GD, no FDW, no smoothing
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This picture is interesting.
The large peaks at 130, 170 and maybe 240 Hz are significant.
Narrow peaks can be ignored, as they are probably measurement artifacts : when the test signal becomes very weak, at the bottom of dips in the frequency response, the phase response suddenly jumps 180° away. Since the signal is barely detectable, the software can't always read if the jump is positive or negative (+180 or -180° both lead to the same value), so it may draw a peak instead of a dip in the group delay graph, and conversely.
But the fact that the group delay is around 80 ms at 130 and 170 Hz is a bit worrying. Except if these parts are at the bottom of dips in the amplitude response curve, as it is often the case. Then it doesn't matter, since these frequencies are nearly silent.
The hills at 240, 390 and 480 Hz are strange. I have nothing like this in the raw group delay graph from my listening position :
What's the sweep size used as a test signal ? For phase and GD measurement from the listening position, I think that the longest one is best (1M). In any case, the length of the test signal has a clear effect on this graph.
I don't know if the fact that the microphone is perfectly still during the measurement matters.
GD, FDW 12 cycles, no smoothing
View attachment 46740
So here, we have the group delay of only a part of the sound : the direct sound and its first reflections (it's completely anechoic only below, say, 1ms, that is only above 1000 Hz in this graph).
It's a bit difficult for me to understand what it means. I can understand what means the amplitude response with Frequency Dependant Window. It's the tonal balance of the attacks in the sound, with reverberations in the room left aside. I can imagine the spectrum changing with time, and being different in the first milliseconds, while we are hearing the direct sound of the speaker, then changing as the sound decays, while we are hearing the sound of the room.
But
phase changing as sound decays ?
If I understand correctly, it gives an idea of the time coherence of the attacks that reach our ears before the sound begins to decay in the room.
The two previous peaks, at 130 and 170 Hz, are still visible here, reduced in amplitude. But we can't tell if they come from the direct sound (then it matters, as this represents the time coherence of the speaker) or from the first reflections in the room, that the 12 cycle windowing includes.
In the later case, they should be ignored, as they are just remnants of the peaks in the initial graph, not completely canceled because of the too wide windowing.
GD, FDW 12 cycles, 1/6 smoothing
View attachment 46742
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It probably also doesn't reflect how we hear things as our hearing doesn't have resolution to catch all those narrow high peeks.
I don't think so. I think that what we hear is the original peak at 80 ms in the raw graph.
I have made some videos with random phase distortion. Unfortunately, all examples include pre-echo, which prevents to hear group delay alone, as pre-echo is much more audible. But anyway, here they are.
Listen to them with headphones, to avoid the group delay of your room masking everything.
In the first part of the video, the effect of amplitude alone is heard. Since the transformation is not minimal phase, an awful lot of pre-echo is audible in low frequencies.
In the second part of the video, the effect of phase alone is heard. Again, a lot of pre-echo can be heard in the bass.
This second video is a bit more intersting :
Here, the same random amplitude distortion as in the first video is added to the sound, but in two different versions, minimal, and linear phase alternately.
Although the pre-echo of the linear phase version is still obvious, we can also hear that the bass rhythm is slightly offsetted in time. This is the audible effect of group delay alone (+74 ms here).
The raw group delay curve of the linear phase example is this :
It peaks around 25 ms (it should have been flat, but the actual corrections are not perfectly accurate).
The group delay of the minimal phase version is that :
And the effect of this narrow peak of group delay is audible in itself, I think (although I can't prove it, since the delay alone can't be separated from time smearing).
If the musical beat had been perfectly centered around the frequency of 54 Hz, it would have been delayed by 100 ms. But since it is not exactly at that frequency, we can measure, on the musical waveform, that the actual delay is 74 ms only.
What I'm meaning is that what we can see, and hear in this example is a 74 ms delay in time, and this is only visible in the group delay graph when it is not smoothed.
Later, I started from the minimal phase version of the distorted file, and applied two reverse filters : one linear phase, and one minimal phase. This time I was able to compare the temporal effects without pre-echo in any of the two files. I must have these files somewhere on my hard drive. I ABXed them with a score of 16/16.
But the main audible difference was not the delay, it was the overall time smearing. Although there was no pre-echo, and all the bass was delayed after the initial attack, the time smearing was still audible. It was easier to focus on it than on the delay to pass the ABX test.
