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Comment by dceddia | Hacker News Reader

I’ve wanted to learn more about DSP for a while and recently started working through The Scientist and Engineer’s Guide to DSP [0] and it’s been fantastic. It’s much heavier on explanations and lighter on math equations than other books or courses I’d seen previously. It’s helping me build some real intuition around this stuff.

That book plus this article’s excellent explanations really helped things click for me and I’m very grateful to both authors!

0: https://www.dspguide.com/

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I've been trying to figure out how to make IIR filters for a software modular synth, off and on for years now. (Basically, given parameters like cutoff frequency and dB per octave rolloff, how do I find the filter coefficients? There must be closed-form functions for this buried inside VCV Rack, Audacity, and LMMS somewhere, but the code is hard to follow. I don't know how all the Wikipedia articles and DSP guides manage to skip over this step, the only step I don't understand. Some of them even punt to "Call this Matlab function" or "Use this PHP page that generates C code for you" Bleh!)

I did encounter this book, but it still couldn't help me figure it out. I bookmarked it to try again.

I've had similar struggles. I found this comparison between Ableton's EQ Eight and Pro-Q by Dan Worrall [1] to be incredibly (and unexpectedly) informative on the subject. He is a very good teacher and an expert in the area. Maybe it might on your journey.

[1]: https://www.youtube.com/watch?v=ebBqP2PteAQ (be sure to watch from 15min+ onwards but the entire thing is a treat)

First: cutoff, resonance, filter slope, etc., can be built with FIR (finite impulse response) filters. You can describe the passive circuit with a transfer function, which can be implemented in DSP using a z-transform. You can also describe a filter with poles and zeroes, and transform those. There's a bunch of resources on the web, e.g. https://ccrma.stanford.edu/~jos/filters/, but many assume you know something of electronics.

Recurrent filters don't have closed form solutions, and their implementation is a bit of an art. Plugin maker Urs Heckmann (from u-he.com) did a (rather successful) attempt at modeling the filter from an old synth with various implementations, and let people test them in the wild. He blogged about it, but I can't find all relevant posts. This might be a starting point: https://urs.silvrback.com/zero-delay-feedback

This course (https://www.staff.ncl.ac.uk/oliver.hinton/eee305/) is based on a book and links to the chapters, but there's a lot more (check the websites of MIT or Stanford's EE department for online courses).

These are the formulas you want:

https://webaudio.github.io/Audio-EQ-Cookbook/Audio-EQ-Cookbo...

They are the classic IIR biquads. If you want steeper filters, just run multiple equal filters in series (high-order IIRs are prone to numeric instability).

A more modern formatted version exists at e.g. https://www.w3.org/TR/audio-eq-cookbook/ .

Conditioned on what you want to achieve, I would suggest against, strongly against, or very strongly against avoiding (applied) mathematics.

In any case, I suggest flipping through the IEEE Signal Processing Magazine [1] and reevaluating your learning path.

[1] https://signalprocessingsociety.org/publications-resources/i...

Can you elaborate on why you so strongly advise against it?

I can only invite you to flip through current technical texts in signal processing and go through the thought exercise of defining the envelope of prior knowledge required.

I recommend the IEEE Signal Processing Magazine as it is the flagship magazine from the IEEE Signal Processing Society. IEEE magazine articles are written “to appeal to non-experts as well as experts in the field” [1] and therefore target a broad engineering audience while remaining current and being peer-reviewed.

[1] https://magazines.ieeeauthorcenter.ieee.org/get-started-with...

I'd say my goal is not so much about avoiding math but more about learning intuition-first rather than equations-first. Top-down vs. bottom-up, maybe. Most of material that I've encountered about math-heavy stuff tends to do the latter.

I imagine there are many people who're great at picking apart an equation and deriving things from first principles; but for me, I find it more manageable to get the big picture first, visualize what's going on, and then finally learn the math behind it. So far the DSP Guide book is doing a great job of presenting things that way.

Another good example of this kind of style is https://betterexplained.com/ (some of their articles are great companions to these DSP topics actually!)

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