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Doppler distortion doesn't make sense (Edit: It actually does!)
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Fluffy
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I don't know how could I perform a blind test like this. If the Doppler distortion only happens (supposedly) when the lower tone is present, I can't not know when it's on and when it's not.
But I did try to measure the effect. I used a cheap condenser microphone that was laying around (Samson CO1, not reference level but good enough), to record to combination of 80hz and 6khz, fed through the Focal clear, Audeze lcd2c, and as a reference also through my powered speakers, Yamaha hs8 (2-way speaker, crossover frequency at 2k, recorded 1 foot away). The speakers were added to show how it would be if there was no Doppler effect due to the same driver producing both frequencies. The Samson was connected to a Focusrite Scarlett 2i2 G2 (which also fed the speakers), and the headphones played through an Arcam rHead amp via Schiit modi 3 dac. Everything is at 44khz sample rate, and recorded in my noisy apartment (that's all I have…).
The test tone was a 6khz sine wave at -30 dbfs played for a few seconds, then add in a 80hz tone at -5 dbfs, and then only the 6k again. Here is the test file, in waveform and spectral form:
Spectral analysis shows no side bands in the test file:
Here it is zoomed on the 6k tone:
The first test was recording the right side driver of the Clears while playing the test tone (left driver disconnected). Here is how the 6k tone looks like when played alone:
And when I add the 80 hz tone:
Suddenly sidebands appear!
With the Lcd2c (only right driver connected), only 6k:
And with 80 hz added:
As you can see, they are both experiencing some kind of distortion, but while the difference betweetn the level of the signal and the sidebands in the Clear is about -30 db, with the audeze it's -45 db. This matches my listening experience, where the clears were distorted a lot strongly than the audeze.
As for the speakers, the 6k tone alone looked like this (left speaker only):
And 80 hz added:
It's interesting, because the 6k alone already produces a sideband. Maybe it's due to the tweeter itself or the internal amplifier, I don't know how distortion free It should be. And when I add the 80 hz tone, the existing sideband stays pretty much the same, and it adds another, higher one. It's about the same level as the one present in the Lcd2c. Not sure what to make of this. Could be the microphone itself is distorting or some other effect I missed. At any case, the Clears show significantly more distortion (whether doppler or IMD) than the rest, which is how it sounded like to my ear.
But I did try to measure the effect. I used a cheap condenser microphone that was laying around (Samson CO1, not reference level but good enough), to record to combination of 80hz and 6khz, fed through the Focal clear, Audeze lcd2c, and as a reference also through my powered speakers, Yamaha hs8 (2-way speaker, crossover frequency at 2k, recorded 1 foot away). The speakers were added to show how it would be if there was no Doppler effect due to the same driver producing both frequencies. The Samson was connected to a Focusrite Scarlett 2i2 G2 (which also fed the speakers), and the headphones played through an Arcam rHead amp via Schiit modi 3 dac. Everything is at 44khz sample rate, and recorded in my noisy apartment (that's all I have…).
The test tone was a 6khz sine wave at -30 dbfs played for a few seconds, then add in a 80hz tone at -5 dbfs, and then only the 6k again. Here is the test file, in waveform and spectral form:
Spectral analysis shows no side bands in the test file:
Here it is zoomed on the 6k tone:
The first test was recording the right side driver of the Clears while playing the test tone (left driver disconnected). Here is how the 6k tone looks like when played alone:
And when I add the 80 hz tone:
Suddenly sidebands appear!
With the Lcd2c (only right driver connected), only 6k:
And with 80 hz added:
As you can see, they are both experiencing some kind of distortion, but while the difference betweetn the level of the signal and the sidebands in the Clear is about -30 db, with the audeze it's -45 db. This matches my listening experience, where the clears were distorted a lot strongly than the audeze.
As for the speakers, the 6k tone alone looked like this (left speaker only):
And 80 hz added:
It's interesting, because the 6k alone already produces a sideband. Maybe it's due to the tweeter itself or the internal amplifier, I don't know how distortion free It should be. And when I add the 80 hz tone, the existing sideband stays pretty much the same, and it adds another, higher one. It's about the same level as the one present in the Lcd2c. Not sure what to make of this. Could be the microphone itself is distorting or some other effect I missed. At any case, the Clears show significantly more distortion (whether doppler or IMD) than the rest, which is how it sounded like to my ear.
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The sidebands look like intermodulation distortions to me. The Doppler frequency shift is proportional to the speed (or, for reflected sounds, the apparent speed) of the movement of the source. Thus, only if the speed is constant will you get a constant frequency shift. Since the 80 Hz signal is sinusoidal, speed is also a varying sinusoid. You should therefore get a side band wandering about the 6 kHz peak, and see a broadening of the 6 kHz peak in your spectrum plot (which I don't see in any significant amounts in your plots).
For your speaker test, I am speculating that the peak at ~6080+ Hz was unrelated. You can see a slight broadening of that peak in the second plot, suggesting there might have been 2 peaks very close to each other. May be you can run another test with test signals of 80 Hz + 5.8 kHz and see if the peak follows.
For your speaker test, I am speculating that the peak at ~6080+ Hz was unrelated. You can see a slight broadening of that peak in the second plot, suggesting there might have been 2 peaks very close to each other. May be you can run another test with test signals of 80 Hz + 5.8 kHz and see if the peak follows.
Intermod shows as bands at f1-f2, f1+f2, and combinations of nf1+/-mf2, where n and m are integers.
Doppler will show frequency shift that's velocity dependent. So if the the bands don't broaden and the broadening isn't a function of the lower frequency amplitude, it's not Doppler.
Non-linearities in the driver, especially the motor and suspension. Same things that cause harmonic distortion.
It's a result of the same causes as harmonic distortion (nonlinearities in the DUT), so when you see HD, there will always be IMD if you run a two tone test.
You can set up a fictitious mathematical model that might have one and not the other, but every real system I'm aware of that has nonlinearities shows both types.
Isn't HD actually a single tone IMD?
WHat I mean is this: Distortion always have a tones harmonic components and inter-tone components. Following that logic single tone test doesn't have inter-tone components but only harmonic component of that single tone.
I have trouble thinking about an "inter" where there aren't two distinct things.
KSTR
Major Contributor
Proposal for Doppler Distortion measurement, using REW:
- Sample-synchrounous record-while-playback of the test signal, so that "no window" (==rectangular) can be used for FFT, having no frequency leakage.
- Large FFT size, 1M points, low sample rates (44.1/48khz) for high frequency resolution.
- Play twin-tone test signal of choice (like 4:1 60Hz/6kHz) and adjust levels until IMD starts to sky-rocket, back off a little.
- Mic in the "near field" but at least some 10x the observed excursion away, if possible.
- Record spectrum (averaged).
- Play high test-tone alone, record spectrum (averaged).
- Look at the number of bins occupied by the high test-tone's fundamental, compare.
- If the single-tone is exactly 1 bin wide but starts to widen in the two-tone spectrum to several bins, then this widening should be the effect of Doppler distortion. IMD frequencies might also show the widening.
Blind testing is in fact difficult. It's feasible when you already have a DSP model for correction and it parameters have been dialed in so the measured response actually betters (and does no degrade performance anywhere else, of course). Then simple switch-off of the correction will assure nothing else is changed to make testing more robust.
- Sample-synchrounous record-while-playback of the test signal, so that "no window" (==rectangular) can be used for FFT, having no frequency leakage.
- Large FFT size, 1M points, low sample rates (44.1/48khz) for high frequency resolution.
- Play twin-tone test signal of choice (like 4:1 60Hz/6kHz) and adjust levels until IMD starts to sky-rocket, back off a little.
- Mic in the "near field" but at least some 10x the observed excursion away, if possible.
- Record spectrum (averaged).
- Play high test-tone alone, record spectrum (averaged).
- Look at the number of bins occupied by the high test-tone's fundamental, compare.
- If the single-tone is exactly 1 bin wide but starts to widen in the two-tone spectrum to several bins, then this widening should be the effect of Doppler distortion. IMD frequencies might also show the widening.
Blind testing is in fact difficult. It's feasible when you already have a DSP model for correction and it parameters have been dialed in so the measured response actually betters (and does no degrade performance anywhere else, of course). Then simple switch-off of the correction will assure nothing else is changed to make testing more robust.
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Not really relevant. Organs (as well as cellos etc.) produce (or amplify) sound by resonance. Resonance depends on the physical measurements of the instrument. With speakers, we try to avoid resonances.
It is relevant due to wavelengths. The point being that a single driver for the full range of audio frequencies really hasn't been built because different sizes are needed according to wavelength. Resonance has nothing whatever to do with my point.
Maybe try the experiment with a subsonic lower frequency.
Even though a speaker may not "produce" the subsonic tone audibly, the driver will likely still be wobbling at that frequency.
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Quick comment: harmonic distortion will also create intermodulation distortion; they are mathematically related. In fact, the IMD terms will be higher than the HD terms (by about 6 dB for second-order products, and about 9.5 dB for the third-order products) given equal peak-to-peak signal values for a single source for HD or two-tone source for IMD.
The derivation is straightforward but tedious using a little algebra and some trig identities. Take a sinusoid, or pair of sinusoids, run through a distortion generation function like (1 + ax^2 + bx^3), then collect terms using trig identities to find magnitudes of fundamental and HD/IMD terms. I have it in an old notebook at home, can probably dig it up or regenerate the equations (as could most of us given time and inclination, and it is undoubtedly posted somewhere on the 'net). My old notes only have 2nd and 3rd order products and that is not too bad; I have done it up to 5th by hand but would not willingly do it again (messy beyond belief and any math program or simulator will do it for you with far less effort).
As stated above, FMD will spread the tones (add "skirts") vs. generating the discrete tones that IMD will produce.
Of course you can have combinations of (many) things going on...
FWIWFM - Don
The derivation is straightforward but tedious using a little algebra and some trig identities. Take a sinusoid, or pair of sinusoids, run through a distortion generation function like (1 + ax^2 + bx^3), then collect terms using trig identities to find magnitudes of fundamental and HD/IMD terms. I have it in an old notebook at home, can probably dig it up or regenerate the equations (as could most of us given time and inclination, and it is undoubtedly posted somewhere on the 'net). My old notes only have 2nd and 3rd order products and that is not too bad; I have done it up to 5th by hand but would not willingly do it again (messy beyond belief and any math program or simulator will do it for you with far less effort).
As stated above, FMD will spread the tones (add "skirts") vs. generating the discrete tones that IMD will produce.
Of course you can have combinations of (many) things going on...
FWIWFM - Don
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The examples you mentioned all were all related to resonance. Wavelength is only an issue at the low end - a 12" speaker has no problem reproducing 20 kHz from a wavelength point of view. The issue is mass (or the strength of the electromagnetic force required to move that mass quickly enough).
Maybe you should study up on beaming. It was my post and I said NOTHING about resonance. Put your words in your own mouth. Don't mis-i
interpret what I say, thank you.
interpret what I say, thank you.
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