Does Phase Distortion/Shift Matter in Audio? (no*)

[audiofooled]

I am not sure what this test tone demonstrates?

To me it clearly demonstrates how phase changes can modify the spectrum in terms of modulating the interference pattern of the frequencies. First half sidebands are modulating between varying degrees of constructive/destructive interference, thus modifying the SPL in the sidebands throughout the spectrum.

Second half is pulse where frequencies of the entire spectrum are in constructive interference, resulting in higher peaks of the waveform (as you may have observed in your Audacity excerpt of the waveform). As far as audibility, the "pulses" of the waveform are profoundly different, not so much in perceived timbre but energy distribution and SPL over time.

I am thinking of a transient which has both high and low frequency components

These I regularly find in electronic music. Transients derived from pitching down sinewaves, and then polished with various tools. No square waves there.

Here you may see an example of how such transients may be created, with a caveat that you can see how short in duration various parts of the waveform are, just by following the mouse cursor and shown time in milliseconds:

 

[antcollinet]

similar to a Dirac pulse several samples wide.

I don't think you'll get anything like that from any musical instrument. For example, see here for my analysis of a cymbal hit waveform. The post was related to a speaker speed discussion - but it shows how musical percussive "transients" last a lot longer than most people expect, compared to even 44.1kHz, and nothing like as short as a typical impulse response waveform.

Speaker "Speed"

I know on ASR, they are so big on measurements and basically saying if you can’t measure it it’s not real, but this seems like a pretty fundamental example for how not everything can be measured. Not agreeing on what to measure != not able to measure it.

audiosciencereview.com

 

[j_j]

I was under the impression that 1st-order low-pass and high-pass Butterworth filters sum together and do not vary the phase response. The latter is necessary for the correct reconstruction of a square wave. Of course, using 1st-order filters in loudspeaker crossovers has other issues that can make them a poor choice.

This is, of course, correct, but only because

s/(s+a) + a/(s+a) = (s+a)/(s+a)

Unfortunately, trying that with a second order function does not quite do what one would prefer.

 

[j_j]

To me it clearly demonstrates how phase changes can modify the spectrum in terms of modulating the interference pattern of the frequencies. First half sidebands are modulating between varying degrees of constructive/destructive interference, thus modifying the SPL in the sidebands throughout the spectrum.

There is no modulation once the signal is created. The difference is PURELY in the perception of the two signals, which have precisely the same power spectrum when analyzed at a proper length. SPL is unchanged (with flat weighting at least). Signal Energy is unchanged between the two signals. Perception may well create a sense of change, certainly it does at the extremes that represent the first and second half of the signal posted a few days ago. (they are extremes in that the "phase shift" between 43 and 50Hz (or was it 50 and 57 Hz?, one of the other) is 180 degrees different in the two halves.

 

[gberchin]

Unfortunately, trying that with a second order function does not quite do what one would prefer.

Try that with a second order function and you have created a second order Linkwitz Riley crossover:

s²/(s² + 2ws + w²) - w²/(s² + 2ws + w²) =
(s² - w²)/(s² + 2ws + w²) =
(s + w)(s - w)/(s + w)(s + w) =
(s - w)/(s + w),

a first order allpass function.

You can add a bandpass function to get perfect reconstruction:

s²/(s² + w/Q s + w²) + (w/Q s)/(s² + w/Q s + w²) + w²/(s² + w/Q s + w²) =
(s² + w/Q s + w²)/(s² + w/Q s + w²) = 1

Bang and Olufsen patented this decades ago; US 4,031,321.

 

[gberchin]

The difference is PURELY in the perception of the two signals, which have precisely the same power spectrum

Could this indicate that nonlinearities in human hearing are interacting with the signals differently?

 

[KSTR]

It is known that the output of minphase filters can not reconstruct a square wave input.

Some can, the best known one is the 1st order XO, which is of the Butterworth type with 90 degree phase offset between the ways.
Higher orders are possible, i.e. 2nd order, but then the phase offset is even larger, like 120deg at the XO point and even more left and right of it. We also have a couple of dB's of peaking before the roll-off starts.
And that's the problem with these filter targets -- besides the directivity issues that could arise: While they sum to flat magnitude and phase they also sum destructively at/around the XO and have a huge overlap region.
This all puts extreme demands on the drivers and the whole construction (directivity control, etc). IMHO a severe compromise not worth it.

 

[audiofooled]

There is no modulation once the signal is created. The difference is PURELY in the perception of the two signals, which have precisely the same power spectrum when analyzed at a proper length. SPL is unchanged (with flat weighting at least). Signal Energy is unchanged between the two signals. Perception may well create a sense of change, certainly it does at the extremes that represent the first and second half of the signal posted a few days ago. (they are extremes in that the "phase shift" between 43 and 50Hz (or was it 50 and 57 Hz?, one of the other) is 180 degrees different in the two halves.

Yes, I understand that the signal itself is perfect, all the same but the phase. I wish I could express myself as precisely as you do, @j_j

I was talking about perceptual differences between the two. In lack of a better term, if I were to imagine the first part as listening to helicopter blades, then part two would be only one blade in comparison. The audible difference is not at all subtle, the perceived envelope is entirely different.

This is what I was able to capture on the scope at MLP:

This is what I mean when I said that the SPL peak is also different, phase summation I suppose?

And if I steal this from @Keith_W :

I can see a striking resemblance?

Btw, my system is aligned such as this:

What is your favorite house curve

I did a little comparison mostly out of curiosity about the measuring methods (hope I didn't messed things up) . All measurements are about a meter away or less while I should have gone farer,maybe I'll repeat sometime. Nevertheless they seem pretty close to me: Red is for MMM method Green is...

audiosciencereview.com

Edit: typo

 

[j_j]

Try that with a second order function and you have created a second order Linkwitz Riley crossover:

s²/(s² + 2ws + w²) - w²/(s² + 2ws + w²) =
(s² - w²)/(s² + 2ws + w²) =
(s + w)(s - w)/(s + w)(s + w) =
(s - w)/(s + w),

a first order allpass function.

You can add a bandpass function to get perfect reconstruction:

s²/(s² + w/Q s + w²) + (w/Q s)/(s² + w/Q s + w²) + w²/(s² + w/Q s + w²) =
(s² + w/Q s + w²)/(s² + w/Q s + w²) = 1

Bang and Olufsen patented this decades ago; US 4,031,321.

Which is not power complimentary, unfortunately.

 

[j_j]

Could this indicate that nonlinearities in human hearing are interacting with the signals differently?

I think it's more likely that the variation in time envelope in the ERB(s) that the signal occupies are different, and you can hear that variation in envelope.
Since this is in the brain, not the ear, it's safe to assume "linearity" is not even on the table.

 

[gberchin]

Which is not power complimentary, unfortunately.

So which is more important, sum-to-unity amplitude or constant power? And why?

 

[j_j]

So which is more important, sum-to-unity amplitude or constant power? And why?

Both, unfortunately. Consider the effects of the phase issues on radiation pattern, as well, and what happens when you're off-axis. Bear in mind that the 5 to 10 microsecond sensitivity still exists.

We have different (electronic) crossovers in our stuff, that are both power compliemntary and sum to unity. Obviously,they are not LR. They are also rather steeper than most people expect.

The lack of power complimentary also reads into driver linearity in a rather annoying fashion. I have used assymetric subtractive crossovers, which work well in some particular applications (at low frequencies) but fail miserably at higher frequencies. Sometimes the reason has not been clear, but it has to do in some fashion with driver radiation patterns and nonlinearities due to cone modes. Since I had better options, when it's a problem, it's outta there.

 

[gberchin]

Both, unfortunately. Consider the effects of the phase issues on radiation pattern, as well, and what happens when you're off-axis.

Seems like the power loss from sum-to-unity amplitude is compensated by mutual coupling if the woofer and tweeter are physically close together. And, of course, the radiation pattern is part of the reason for the popularity of Linkwitz-Riley crossovers in sound reinforcement -- they are in-phase at all frequencies.

 

[j_j]

Seems like the power loss from sum-to-unity amplitude is compensated by mutual coupling if the woofer and tweeter are physically close together. And, of course, the radiation pattern is part of the reason for the popularity of Linkwitz-Riley crossovers in sound reinforcement -- they are in-phase at all frequencies.

Even when the drivers are close, you'll find that off-axis behavior can be quite obvious. They are better than third order BW with phase inversion, certainly.

But when you're in the digital domain, it's much easier to not do either.

 

[gberchin]

Different situations require different optimizations. One-hundred percent of my listening occurs in my living room, on-axis. So I am a strong advocate of perfect-reconstruction crossovers -- matched-delay subtractive crossovers in particular. Designing for an auditorium, well, that's a much more difficult problem, particularly if the radiation pattern of the woofer and tweeter are significantly different around the crossover frequency. I might still use perfect-reconstruction as a starting point, with adjustments as-necessary.

 

[j_j]

Different situations require different optimizations. One-hundred percent of my listening occurs in my living room, on-axis. So I am a strong advocate of perfect-reconstruction crossovers -- matched-delay subtractive crossovers in particular. Designing for an auditorium, well, that's a much more difficult problem, particularly if the radiation pattern of the woofer and tweeter are significantly different around the crossover frequency. I might still use perfect-reconstruction as a starting point, with adjustments as-necessary.

The off axis response colors the timbre of your listening room, and that's where , for me, the problem with non-power-conserving crossovers come into play. Even though the direct is correct, you can't count on atmospheric coupling in any useful fashion, and so you will have peaks in the room timbre.

 

[gberchin]

The off axis response colors the timbre of your listening room ...

The solution to this in the living room then becomes the same as the solution in the auditorium: pattern control. That implies waveguides (horns) or arrays, in addition to treatment of room acoustics. I'm not dedicated enough as an audiophile to address those in anything more than a cursory manner.

 

[j_j]

The solution to this in the living room then becomes the same as the solution in the auditorium: pattern control. That implies waveguides (horns) or arrays, in addition to treatment of room acoustics. I'm not dedicated enough as an audiophile to address those in anything more than a cursory manner.

Well, pattern control is much easier with a constant-delay arrangement. Further, I prefer not to deal with horn resonances, etc. But that's a different issue.

 

[gberchin]

Well, pattern control is much easier with a constant-delay arrangement.

Having worked with SONAR beamformers in a previous life, I know that there is an entire mature technology that is only just starting to be exploited for audio.

 

[Keith_W]

Having worked with SONAR beamformers in a previous life, I know that there is an entire mature technology that is only just starting to be exploited for audio.

You might be interested in participating in the constant beamwidth transducer thread. I watched Don Keele's video. He said he got his inspiration from submarine sonar systems.