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Wave-front shape and impulse response: spherical, cylindrical, plane-wave
Wave-front shape and impulse response: spherical, cylindrical, plane-wave
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Old 11th November 2015, 11:41 AM   #1
keyser is offline keyser  Netherlands
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Default Wave-front shape and impulse response: spherical, cylindrical, plane-wave

Wave-front shape and impulse response: spherical, cylindrical, plane-wave

If I am not mistaken, a theoretical point-source, infinite line-source and infinite plane source are all capable of perfectly reproducing an impulse. I always thought that the 'impulse train' you see when you measure a real-world line-array is caused by practical limitations in driver size and spacing. However, now I'm not so sure.

According to the Huygens principle any point on a wave-front can be represented by imagining that on every point on the wave-front there is a point-source that emits a spherical wavefront. The complex sum of this infinite number of point-sources describes how the initial wave propagates. This means that a line-source and a plane-source can be modeled as an infinite number of point-sources.

Click the image to open in full size.
From wikipedia

I think I understand how this works with continuous signals such as a sine-wave. But what happens when we send an impulse to for instance a line-source? If the wave-front truly is cylindrical in shape, I imagine the impulse-response would be perfectly reproduced. But if the wave-front is the result of an infinite number of point-sources as per Huygens, I would expect to see a first relatively strong impulse followed by an infinite number of ever smaller impulses. Is this really what happens in the case of the theoretical ideal line source and plane source?
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Last edited by keyser; 20th November 2015 at 09:57 AM.
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Old 11th November 2015, 11:13 PM   #2
AllenB is offline AllenB  Australia
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It may be useful to view the impulse as an infinite band of independent sinewaves. There may indeed be some spatial behaviour that is displayed at one end of the band that differs from the other end.
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Old 11th November 2015, 11:26 PM   #3
rayma is offline rayma  United States
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Quote:
Originally Posted by keyser View Post
I would expect to see a first relatively strong impulse followed by an infinite number of ever smaller impulses.
Is this really what happens in the case of the theoretical ideal line source and plane source?
Yes, only a point source would give a good impulse response. Sine wave frequency response tests
would just show directivity, though.

Last edited by rayma; 11th November 2015 at 11:31 PM.
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Old 11th November 2015, 11:40 PM   #4
wesayso is offline wesayso  Netherlands
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Could you give an example of what a good impulse would look like?
Because the impulse of my straight line array looks pretty normal to me:
Click the image to open in full size.
By the way, that flying line at the top is the STEP response. Wiggles are probably comb filtering, as that is very real. Distance between speakers for this array: 85.5 mm, 25 drivers.
Time difference between out most driver arrival at ear vs the driver at ear height 0.6 ms.
Click the image to open in full size.
21.6 cm time difference to ear at 3 meter distance.
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Old 12th November 2015, 12:37 AM   #5
rayma is offline rayma  United States
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Quote:
Originally Posted by wesayso View Post
Could you give an example of what a good impulse would look like?
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Old 12th November 2015, 03:08 AM   #6
bbutterfield is offline bbutterfield  United States
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Quote:
Originally Posted by keyser View Post
if the wave-front is the result of an infinite number of point-sources as per Huygens, I would expect to see a first relatively strong impulse followed by an infinite number of ever smaller impulses. Is this really what happens in the case of the theoretical ideal line source and plane source?
Your expectation isn't far from the truth. Considering a line array of infinite length made up of an infinite number of point sources, with each point source producing a flat frequency response, the impulse response at the listening position will consist of a step up followed by a decay that asymptotically approaches 0 but never quite reaches it.

However, despite the flat frequency response of the point sources, the frequency response of the array at the listening position will have a low-pass response with a slope of -3dB per octave. Equalization back to a flat frequency response will change the impulse response, and you will no longer have the step-decay scenario I described earlier. What you end up with will depend on your method of equalization, I suppose. I haven't looked too deeply into that, but it looks like Wesayso has achieved nice results.

Last edited by bbutterfield; 12th November 2015 at 03:10 AM.
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Old 14th November 2015, 08:20 AM   #7
keyser is offline keyser  Netherlands
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Quote:
Originally Posted by rayma View Post
Yes, only a point source would give a good impulse response. Sine wave frequency response tests
would just show directivity, though.
I'm not sure I understand. A point source has no directivity.
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Old 14th November 2015, 01:37 PM   #8
rayma is offline rayma  United States
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Quote:
Originally Posted by keyser View Post
I'm not sure I understand. A point source has no directivity.
Right, a line or plane source would show directivity, not a point source.
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Old 16th November 2015, 05:31 PM   #9
bbutterfield is offline bbutterfield  United States
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Originally Posted by bbutterfield View Post
Your expectation isn't far from the truth. Considering a line array of infinite length made up of an infinite number of point sources, with each point source producing a flat frequency response, the impulse response at the listening position will consist of a step up followed by a decay that asymptotically approaches 0 but never quite reaches it.

However, despite the flat frequency response of the point sources, the frequency response of the array at the listening position will have a low-pass response with a slope of -3dB per octave. Equalization back to a flat frequency response will change the impulse response, and you will no longer have the step-decay scenario I described earlier. What you end up with will depend on your method of equalization, I suppose. I haven't looked too deeply into that, but it looks like Wesayso has achieved nice results.
I wanted to come back to this point, because I still see a lot of posts associating a "time smear" with line arrays.

Here's a picture that roughly represents the impulse response I was describing for an array of elements each with a flat frequency response (and minimal or no phase distortion). The closest speaker impulse arrives first, and is the loudest. Subsequent arrivals are delayed and attenuated.
Click the image to open in full size.

As mentioned, this results in a low-pass effect at the listening position when the response to all the elements is taken together. In order to correct for that, the response needs to be shaped. A high pass filter needs to be applied to counteract the low pass effect of the line array element combination.

Here's an example of a sloping high pass response:
Click the image to open in full size.

Ignore the stuff above 20 khz.

Here's the associated impulse response:
Click the image to open in full size.

Now let's re-imagine our line array impulse response when each element is high-pass filtered to offset the low-pass system response. If each element is producing an impulse response like that shown above, then the positive spike of each subsequent arrival is offset by the negative spike of the prior arrival. This can give the effect of a nice clean impulse on the listening axis, with no "time smear".

Sorry I don't have the time to post simulations at this time... I have other things going on.
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Old 16th November 2015, 07:53 PM   #10
keyser is offline keyser  Netherlands
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Originally Posted by bbutterfield View Post
Now let's re-imagine our line array impulse response when each element is high-pass filtered to offset the low-pass system response. If each element is producing an impulse response like that shown above, then the positive spike of each subsequent arrival is offset by the negative spike of the prior arrival. This can give the effect of a nice clean impulse on the listening axis, with no "time smear".
Thanks bbutterfield. So basically what you are saying, is that a line-array is still a minimum-phase system and its smeared impulse response can be fixed simply by means of a minimum-phase filter. This filter fixes both the transfer function, as well as the impulse. Very interesting! I think it makes sense.

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Originally Posted by bbutterfield View Post
Sorry I don't have the time to post simulations at this time... I have other things going on.
If you can find the time, I'd still love to see it. What software do you use to run those sims?
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