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Minimum Phase vs Linear Phase

maty

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In the speakers design, DSP crossover must work like passive filters: minimum phase -> PEQ better if works as minimum phase too.

Grimm LS1
[PDF] https://www.grimmaudio.com/site/assets/files/1088/speakers.pdf

Grimm-LS1-DSP-minimum-phase.png


Grimm-LS1-DSP-minimum-phase-2.png


In the DAC, to the taste of the user or designer, I say.

The problem is that the audio system is complex and has a multitude of components so we cannot be sure how the sum of all of them will be.
 

solderdude

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Crossover filters work inside the audible range, even where the hearing is very sensitive, where as the reconstruction filter works outside of the audible range so different rules apply for these different circumstances.
 

KSTR

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@maty, you got that one wrong.
Grimm's approach is to design a textbook perfect minimum phase *crossover* and then apply a mathematically derived global "phase-unwrapping" ahead of it (via one single and simple FIR filter) to obtain a linear phase overall behavior. IMHO, this is the best way to achieve the goal, with the smallest set of compromises.
 

maty

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If I do not misunderstand, get the best of the two philosophies.

In any case, the PEQ is better than a minimum phase, which is what I really wanted to infer. This week I have been playing with rePhase: https://rephase.org/ with the same parameters of PEQ (JRiver MC). With the modded KEF Q100 5.25" coaxial speakers:

Rephase-PGEQ-KEF-q100.png


Rephase-PPEQ-bypass-KEF-q100.png


Rephase-PPEQ-KEF-q100.png
 
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maty

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bennetng

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Isn't the overshoot (when a clipped audio sample is present for instance) not a question of digital reconstruction filtering before or in the DAC chip ?
In that case extra headroom in the analog circuit isn't going to help when the DAC chip clips against its power supply rail as the gentle post filtering can't do anything against it. That filter acts more like that on Mansr's plot of the squarewave.

I figure in such a case the digital filter and DAC chip must have the 3dB extra headroom. If they don't you get the squarewave plots as often seen in many of Archimago's posts where one can see clipped ringing at 0dBFS squarewaves in a lot (but not all) DACs.

So both the digital and analog parts should have enough headroom to allow for this.
There is a good reason to not imposing a fixed amount of attenuation (like 3dB) from the DAC manufacturer.

[1] 3dB is not always enough, even in published music instead of test signal.
[2] Not all music genres or recordings are mastered to exhibit severe intersample clipping.
[3] Modern software players often decode lossy codecs in floating point domain and generate non-intersample peaks over 0dBFS which cannot be protected by having intersample headroom in the DAC.
The three points above are covered in this article:
https://archimago.blogspot.com/2019/06/guest-post-why-we-should-use-software.html

[4] Intersample headroom in DAC is essentially a fixed amonut of digital attenuation, end users themselves can always do the same provided that they are willing to do so.
https://hydrogenaud.io/index.php?topic=98753.msg826323#msg826323
 

scott wurcer

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MC_RME

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However, @mansr's "square looking wave" is not the only band limited signal that resembles a square wave. Here I created a band limited 2 kHz square wave (blue curve) by summing only the first 5 terms of the expanded sine series (i.e. 2 kHz fundamental, 6 kHz 3rd harmonic, 10 kHz 5th harmonic, 14 kHz 7th harmonic and 18 kHz 9th harmonic). This is a totally legitimate band limited signal with no spectral contents above 20 kHz.
View attachment 33429

Here I pass this legitimately band limited signal through a 8th order low pass Butterworth filter with 20 kHz cutoff. You can see that because of the phase distortion, the peak-to-peak voltage is higher than the original signal. My point is that this phase distortion eats into the available headroom of the output circuitry.
View attachment 33430
I reproduced this example in a real world setup. You are right. Although the original sample seems fully ligit the DA filters * cause a peak amplitude that looks like ringing (due to the test signal itself), but is not. A similar, yet not fully identical effect can also be found when playing with EQ, as explained here:
https://sound.stackexchange.com/questions/24981/why-is-my-cutting-equalizer-increasing-output-level

* Mainly SD Sharp/SD Slow. Others seem less affecting the signal, which is as expected due to their smaller or missing phase shift.
 
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However, @mansr's "square looking wave" is not the only band limited signal that resembles a square wave. Here I created a band limited 2 kHz square wave (blue curve) by summing only the first 5 terms of the expanded sine series (i.e. 2 kHz fundamental, 6 kHz 3rd harmonic, 10 kHz 5th harmonic, 14 kHz 7th harmonic and 18 kHz 9th harmonic). This is a totally legitimate band limited signal with no spectral contents above 20 kHz.
View attachment 33429
Could you provide the amplitudes of the different waves and the sampling rate please? What software did you use for the plot? It looks like Matplotlib to me.
 

Yviena

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Yviena

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Why? What could you possibly hope to learn from that?
Well the linked PDF US6337645.pdf i uploaded basically says: If, however, one plots the magnitude of the impulse response on a logarithmic scale, one can see some very interesting results, Which do correlate With listening tests.

I don't know how applicable it is to the digital filters in a dac though.
 

NTK

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Could you provide the amplitudes of the different waves and the sampling rate please? What software did you use for the plot? It looks like Matplotlib to me.
Here is my Python code I used to generate the plot.
Python:
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt

# Create low-pass filter (8th order Butterworth, f_cutoff = 20 kHz)
fs = 192000
N = 8
f_cutoff = 20000
butter_sos = signal.butter(N=N, Wn=f_cutoff, btype='low', output='sos', fs=fs)

# 2 kHz square wave band-limited to its first 5 terms
f_signal = 2000
duration = 1.0
omega = 2 * np.pi * f_signal

t = np.linspace(0.0, duration, int(duration * fs), endpoint=False)
n_pts = t.shape[0]
x = np.empty([5, t.size])
for idx, k in enumerate([1, 3, 5, 7, 9]):
    x[idx, :] = (4 / np.pi) * np.sin(k * omega * t) / k
x_sum = np.sum(x, axis=0)

# Band-limited square wave filtered by the low-pass filter
x_butter = signal.sosfilt(butter_sos, x_sum)

# Plot original and filtered square waves
plot_pts = np.arange(int(3 * fs / f_signal)) + int(3 * fs / f_signal)

fig2, ax = plt.subplots(figsize=(8, 5))
ax.plot(t[plot_pts], x_sum[plot_pts], label='$x_{orig}$')
ax.plot(t[plot_pts], x_butter[plot_pts], label='$x_{butter}$')

ax.legend(loc='upper right')
plt.tight_layout()
plt.show()

...
also i found some documents that are maybe worth a read for someone, i myself don't understand them.

http://boson.physics.sc.edu/~kunchur/align.pdf
...
I'm a little bit familiar with the first paper by Kunchur. I believe there are (at least) a couple of flaws in Kunchur's test methodology. He set up his test by stacking 2 loudspeakers on top of each other, move the top one back and forth, and asked listeners if they detected any differences in the sound. When the listener heard a difference, Kunchur attributed the cause to the "time-smearing" of the signals. The first flaw, IMO, was in his choice of test signal. He fed the same 7 kHz square wave to both speakers.

The issue is that when you have 2 adjacent sources producing tones of the same frequencies, they interfere with each other. How they interfere is dependent on the differences in the distances between the loudspeakers and the listener. When a listener hears a difference, it is not possible that he or she can attribute the difference to a sound loudness change due to interference, or to the time “smearing” effect (which was his claim).

A second flaw is ignoring the diffraction effects due to the changing degrees of mismatch between the front baffles of the loudspeakers. These 2 flaws (instead of "time smearing") could have caused the sound to be audibly different to the listeners.
 

Julf

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I would actually have liked to see log squared impulse response of the different filters.

also i found some documents that are maybe worth a read for someone, i myself don't understand them.

http://boson.physics.sc.edu/~kunchur/align.pdf

http://boson.physics.sc.edu/~kunchur/temporal.pdf

the last one is especially interesting as it's about digital filters.
The Kunchur papers occasionally surface among audiophiles, but they have been pretty thoroughly discredited. I remember one of our leading resident experts, @j_j , describing them as "utterly full of cow patties". :)
 
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PaulD

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The Kunchur papers occasionally surface among audiophiles, but they have been pretty thoroughly discredited. I remember one of our leading resident experts, @j_j , describing them as "utterly full of cow patties". :)
Yes, great examples of where 'peer review' did not work... Along with the things like the paper a couple of years ago in the AES where MP3 coding made people feel "sad". ...

Just because it is published does not mean that it is not BS. Everyone needs to think critically.
 

DonH56

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I have in the past been a reviewer/editor for an electrical engineering society (IEEE JSSC). This is all my personal experience/observations -- I have no idea if it is the same at other journals nor if it is the same now for the JSSC.

The reviewers are a mixed bag; some spend a lot of effort going through the papers, others glance at them. It was strictly volunteer for the low-level reviewers, no pay or other real incentive (at least I never got anything more than being listed with the bazillion other reviewers once a year). I would sometimes go for months without a paper to look at, then get half a dozen dumped on me before some publishing deadline (and usually when I was similarly swamped at work). Papers tended to go to subject matter experts but sometimes the title or abstract were misleading, or for some other reason (availability?), I'd get one that had me scratching my head wondering why it was in my hands. Once or twice fairly glaring errors got through but usually there were enough folk to catch then even if several were busy. The scary ones had just one or two reviewers and I admit at times I could do no more than take a glance in hopes I found anything obvious and ship it back. Some of the subjects had a fairly small group of reviewers and you can suffer from groupthink. Every now and then I'd get a paper that was clearly impractical and get shouted down by the student's prof or whatever. My experience is more applied than basic research but the papers were supposed to be implementable and represent actual measured work; other journals were more theoretical but I was not a reviewer for them except very rare occasions. Sometimes other reviewers agreed, and other times they were more academic, and the paper would pass. A couple of times I was wrong, and a few times the paper was eviscerated after publishing or presentation.

The bottom line is that peer-reviewed does not mean it has been through some lengthy and rigorous process of microscopic examination by highly-esteemed experts poring over every word. Sometimes it's just a guy with some knowledge taking a quick read and hoping there's nothing badly wrong in it that for which he'll get yelled at later.

Again, in my experience, and I have not done it for going on ten years now. Not that the papers I read today strike me as much different...
 

Yviena

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I wonder how sensitive someone is to time smearing, and how age affects it, depending on the person in question there could be someone out there who can reliably tell a difference in their younger years.

I still don't get why sometimes linear phase filters both with perfect frequency response upto around 22.05khz but with different slopes sound different in some specific passages of music, especially cymbals.
 
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Julf

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I wonder how sensitive someone is to time smearing, and how age affects it, depending on the person in question there could be someone out there who can reliably tell a difference in their younger years.
No, not really. While our ability to hear higher frequencies decreases with age, the mechanisms by which our ears work don't change.

I still don't get why sometimes linear phase filters both with perfect frequency response upto around 22.05khz but with different slopes sound different in some specific passages of music, especially cymbals.
How have you compared?
 

Yviena

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No, not really. While our ability to hear higher frequencies decreases with age, the mechanisms by which our ears work don't change.



How have you compared?
Basically quickly changing filters, and restarting the track in under 10 seconds, once I even used a apod linear phase filter with roll off starting around 22.05 , and it was even more obvious, weirdly enough I can only detect the change in some songs, mostly in amateur recordings, or older songs from around year 2000. There was no change in output level so I ruled out that
 
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