Butterworth 3rd order

boris81 · Jan 23, 2011, 08:34 PM

Hi,
I'm looking to implement a 3rd order Butterworth LowPass and HighPass.
I understand that in order to get a 3rd order filter I need to cascade a 2nd order with a 1st order.
A Q-factor look-up table can be found in this datasheet p58.
http://focus.ti.com/lit/ml/sloa088/sloa088.pdf

KX currently only implements a 2nd order filters. I found the formulas to compute the biquad coefficients for 1st order filters.
Cascade form IIR Filters | Comp.DSP | DSPRelated.com

Quote:

if it's an odd order Butterworth, you'll need an additional 1st order
section:

H(z) = (b0 + b1*z^-1)/(a0 + a1*z^-1)

1st order LPF: H(s) = 1/(s+1)

b0 = sin(w0)
b1 = sin(w0)
a0 = cos(w0) + sin(w0) + 1
a1 = sin(w0) - cos(w0) - 1

1st order HPF: H(s) = s/(s+1)

b0 = cos(w0) + 1
b1 = -(cos(w0) + 1)
a0 = cos(w0) + sin(w0) + 1
a1 = sin(w0) - cos(w0) - 1

I've been trying to compute and replace these coefficients into the "EQ Lowpass" filter but I can't get it to work.

Does what I'm trying to do seem right?

I don't quite understand how the "EQ Lowpass" biquad implementation uses the coefficients and I have some questions.

- Are all of the coefficients divided by 2?
- From the EQ-Cookbook a0 = 1 + alpha doesn't come up to 1, does that mean that the rest of the coefficients must be offset by -alpha?
- Can I type decimal fractions into the Dane editor or do I need to convert to hex?

Russ · Jan 24, 2011, 12:56 AM

I cannot answer all yor questions, but...

Quote:

Originally Posted by boris81

- Are all of the coefficients divided by 2?

I do not have kX or the SDK installed at the moment, so I cannot look at the code for that plugin, but:
Often a scale factor is used to ensure that the coefficients do not exceed 1 under all possible settings (with filters that have adjustable settings), etc. IIRC, that plugin does use a scale factor of 2 (the coefficients are divided by 2, and then in the DSP, the output of the filter is multiplied by 2 to correct for it).

Quote:

Originally Posted by boris81

- From the EQ-Cookbook a0 = 1 + alpha doesn't come up to 1, does that mean that the rest of the coefficients must be offset by -alpha?

To normalize, all coefficients should be divided by a0 (i.e. 1 + alpha).
(a0 thus becomes 1, as it is divided by itself)

Note: In some cases, a coefficient might be made negative or positive to work with the DSP instruction that you want to use (where the result would be the same... e.g. (a - b) is the same as (a + (-b)) ).

Quote:

Originally Posted by boris81

- Can I type decimal fractions into the Dane editor or do I need to convert to hex?

Yes, you can use decimals in the Dane editor.

boris81 · Jan 24, 2011, 05:22 PM

Thank you, Russ!

I wasn't able to find the plugin code in the SDK at first.

After your comment I was inspired to search harder.

I will probably have some further questions about compiling a *.kxl plugin.

Jan 24, 2011, 05:22 PM	Thread Starter #3
boris81 HardwareHeaven Newbie Join Date: Dec 2009 Location: White Plains, NY Posts: 17 Rep Power: 0	Re: Butterworth 3rd order Thank you, Russ! I wasn't able to find the plugin code in the SDK at first. After your comment I was inspired to search harder. I will probably have some further questions about compiling a *.kxl plugin.