Minimum Phase vs Linear Phase

[Ron Texas]

This choice shows up in various places:
1. Many DAC's, including several reviewed here.
2. Most implementations of SOX
3. Rephase (default is minimum phase.)

My understanding is linear phase filters have pre-ringing. Minimum filters put all the ringing after the pulse. When lossy audio compression was under heavy development pre-ringing was often discussed and it could be identified in double blind testing. At the time developers were trying to reduce pre-ringing.

I haven't done any blind testing, but there appears to be a certain harshness in loud and high notes of some female vocalists which goes away when the DAC is set for minimum phase. The Topping D30 has this problem, in my opinion. When I use my Topping DX3 Pro with a linear phase filter, it sounds just like the D30. Switch to a minimum phase filter and the harshness goes away. This was noted on both LSR305 Mk II's and LS50's powered by a Crown XLS 1502. The difference is subtler wiith my Grace M9XX which might mean something else is going on.

So, what kind of filters should we be using, or is this from the marketing department? Does it make a difference if the application is a DAC, SOX or Rephase? Note the JRiver implementation of SOX is fixed, probably with linear phase and they are adamant about not making it configurable.

 

[mansr]

My understanding is linear phase filters have pre-ringing. Minimum filters put all the ringing after the pulse. When lossy audio compression was under heavy development pre-ringing was often discussed and it could be identified in double blind testing. At the time developers were trying to reduce pre-ringing.

Your understanding is incomplete. Firstly, the filters under discussion do not ring. It is mathematically impossible for a FIR filter to ring since there is no feedback. The proper term is ripple, you are correct in that minimum phase filters put the ripple entirely after the main peak. Whatever you call it, the ripple/ringing is of a fixed frequency above the audible range, assuming CD quality or better. At lower frequencies, the effect can become audible.

Secondly, lossy codecs can suffer from pre-echo, which is something else entirely. When this occurs, a (distorted) sound fragment can be heard 10 ms or so ahead of the real event, like an echo but before the main sound rather than after, hence the name. It is most commonly noticed with percussive sounds. The cause is similar to that of the blurring seen in JPEG-compressed images of line art or text.

Pre-echo can also occur as a result of print-through in tapes or inter-groove interference in vinyl. Yet for some reason, nobody ever calls mp3 "analogue like." Strange.

 

[Jim777]

Ron did not mention if he was thinking of FIR or IIR filters. But here I made (in blue) a half band FIR filter, and (in red) a filter with the exact same magnitude response, but all the roots were flipped inside the unit circle. The difference is only the phase. There is what I would call pre-ringing with the symmetric FIR, even though it is of finite length. The comment about voices is interesting, because we know a speech codec will use a minimum phase filter (LPC), even though the real reason has to do with remaining stable when you invert it. I'm not sure about audibility; psycho-acoustics tell us that pre-masking is way shorter than post-masking, so there might be an advantage to the minimum phase for that. So I don't know if there is a scientific answer, but I generally fool myself into preferring minimum phase when I listen.

 

[mitchco]

Hey Ron, lots of objective measurements and subjective listening tests on this subject over at Archimago's blog.

 

[scott wurcer]

It's dangerous to use the term echo in the same conversation with the "ringing" of some filters (really the Gibbs effect). You can design minimum phase or linear phase versions of both IIR and FIR filters (there are some limitations with IIR filters). The ringing of most common concern is simply related to the sampling theorem and the fact that if you limit either the time or frequency domain the other will have infinite extent.

I have not seen any controlled testing that shows brickwall filtered music at 22.05kHz has any audible effect.

 

[RichB]

The Oppo UPD-205 has filter selections and IMO, the filters sound remarkably different. I suppose I could setup a SBT using the IPAD to select different filters. It seems ideal for this type of test.

For Filters, I think we need a new type of measurement that examines phase with 2 channels measured channel.

If there is a justification for MQA sounding different, I suspect it is the slow roll off filter. These and everything else about MQA seems to be a degradation preferred by some. That makes a lot more sense than their marketing drivel.

- Rich

 

[Julf]

View attachment 32266

What are the axes? Without any units, this is pretty meaningless.

 

[Jim777]

What are the axes? Without any units, this is pretty meaningless.

It's a digital filter.. samples on the x axis and amplitude on the y axis. It's short, but it's only to illustrate the difference.

 

[Ron Texas]

Hey Ron, lots of objective measurements and subjective listening tests on this subject over at Archimago's blog.

I have read lots of his stuff. He likes to upsample with SOX before sending PCM to his Teac DAC. It appears the preference is for minimum phase in this application.

@Jim777 in the context of Rephase it's FIR filters and the program has the option to make them minimum phase or linear phase. For the other two cases, I don't know how it is done.

After doing some reading it appears as far as equalization of low frequencies is concerned, it's better to use minimum phase filters and avoid having a disturbance before the signal. Room EQ is mostly about low frequencies.

On more than one DAC, I am (subjectively) hearing a difference, preferring minimum phase with 2 DAC's both having AKM converters.

I don't know if we are dealing with one issue here or two separate issues being equalization an upsampling.

 

[RichB]

Here are some posts by @John_Siau concerning phase.

Concerning amp phase:

https://www.audiosciencereview.com/...f-benchmark-ahb2-amp.7628/page-21#post-181191

I would add one more: The phase response needs to be linear. You can have a flat frequency response without having a linear phase response and the non-linear phase response will change the way transients sound. A non-linear phase response will have no impact on a continuous set of tones, but it will change the apparent frequency response of transients.

Concerning DAC filters:

https://www.audiosciencereview.com/...of-benchmark-ahb2-amp.7628/page-7#post-179006

Some DACs add delay to the high frequencies and this seems to make reverberation more audible. The delay is produced if linear-phase filters are not used when reconstructing the analog signal.

The Benchmark DACs use linear-phase filters. Some DACs use filters that change the phase response and this can cause an audible effect.

I assume that delaying high frequencies is "Minimum Phase".

https://www.audiosciencereview.com/...f-benchmark-ahb2-amp.7628/page-17#post-180486

Our ears are relatively insensitive to phase response on steady-state combinations of a fundamental and a series of harmonics. However, we are quite sensitive to phase response on transients. If the high-frequencies arrive first, they are accentuated. If the high frequencies arrive late, the impression will be that they are rolled off. An impulse, such as drum rim shot produces a broad spectrum of frequencies. A perfect impulse produces all frequencies simultaneously. The sound of this impulse will change when the phase response is changed. Many D/A converters use filters with a non-linear phase response. These filters change the way an impulse sounds. The changes will be most noticeable in the percussive content of the music. It has become popular to manipulate the sound with non-linear filters. These filters are an effect and some people enjoy having these effects applied to their music upon playback. The down side is that these effects are cumulative. Each pass through a non-linear phase filter will add more audible effects. In contrast, many A/D and D/A processes can be cascaded when the converters have a linear phase response. We have demonstrated this with some in-house listening tests that we conducted with cascaded converters.

The differences can be measured if you run the right tests. The differences will not show up in the frequency response (amplitude response).

Beware of time-domain response plots because they often look at only one phase relationship to the sample clock. An "improved" filter response may not look so good at other phase relationships to the sample clock. Filters that allow aliasing will pull transients toward the nearest sample clock edge (distorting the transient).

- Rich

 

[March Audio]

The pre ringing is a huge red herring that has surfaced over recent years. Here is an actual measurement of my DAC1 replaying (attempting) a Dirac pulse which is often used to characterise filters. . It's the classic waveform you'll see in magazines.

However if you look more closely youll see the time base of the ripples is around 50uS. That's 20kHz.

Another thing to consider is that real musics HF content (not illegal test signals) around this frequency and into the transition band is very low in level, maybe - 70dB. So any generated ripple is going to be much lower again.

So basically it's at a frequency above your hearing range at a volume thats too low to hear even if you could hear ultrasonics.

 

[NTK]

The pre ringing is a huge red herring that has surface over recent years. Here is an actual measurement of my DAC1 replaying (attempting) a Dirac pulse. It's the classic waveform you'll see in magazines.

View attachment 32272

However if you look more closely youll see the time base of the ripples is around 50uS. That's 20kHz.

Another thing to consider is that real musics HF content (not illegal test signals) around this frequency is very low in level, maybe - 70dB, so any generated ringing is going to be much lower again.

So basically it's at a frequency above your hearing range at a level thats too low to hear even if you could hear ultrasonics.

This is the classic sinc function you get from a bandwidth limited reproduction of an impulse. The sinc filter passes 100% in its passband and rejects 100% in its stop band -- the ideal brickwall filter. To understand, the digital samples of an impulse (let's center it at 0) is 1 at 0 and 0 everywhere else. To reproduce it in analogue with a 'smooth' continuous function, the function needs to pass through 0 at all sampling points except at 0 it needs to pass through 1. The sinc function is the smoothest possible function that satisfy this requirement. (It oscillates around zero everywhere else except at 0) The oscillation frequency is the Nyquist frequency.

An impulse has spectral contents all the way to infinite frequency. So having frequency contents all the way to Nyquist for a band limited version should not be unexpected.

 

[March Audio]

This is the classic sinc function you get from a bandwidth limited reproduction of an impulse. The sinc filter passes 100% in its passband and rejects 100% in its stop band -- the ideal brickwall filter. To understand, the digital samples of an impulse (let center it at 0) is 1 at 0 and 0 everywhere else. To reproduce it in analogue with a 'smooth' continuous function, the function needs to pass through 0 at all sampling points except at 0 it needs to pass through 1. The sinc function is the smoothest possible function that satisfy this requirement. (It oscillates around zero everywhere else except at 0) The oscillation frequency is the Nyquist frequency.

An impulse has spectral contents all the way to infinite frequency. So having frequency contents all the way to Nyquist for a band limited version should not be unexpected.

A Dirac pulse is fundamentally an illegal signal. An ADC will always low pass filter at half sample rate. It's bandlimited. A 0 — 1 — 0 sample signal can't exist. We already know this. As Scott mentioned above, Gibbs effect.

Which also brings into question the futility of trying to solve the problem in the dac.

 

[restorer-john]

The pre ringing is a huge red herring that has surface over recent years. Here is an actual measurement of my DAC1 replaying (attempting) a Dirac pulse. It's the classic waveform you'll see in magazines.

You should note that the original use in magazines of the single sample 0dBfS pulse was not to show filter characteristics in magazine reviews, it was to show absolute polarity or reversal.

Here's one of my CDP-101s on the same signal:

https://www.audiosciencereview.com/...rt-answers-questions.7623/page-11#post-183553

The type of filtering (IIR or FIR) was usually depicted by using square waves.

 

[March Audio]

You should note that the original use in magazines of the single sample 0dBfS pulse was not to show filter characteristics in magazine reviews, it was to show absolute polarity or reversal.

Here's one of my CDP-101s on the same signal:

https://www.audiosciencereview.com/...rt-answers-questions.7623/page-11#post-183553

View attachment 32277

The type of filtering (IIR or FIR) was usually depicted by using square waves.

That may have been its original use but it is frequently used to show filter characteristics.

 

[gvl]

I find linear phase sharp sounds noticeably cleaner and more focused on the Dx3pro, on the DX7s however there's barely any difference.

 

[Cosmik]

Audiophilia becomes obsessed with the bits of the system that it can access and modify with garage technology: interconnects, power cords, rubber feet. In digital audio, the only bit that was amenable to such hobbyism was the filter after the DAC so it was inevitable that this would become the focus of efforts eventually. People realised that you can fiddle with the filter or even remove it completely, and the system still 'works'.

At the same time, knobs and switches to fiddle with that don't actually do anything are a win-win for manufacturers, because they allow the customer to create their own settings which they can feel some pride in, and which they will defend because it is their placebo. If the switches do something that can be seen on an oscilloscope when you feed in a special test signal then this is a perfect blend of voodoo and high technology.

 

[March Audio]

I find linear phase sharp sounds noticeably cleaner and more focused on the Dx3pro, on the DX7s however there's barely any difference.

When I have played with DACs that have adjustable filters the only ones I thought had any noticeable effect were those that rolled off early into the audible band.

 

[maty]

In the DAC, minimum phase by default, of course.

But if you make resampler from a computer, depending on the recording, it may sound better in another way, something I have verified many times. Usually I prefer Intermediate, if the original sound does not convince me. If after the process still does not convince me, I delete the files.

I can differentiate between the Pass Band choiced. Of course, I talk about very good recordings with high DR.

 

[gvl]

When I have played with DACs that have adjustable filters the only ones I thought had any noticeable effect were those that rolled off early into the audible band.

Yup, apodizing filter secret revealed.