NumberChallenged
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- Joined
- Oct 4, 2020
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Hi, I have terrible math skills. It's so bad that reading math feels like reading a foreign language. But I'm building home audio speaker arrays and I need to figure out how to plug the right numbers into an equation so the numbers I need come out.
Here's the paper discussing the home audio speaker arrays: https://faculty.tru.ca/rtaylor/publications/cbt_dipole.pdf
The basic idea of the speaker is that when you have a vertical array (e.g. 24 small speakers that positioned in a vertical array) you decrease the volume level of the speakers ("Shade" the speakers) as you go from full volume at the lowest speakers at the floor to lower volume speakers at the top of the array. I have built these speakers in the past but I built an exact copy of existing speakers so I didn't need to calculate the shading. Now I'm building a custom sized array and need to figure out what volume level to assign each speaker.
On page 4 of the paper the authors describe their Chebychev polynomial volume level shading function:
And they give an example:
The angles (θ ) they are talking about in the equations regard the physical curvature of the speaker array. The reason they talk about a "half-arc" is because they cut the arc in half and set it on the ground (a "ground plane" array.) They do that because a hard surface will reflect the sound similar to a mirror and effectively double the length of the array in the audio spectrum, a 3 foot array sounds like a 6 foot array.
My problem is I don't understand how they use TN (the Chebychev polynomial). When they use "T6" in the example it looks like spooky magic to me. I don't even understand the terminology. They say it is a degree-6 Chebychev polynomial. Is that just a confusing way of saying plug 6 degrees into a Chebychev function? (I'm guessing they are breaking their arc up into 6 degree segments but I'm not sure.)
I'm so lost I don't even know how to ask the right questions to figure out how to calculate the speaker shading.
Here's the paper discussing the home audio speaker arrays: https://faculty.tru.ca/rtaylor/publications/cbt_dipole.pdf
The basic idea of the speaker is that when you have a vertical array (e.g. 24 small speakers that positioned in a vertical array) you decrease the volume level of the speakers ("Shade" the speakers) as you go from full volume at the lowest speakers at the floor to lower volume speakers at the top of the array. I have built these speakers in the past but I built an exact copy of existing speakers so I didn't need to calculate the shading. Now I'm building a custom sized array and need to figure out what volume level to assign each speaker.
On page 4 of the paper the authors describe their Chebychev polynomial volume level shading function:
And they give an example:
The angles (θ ) they are talking about in the equations regard the physical curvature of the speaker array. The reason they talk about a "half-arc" is because they cut the arc in half and set it on the ground (a "ground plane" array.) They do that because a hard surface will reflect the sound similar to a mirror and effectively double the length of the array in the audio spectrum, a 3 foot array sounds like a 6 foot array.
My problem is I don't understand how they use TN (the Chebychev polynomial). When they use "T6" in the example it looks like spooky magic to me. I don't even understand the terminology. They say it is a degree-6 Chebychev polynomial. Is that just a confusing way of saying plug 6 degrees into a Chebychev function? (I'm guessing they are breaking their arc up into 6 degree segments but I'm not sure.)
I'm so lost I don't even know how to ask the right questions to figure out how to calculate the speaker shading.