Talk:Digital biquad filter

Why Digital?
The biquad filter can equally be used in the s-plane for analog filters.

$$H(s) = (b_0 s^2 + b_1 s + b_2) / (a_0 s^2 + a_1 s + a_2)$$


 * Because the article is Digital biquad filter. Constant314 (talk) 02:44, 17 February 2020 (UTC)

Why Only Audio?
The single section biquad filter is a general purpose second order filter involving conjunct pair of zeros and poles.

It can be used in a infrasonic AGC filter


 * Hello. Including this article in the scope of Professional sound production does not exclude it from other scopes. Constant314 (talk) 02:43, 17 February 2020 (UTC)

Coefficient notation
Some authors use b0, b1, ... for zero coeffs and a1, a2 for poles, others use a0, a1, .. for zero coeffs and b1, b2 for poles. As I know, both are used in practice. I prefer the second one, don't know if any of these is 'official'. scoofy 16:11, 26 March 2007 (UTC)


 * I have never seen the second version in anything "offical" (i.e. a textbook), but that's not to say that it isn't used. I think for consistency with other Wiki articles (e.g. IIR, Z-transform), we should stick to b for numerator, and a for denominator.


 * I don't think it's necessary to have a disclaimer "some authors may use a for numerator..." as was in this article previously, as this could be said about any choice of variable name in any article on Wikipedia. Oli Filth 16:19, 26 March 2007 (UTC)


 * Hehe, true. Digital filter uses that notation, too, so it's OK for me. One textbook which uses a0, a1... for numerator coeffs is The Scientist and Engineer's Guide to Digital Signal Processing. (Sometimes $$\alpha$$ and $$\beta$$ is also used instead a and b.) scoofy 16:28, 26 March 2007 (UTC)

a_0
I think a_0 should be included for completeness first, including in the diagrams, and then say that it's usually set to 1 and why.

$$H(z)=\frac{b_0+b_1z^{-1}+b_2z^{-2}} {a_0+a_1z^{-1}+a_2z^{-2}}$$

$$y[n] = \frac{1}{a_0}(b_0x[n] + b_1x[n-1] + b_2x[n-2] - a_1y[n-1] - a_2y[n-2])$$

There are erroneous diagrams floating around like this:

http://synthmaker.co.uk/forum/viewtopic.php?p=16954&sid=91ef57aa95be8f3a07b6cff184a9b718#p16954

http://i.stack.imgur.com/GGrUq.png

and it should actually be 1/a_0 like so:

http://www.mathworks.com/help/dsp/ref/biquadfilter.html

http://i.stack.imgur.com/Cz8CZ.png

it is not always set to 1: http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt — Preceding unsigned comment added by 71.167.66.160 (talk) 00:22, 13 June 2014 (UTC)

What does it sound like?
This is a filter used in digital audio. You don't discuss that at all, let alone what it sounds like. The SoX documentation specifically says to check here to find out about it. How can we? — trlkly 00:31, 25 October 2014 (UTC)


 * Hi trlkly, I think the biquad concept is merely a recipe to build digital filters. This recipe can be used to cook-up all kinds of filters like bandpass/highpass/lowpass/notch etc, audio or otherwise. The audio filters made according to this recipe will sound like any other bandpass/highpass/lowpass/notch filter with the same specifications. How it sounds depends on the actual implementation (the constants an and bn in the article), not on the fact that it is a biquad filter. The fact that it is a biquad filter is only important for the people or systems that determine these constants. - Snaily (talk) 03:52, 25 October 2014 (UTC)


 * In audio applications, the biquad is typically used to implement a parametric filter. 12:57, 1 November 2014 (UTC)