment they're happening at a frequency well above what the ear can resolve.

But for a number of people, myself included, it is audible.

And the industry has accommodated this. DAC chip manufacturers now often supply chips with selectable filters (some of them having no or very little pre-ringing) and hi-fi manufacturers (like Mytek in the image above) allow these filters to be selected by the end user.

Still, lots people people debate the audibility and attribute all of this to companies marketing to people who imagine things that aren't there.

Until we understand the human ear better, this is likely to remain contentious.

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