KVR Audio

soundmodel · Post by **soundmodel** » Wed Jul 29, 2015 12:40 pm

Know any recommendable sources for learning about all the concepts (e.g. phase, poles, group delays, impulse responses) in digital filters?

Can the subject be approached from a purely mathematical viewpoint (since most sources I seem to find use an electrical engineering style language, which I'm not that familiar with). Reading text that would be closer to mathematics would seem simpler.

Miles1981 · Post by **Miles1981** » Wed Jul 29, 2015 2:18 pm

IMHO, DAFX from Zolzer is the bible for all digital audio effects! There is a complete mathematical approach in it as well, although it's more general than IIR LTI filters (I don't like calling filters the subpart of filters that can be described with a transfer function like H(z) = fraction of 2 polynomials).

soundmodel · Post by **soundmodel** » Wed Jul 29, 2015 2:38 pm

I guess the reason for most texts using EE style language is that that's probably where the field sort of emerged. Then perhaps later on, after digital computers, it was approached also by mathematicians. I'm more interested into the mathematics of it, that is, in order to understand what kind of mathematical contructs lead to filters. Which of course is usable in EE as well, but since digital computers do arithmetic, then one can approach it purely mathematically rather than "EE-heuristically" (trial and error electronics).

Max M. · Post by **Max M.** » Wed Jul 29, 2015 2:44 pm

Fluky wrote:I'm more interested into the mathematics of it

Then you'll be also interested in https://ccrma.stanford.edu/~jos/filters/ (For me JOS always was too mathematical...

though I learned many useful things there anyway).

Miles1981 · Post by **Miles1981** » Wed Jul 29, 2015 2:47 pm

Fluky wrote:I guess the reason for most texts using EE style language is that that's probably where the field sort of emerged. Then perhaps later on, after digital computers, it was approached also by mathematicians. I'm more interested into the mathematics of it, that is, in order to understand what kind of mathematical contructs lead to filters. Which of course is usable in EE as well, but since digital computers do arithmetic, then one can approach it purely mathematically rather than "EE-heuristically" (trial and error electronics).

I don't think that way. Digital signal processing may try to mimick some amalog signal processing equipments, but the math behind digital signal processing (mainly for communication I think) was, as usual, written by mathematicians first. Then EE came and messed up with their j instead of i and other things.

Z1202 · Post by **Z1202** » Thu Jul 30, 2015 11:58 am

When writing the "VA Filter Design" book, the main intention was that this book is used as the introductory text into the music DSP filter design, superseding the classical texts (yeah, I know, it's a bold statement

) by focusing on the topics specifically relevant to music DSP and skipping the others. The other book of a similar direction (which I didn't read though) is the one by Will Pirkle. Apparently none of them get often suggested as intro texts. It would be interesting to hear your feedback, why this is not the case, what is missing, doesn't work etc.

Regards,
{Z}

matt42 · Post by **matt42** » Thu Jul 30, 2015 12:34 pm

I'd recommend both The Scientist and Engineer's Guide to DSP and Designing Audio Effect Plug-Ins in C++

The same topic was discussed here not too long back.

matt42 · Post by **matt42** » Thu Jul 30, 2015 12:36 pm

@ Z1202 A big difference between yours and Will's books is the entry level knowledge requirement. I didn't read his synth book, but his effects book explains concepts, for example, such as why multiplying by z−1 results in a one sample delay in a mathematically intuitive way that can be grasped by someone with a high school level of mathematics. Your book while awesome and clearly bringing trapezoidal integration/ZDF/TPT to a wide audience has higher entry requirements. It would appear to me that you were a big influence on a lot of the synth filter design pages on his website, but I couldn't know for sure.

Z1202 · Post by **Z1202** » Thu Jul 30, 2015 1:33 pm

matt42 wrote:@ Z1202 A big difference between yours and Will's books is the entry level knowledge requirement. I didn't read his synth book, but his effects book explains concepts, for example, such as why multiplying by z−1 results in a one sample delay in a mathematically intuitive way that can be grasped by someone with a high school level of mathematics. Your book while awesome and clearly bringing trapezoidal integration/ZDF/TPT to a wide audience has higher entry requirements. It would appear to me that you were a big influence on a lot of the synth filter design pages on his website, but I couldn't know for sure.

Thanks for the comments. In regards to this a) I wonder how one can explain z^-1 without complex algebra, maybe I should check Will's book and b) differently from classical DSP theory, z^-1 is not so central to the ZDF filter design. But my point was that Will's synth book doesn't often get recommended either. So people begin to learn the DSP concepts from a standpoint which IMHO is working only to an extent in music DSP and then they keep running into the same pre-ZDF-era problems over and over again.

matt42 · Post by **matt42** » Thu Jul 30, 2015 2:03 pm

Hi Z1020,

Z-1 was purely an example of a single concept. I'm not saying reading Will Perkil's effect book will expain ZDF stuff, because it doesn't. I also don't mean that you necessarily need to explain Z-1 either. However in order to explain Z-1 Will builds on high school maths to go on to complex numbers and Euler and finally Z-1.It's probably not fair to compare your writing with Will's, but I was going at the angle of an introductory text.

Miles1981 · Post by **Miles1981** » Thu Jul 30, 2015 2:18 pm

Z1202 wrote:When writing the "VA Filter Design" book, the main intention was that this book is used as the introductory text into the music DSP filter design, superseding the classical texts (yeah, I know, it's a bold statement ) by focusing on the topics specifically relevant to music DSP and skipping the others. The other book of a similar direction (which I didn't read though) is the one by Will Pirkle. Apparently none of them get often suggested as intro texts. It would be interesting to hear your feedback, why this is not the case, what is missing, doesn't work etc.

Regards,
{Z}

I wouldn't recommend Will Pirkle's book. Terrible code and some bad maths/explanations as well. Haven't read the new synth one though.

matt42 · Post by **matt42** » Thu Jul 30, 2015 2:26 pm

Good sources for learning the theory in digital filter design