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Re:Linkwitz transform 10 years 10 months ago #3668

  • dreite
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Charlie,

I will most likely be at the Burning Amp festival this year. If you find me we can touch base and maybe I can help you with miniDSP-related items.

Dave.

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Re:Linkwitz transform 10 years 10 months ago #3671

  • CharlieLaub
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Hi Dave,

Luckily I'm not really having any issues. Using all the filter types on knuisje's spreadsheet, I was able to implement a slightly different version of my crossover using the programmable biquads. Please stop by. I'll be in the Tesla room. I'd love to chat. I might even bring a computer along and I can show you the crossover design spreadsheets...

Here's a thread about the speakers, on the PE TechTalk forum:
Charlie's big 3-way 4-cube tower of fun

-Charlie

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Last edit: by CharlieLaub.

Re: Linkwitz transform 10 years 7 months ago #4190

  • Crumboo
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Hi,

Thank you guys so much for the excel file for calculating biquad parameters. I look for a way of calculating the frequency and phase response from an arbitrary biquad filter (with choosen biquad coefficient).
In the excel file the following expression is used for calculating frequency respons:

10*LOG10( (b0+b1+b2)^2 + ( b0*b2*phi - (b1*(b0+b2) + 4*b0*b2) )*phi ) -
10*LOG10( (1+a1+a2)^2 + ( 1*a2*phi - (a1*(1+a2) + 4*1*a2) )*phi)

with phi = 4*SIN(w/2)^2 and w = 2*PI()*f / f_s

I am not sure how the above expression is derived from the biquad function, H(z)=(b0+b1*z^-1+b2*z^-2) / (a0+a1*z^-1+a2*z^-2). Can anyone out there please show the corresponding expression for H(s), with s being the complex frequency, as a function of the biquad coefficient? The absolute number (IMABS) of H(s) should generate the same curve as the expression used in the excel file, and the phase response should be obtained as the argument (IMARGUMENT) of H(s). I have been trying to derive this myself, but for some reason the result is not correct. :unsure:

The reason why I want the expression for H(s) is for being able in a simple way to combine biquad filters and evaluate the resulting filters frequency and phase response. I would be very thankful if someone can help me with this. :)

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Last edit: by Crumboo.

Re: Linkwitz transform 10 years 7 months ago #4191

  • CharlieLaub
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You can calculate the magnitude and phase responses versus frequency in Excel. Here is how to do it:
1. Calculate z^-1 versus frequency
2. use the biquad coefficients to calculate the transfer function using Excel's complex number functions. See "digital crossovers" in the Applications menu on this web site for info on the IIR transfer function
3. Calculate the magnitude (use IMABS) and phase (IMARGUMENT) of the transfer function for each z^-1

I do this in a loudspeaker crossover design spreadsheet that I have recently put together, which I will be releasing early next year in order to plot the response of the filters for the MiniDSP and compare them to analog filter functions.

-Charlie
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Re: Linkwitz transform 10 years 7 months ago #4195

  • Crumboo
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Thank you,

I think that it is the first step that is wrong in my calculations. How do you express z^-1 vs. frequency?

I have used z=exp(j*2*PI*f/f_sample). I believe the frequency should be corrected for frequency warping, but the result I get is wrong I'm afraid. :unsure:

Interesting about your spreadsheet, are you releasing it for free? :)

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Re: Linkwitz transform 10 years 7 months ago #4196

  • CharlieLaub
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Yep, free.

You can read all about it here:
www.diyaudio.com/forums/multi-way/201963...er-design-tools.html

The LT is one of the filter types that you can implement as a "biqudratic filter" section. But there isn't a need to go in to all the details about it if you use my crossover design tools.

After designing the loudspeaker crossover using the Excel tools, you just copy and paste the transfer coefficients (already formatted for import in to the MiniDSP "advanced biquad" input window) to implement the crossover functions using a MiniDSP product with the "advanced" plug-in. I've tested it out with a couple of systems that I am working on and it works great.

I'll get back to you later about how to calculate z, z^-1, etc. and will post a follow-up.

-Charlie

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