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

[j_j]

Regarding timbre shift, I have preciously shown my own positive DBT rewults which I hear when all-passed at lower frequencies. Some people seem not to hear it though. But above 1 kHz. I can’t hear it.

More less above 1khz (you start to lose sensitivity to direct phase changes at 500Hz, and it's pretty much gone by 2kHz) you're sensitive to envelope changes, rather than direct phase changes.

Allpass filters can, of course, quite handily change an envelope.

 

[gberchin]

... if you give me the phase response of the LR crossover, I can probably design a signal that's audible ...

A 4th-order Linkwitz-Riley crossover sums to a 2nd-order allpass filter, Q = 1/sqrt(2):

(s² - sqrt(2)s + 1) / (s² + sqrt(2)s + 1)

 

[j_j]

A 4th-order Linkwitz-Riley crossover sums to a 2nd-order allpass filter, Q = 1/sqrt(2):

(s² - sqrt(2)s + 1) / (s² + sqrt(2)s + 1)

So, how many degrees per ERB? That's the question.

 

[bmc0]

So, how many degrees per ERB? That's the question.

Looks like about 16° 31° for a center frequency of 300Hz (ERB: 28.6Hz 57.1Hz) or about 21° for a center frequency of 1kHz (ERB: 128Hz).

 

[j_j]

That would mean it's marginally audible for the most sensitive signal, say if you put pure FM with a 25 Hz tone modulation in it, you'd most likely hear some modulation.

You will hear some phase inversion effects, maybe, as well.

This is one of the reasons why you use a constant delay crossover. There is no "but".

Btw, thank you for calculating that, I wasn't near Matlab this morning.

 

[Keith_W]

So, how many degrees per ERB? That's the question.

What is the target of degrees per ERB that would make the phase change inaudible? And are we talking about the difference in degrees between left/right speaker, or (say) 30 deg/ERB in both speakers?

I know you said that you don't publish papers any more (pity!) but a link to an article or a video would be really useful. Whilst talking to you on a forum is great (and educational!) nothing beats a more substantial article to sink your teeth into.

 

[j_j]

What is the target of degrees per ERB that would make the phase change inaudible? And are we talking about the difference in degrees between left/right speaker, or (say) 30 deg/ERB in both speakers?

I know you said that you don't publish papers any more (pity!) but a link to an article or a video would be really useful. Whilst talking to you on a forum is great (and educational!) nothing beats a more substantial article to sink your teeth into.

This is intRAaural, one channel, one ear. 15 degrees has been proposed as a limit.

I know in some of my tutorials I've given that number already. Of course, that doesn't help because I've given maybe 100 or so.

 

[bmc0]

Btw, thank you for calculating that

Turns out I screwed it up. ERB at 300Hz is 57.1Hz (somehow I divided by two), so the phase shift is about 31°. Here's a plot:

Edit: Added grid and title to plot.

 

[gberchin]

What was the crossover frequency used for this analysis?

 

[gberchin]

That would mean it's marginally audible for the most sensitive signal ...

Siegfried Linkwitz would have disagreed with you vehemently. I was once in an online conversation with him, in which I advocated for matched-delay subtractive crossovers because they sum to delay, rather than to allpass. Linkwitz sternly declared that phase is not audible, then terminated the conversation.

 

[j_j]

Siegfried Linkwitz would have disagreed with you vehemently. I was once in an online conversation with him, in which I advocated for matched-delay subtractive crossovers because they sum to delay, rather than to allpass. Linkwitz sternly declared that phase is not audible, then terminated the conversation.

It occurs to me, did the person measuring phase take the difference between the lower and upper edge of the ERB? That is the 15 degree or so measure. The total phase shift really doesn't matter too much except as it represents delay.

Somewhere on this board is an extreme example of low frequency phase shift, but I doubt that most phase shift is as extreme as that.

 

[gberchin]

The total phase shift really doesn't matter too much except as it represents delay.

I was thinking about the very same thing. It seems like the phase deviation from linear is what really matters. One could have thousands of degrees of phase shift per ERB, but if it was part of a pure delay then it would not be audible except for the time shift.

 

[j_j]

I was thinking about the very same thing. It seems like the phase deviation from linear is what really matters. One could have thousands of degrees of phase shift per ERB, but if it was part of a pure delay then it would not be audible except for the time shift.

Correct, you have to do a line fit across the ERB, and then measure the deviation from that.

 

[j_j]

Correct, you have to do a line fit across the ERB, and then measure the deviation from that.

Of course, different time delay across frequency that's under the limit for timbre can still create audible effects, but across frequencies rather than in a narrow band. Isn't hearing fun?

 

[Doodski]

@j_j. What is a ERB? I'm following with what I'm guessing is the complex number stuff but I have no idea what a ERB is. I Googled the abbreviation under trig, math and other non-useful terms and no joy.

 

[Keith_W]

@j_j. What is a ERB? I'm following with what I'm guessing is the complex number stuff but I have no idea what a ERB is. I Googled the abbreviation under trig, math and other non-useful terms and no joy.

Equivalent Rectangular Bandwidth. If two tones are played within the same ERB, the softer tone is masked by the first.

Here, the ERB bandwidth of 100Hz is 30Hz, and the bandwidth for 10kHz is about 1000Hz.

 

[bmc0]

What was the crossover frequency used for this analysis?

It doesn't show a single crossover frequency. The X-value is the crossover frequency (center frequency of the all pass filter) and the Y-value is the absolute value of the phase difference over the ERB centered at the given frequency.

The ERB in Hz is ERB(f) = 24.7×(4.37f+1), where f is the center frequency in kHz.

For example, the plot shows a value of about 21° at 1kHz. This means that an LR4 crossover at 1kHz results in about 21° of phase rotation from 936Hz (lower bound of the ERB) to 1069Hz (upper bound of the ERB).

It occurs to me, did the person measuring phase take the difference between the lower and upper edge of the ERB?

Yes, I simply calculated the phase difference between the upper and lower ERB bounds for each center frequency (see above for more detail). Shown graphically for 1kHz only (vertical lines are the bounds):

Is that the correct way to calculate it?

What is a ERB?

Equivalent rectangular bandwidth.

 

[Doodski]

Equivalent Rectangular Bandwidth. If two tones are played within the same ERB, the softer tone is masked by the first.

View attachment 380833
Here, the ERB bandwidth of 100Hz is 30Hz, and the bandwidth for 10kHz is about 1000Hz.

This explains why I hear stuff over stuff I suppose. Thank you for explaining that for me. MuchO appreciated.

 

[audiofooled]

I listen to my stereo about 3.5m away, and the system is spaced away from the side walls so that the floor bounce is much earlier than the sidewall reflection. I suppose that I am getting mostly diffuse floor and ceiling reflections.

My listening distance is also 3.5m away. I have multiple low frequency sources. Sub on the floor (sealed), mains stacked up (also ported, with rear ports close to the wall). At the time I thought it sounded great. Here's what it did close to the floor, with measurement positions centered to the sub cone level, with uniform distance increments from close field to 3m away:

Phase for the same set of measurements:

If you look at the room modes, what stands out is that modes are sadly supported. Room does what it wants with regards to gradient. You would think that what's important is only what happens at ear level, indeed it levels out at 49Hz mode, but 24,5Hz was nothing I could do about. Simply no output at ear level.

Now let's see what if I plug the ports. Entirely different situation:

Let's take a look at the phase:

This is at ear level, 3,5m away:

Modes are no longer supported which gives room for PEQ to further flatten the FR and phase:

All I can say is that the difference is very audible. Here is the plot for the entire audible band:

It's hard to describe what this does to correlated signals, signals with sharp envelope, or, for example, to signals with inverse envelope in between the channels. Or pure tones, for that matter. Proximity effects are on the recording and system can be such that perception of depth is preserved over distance.

I don't know how much correlation there can be with respect to room decay, but I suspect that TOPT is smooth enough that what room does can be "thrown away" more easily:

 

[gberchin]

Is that the correct way to calculate it?

That's the correct way to calculate it for a 1 kHz crossover frequency. If the crossover frequency is not 1 kHz, then the Phase vs. Frequency will be the same shape, except that it will shift left or right so that the inflection point is at the new crossover frequency.

This matters, because the ERB changes with frequency. According to the equation provided by @bmc0, the ERB at 1 kHz is around 133 Hz, or about 0.19 octaves. But at 100 Hz the ERB is around 35.5 Hz, or about 0.51 octaves. So the ERB at 100 Hz spans a greater portion of the LR4 phase curve than it does at 1 kHz.

EDIT: corrected attribution