I posted a similar thread a few years back, and it seemed to come down to this book. I bought it, but it's pretty above my head and I haven't had the time to really try and delve in.
Have you looked into MaxMSP?
There's a lot of energy in Python right now and there's a great library http://ajaxsoundstudio.com/pyodoc/ which I use for quick testing, but on the synthesis side it looks great. PD is amazing and has a great history. I first ran into it 30 years ago! Yikes.
I do think rust has a lot that will eventually make it great for audio, but I'd suggest looking at PD/CSound/Supercollider/PYO to understand their APIs and the choices they make around runtime, organizing music rather than sound, etc. Very very different choices, all can work.
https://www.amazon.com/Audio-Programming-Book-MIT-Press/dp/0262014467
https://monoskop.org/images/d/d1/Roads_Curtis_Microsound.pdf
https://mitpress.mit.edu/9780262044912/the-computer-music-tutorial/
https://mitpress.mit.edu/9780262680516/foundations-of-computer-music/
Some classics.
My teacher in college, Dr. Richard Boulanger, has a book that might help: https://www.amazon.com/Audio-Programming-Book-MIT-Press/dp/0262014467
The Audio Programming Book, if you're interested in music: http://www.amazon.com/Audio-Programming-Book-Richard-Boulanger/dp/0262014467/ref=sr_1_1?ie=UTF8&qid=1452310130&sr=8-1&keywords=audio+programming
The other guys covered your specific filter question, so here's some general info on learning/implementing DSP via code. I don't know whether you're a programmer already or not, so if you're not, DSP is not a great way to learn C programming from the beginning. Basic DSP like your low-pass filter is not very demanding of more advanced programming skills, but it IS (relatively) hard to debug. I don't even want to imagine how awful debugging DSP output would be for a new programmer who's not yet sure his basic code even works properly. Much easier to learn C by writing some scrubby text output programs rather than staring at a huge pile of output floats.
If you're already comfy with C, you're just going to have to dig into some textbooks and work your way through them. Don't let them scare you. The math looks ugly, but it REALLY isn't! I highly recommend combining at least two sources for each topic.
http://www.dspguide.com/ is free and great for understanding what you're doing. Very little math, very heavy on explanations of how DSP works. Read the section on filters or whatever from this book first.
http://www.amazon.com/Audio-Programming-Book-Richard-Boulanger/dp/0262014467 is the math side of the same DSP topics + lots of actual C code implementations of each
If you make it through the pair all the way, you've pretty much got an entire foundation
More links:
The Audio Programming Book - highly recommended** to** me
Designing Audio Effect Plugins in C++
Some relevant stuff in this thread too
edit: I forgot an important one. Steinberg's VST SDK. Complete with example projects to get started with.
edit: basically people are saying Juce, WDL, Steinberg, C++. And lots of math.
Also this looks interesting coming from a java point of view: Java VST Wrapper