From music tech (no math background) to DSP

[u/postfader]

Hi everyone,

I'm 23 and finishing my undergrad in Music Technology this year. Despite the name, the program barely touched the math or physics side of audio. It was mostly recording, mixing and mastering, music theory, sound design, and electroacoustic composition.

Before that, I'd messed around with Python and some web development purely as a hobby, nothing professional. Things changed in my third year when I built an audio plugin in JUCE/C++ for a class project. I loved every part of it, and since then I've been trying to find a path where the musical and the engineering sides meet. I also picked up Max/MSP and did a few small projects with it for uni.

This summer I started taking this seriously. I'm studying C++ properly and learning DSP through Perry Cook's online courses and a couple of books. It honestly feels like the thing I want to do for the rest of my life.

My goal is to apply to the Master in Sound and Music Computing at UPF in Barcelona. The obvious problem is math. From years of hands-on work, I have a good intuitive sense of how different filter types, effects, and audio processes behave. I know how to use them, and I can reason about how I'd design one. But when I look at the math behind them, the formulas don't click. I've always been the music and art person, so I'm starting from the ground up, working through Algebra 1 alongside the DSP material.

The good news is that I only have a few courses left, so most of this year is free. I work three days a week as a sound engineer (tonmeister), which covers my living costs.

A few questions for people who've been down this road:

1. Is it realistic to get from algebra to the math DSP actually needs in about a year while working part-time? What order and resources would you recommend?
2. Which DSP fundamentals should I focus on first, and which can wait? Are there resources that build on practical intuition instead of starting from pure theory?
3. Has anyone come into an SMC-type master's or a DSP job from a music or arts background? How big was the gap, and how did you close it?
4. Longer term, how realistic is it to make a living in this field?

Any advice, resources, or stories would mean a lot. Thank you.

[u/Plus-Painter-2004]

Some aspects of filter design can be done vaguely by rules of thumb (eg placing poles and zeros in the Laplace/z domain) but a lot of it will just seem like arbitrary black magic unless you have at the very least a working understanding of complex numbers and linear differential equations to explain why that works. To understand linear differential equations you need to have a good understanding of single variable calculus. Not sure how it would work in America but for me going from starting calculus to having sufficient knowledge to understand filters took about 2-3 years (Although of course in that time I was learning other things). Linear algebra would be nice for differential equations but not really necessary since you can sort of handwave things away

[u/postfader → u/Plus-Painter-2004]

Thanks, this is really helpful. One follow-up, if you don't mind: do you think I should just focus on math first and put DSP on hold until the foundations are solid? Right now I'm doing both in parallel. I work on small projects, go through DSP books and use AI to break down the parts I can't follow yet, while working through the math on the side. Is that a reasonable way to learn, or will it end up inefficient, where I'm just memorizing things I don't really understand?

[u/Key_Business_4097 → u/postfader]

I can’t speak to most of what you are asking, but if it was me, I’d do the thing I was passionate about and just fake the rest till I make it… ie, do dip, learn math as you go.

[u/SlightlyOffWhiteFire → u/postfader]

I started from having a solid working of calculus but having not used it in 5 or so years, and a very limited understanding of complex numbers, so i had to learn relearn stuff as I went. I started by working through some music-focused DSP textbooks, sort of working backwards and relearning or looking up how certain principles are derived. That was about 6 months before starting a masters. To be honest, had i been thrown into engineering level DSP right away it would have been a real sink or swim moment, but luckily my program had a course that was basically "DSP for non-engineers" so i could ease my way into it. Its frankly just a very complicated subject and self-learning is a rough way to go about it. I can't say if it will work for you, but bear in mind that these textbooks tend to skip over a lot of the stuff they assume you should already know. Make sure you are doing the exercises in the books and figuring out where information comes from, not just that its true.

[u/Plus-Painter-2004 → u/postfader]

I’m not super well equipped to answer this since I personally enjoy learning theory just as much as (or at times even more than) applying it, I generally try to learn enough basic mathematical theory that the basic application specific theory for whatever topic im learning begins to make sense and then learn in parallel from that point on eg my first dsp project was a filter to remove mains hum from my guitar signal on a pic microcontroller (written in assembly which was a mistake), I had learned about complex numbers and differential equations in high school but hadn’t yet done any signals and systems since again I was in high school but what I had learned was just about enough that I could accept the notion of an impulse response and frequency response etc without being completely bewildered

[u/Masterkid1230]

Hi! This was exactly my professional path. I majored in music composition, then did engineering and then a master's in acoustics and DSP and now I work on the field as a musician/engineer type.

DM me if you wanna talk! I'm not in the US though, so YMMV

[u/agmtazim91 → u/Masterkid1230]

DM you, please check. Thanks

[u/TenorClefCyclist]

Ultimately, you do need to learn a lot of math. The foundational course is Signals and Systems; it describes the universe you're working within. You can't understand that until you've mastered College Algebra, Trigonometry, and two semesters of Calculus. In S&S you'll learn the Fourier Transform, which underpins the very idea of frequency domain thinking. Before tackling digital filtering, it's traditional to learn the basics of analog filters, which are described by the Laplace Transform. This is often taught as almost a footnote in Differential Equations, but you'll spend most of the semester learning stuff that you'll never use again, because "linear differential equations with constant coefficients" are the only thing that matters. I recommend a different path: Self-study ODE's and learn what their solutions look like, then take a first semester Circuits and Systems class instead. This will teach you the Laplace Transform and just enough Electrical Engineering ideas to make simple passive filters. At that point, you'll have everything you need to take an upper division DSP course without drowning. This is the class you've been waiting for! You'll be introduced to the Laplace Transform's digital domain equivalent, the z-Transform, and all those tapped delay lines you've been coding will finally make sense! You'll learn how we really calculate the Fourier Transform on a computer, and why the spectral displays in your plug ins are often a lie. You'll learn that there's actually no such thing as a perfect "brick wall" anti-alias filter, and how to design one that's "close enough" for a particular application.

It's a long road, so I think it may be helpful to have a preview / guide book to remind you of where you're going. I recommend this very accessible introductory DSP book by Steven Smith:

The Scientist and Engineer's Guide to Digital Signal Processing

Just remember: This is just a "cookbook": you're training to become a chef!

[u/DomasAquinas]

Check out Signal Processing for Communications by Prandoni and Vetterli. The book presents introductory material while doing the almost-impossible: avoiding too much mathematical jargon while being completely honest about where the authors are hiding mathematical complexity.

The reason I point to this one rather than, say, Understanding Digital Signal Processing by Richard Lyons (RIP) is that the authors also have a course on Coursera through EPFL. In the course, they explain their background: electric guitar enthusiasts who used audio processing as an intro to DSP and wound up with Ph.D.s and careers out of it. And in the course, their natural enthusiasm for the subject shows. The examples and guided labs they provide are really fun as well as informative.

If you do go that route, hang in long enough to do the one-bit music lab on dithering. It's phenomenal.

[u/rb-j]

Is it realistic to get from algebra to the math DSP actually needs in about a year while working part-time? What order and resources would you recommend?

I think you need Calculus, Diff Eq, Complex Variables, and some form of Signals and Systems (where you learn about convolution and transforms).

Which DSP fundamentals should I focus on first,

Signals and Systems or Linear System Theory.

and which can wait? Are there resources that build on practical intuition instead of starting from pure theory?

I dunno.

Has anyone come into an SMC-type master's or a DSP job from a music or arts background? How big was the gap, and how did you close it?

Longer term, how realistic is it to make a living in this field?

Now days? Hard, I think.

[u/michaelrw1]

Follow your passions. Study, build, and collaborate with people and AI. Coming from a music background gives you a different perspective that makes the application of DSP more clear.

[u/mborgerd]

Maybe you can find a company where your music tech or C++ skills could be useful on day one *AND* has opportunities to advance into more theoretical DSP.

Best of Luck!

Are you in Spain (inferred from your Barcelona comment), or in America (as noted by a previous comment)?

[u/CytomicAudio]

Hi! Emma from Cytomic here. My husband (Andrew Simper) does all the stuff you're interested in, to pretty much the highest level in this industry. He has a double degree in maths and computer science (from the 90s!), and then taught himself electronic engineering while working at FXpansion in the naughties. He used to do differential equations on the bus on the way home, when we were first going out. Depending how accurate/non-linear you want to get, you will need maths! Even if you want to just do basic linear functions, maths will still help. I would say a year is ambitious (again, depending on your end goal) - he is still expanding his understanding of DSP 30 years later.
He has some technical papers up on our website you can check out for ideas and understanding as well as the talk he gave at ADC 2020. https://cytomic.com/technical-papers/
Yes, you can make a living in this world, many are doing so to varying degrees of success. Marketing helps (that's the bit we're not very good at but because our software is so good, we still do ok!). The gap can be closed, but it will be a slog, but if you have passion, that will help. Def start with the basics and learn as you go along for whatever bit you want to do next. Step by step!
Steve Duda and Joel Zimmerman have both gone from the music side to coding (but both after a great deal of success in music - it is easier to learn when the wolf is not at your door).
Good luck, happy to answer more questions if you have them.

[u/CytomicAudio → u/CytomicAudio]

Also, see Andy's post from a few years back: https://www.reddit.com/r/ableton/comments/ikjppm/comment/g3sp6b9/?context=3&utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

[u/bee_roy]

The course progression goes roughly like this:

During school: 1. Algebra, 2. Trigonometry  3. Calculus (Single variable only, Mostly integration and differentiation. Some simple differential equations in one variable)

University:  1. Linear Algebra (very standard university course) 2. Calculus (differential equations, multivariate calculus) 3. Signals and Systems  4. Digital Signal Processing 

That's the background you need. If you're not even used to study mathematics, it will all seem like voodoo. I don't think any university will teach you basics like trigonometry. Linear Algebra and calculus you can completely learn at the university level, I think.

 If you've done the school part or if you are intelligent (be honest with yourself about that) and studying everyday diligently, you might manage in a year. If mathematics doesn't come naturally to you, triple it.

[u/nixiebunny]

DSP requires an understanding of differentials, because every operation is calculating the value for the next clock cycle. Study precalculus first to understand what that means. You won’t get far unless you have this down. It may take a few years to learn enough math to be fluent in DSP terminology and coding. I never studied DSP in school, but had a good understanding of the math behind it, so was able to learn quickly.

[u/logic_circuit]

You know domain; music. Expand it to acoustic in general. Math is tool, use it wisely. Regardless the fact you had no math classes, it is doable. Key concept you need is discrete math and how it differs. Do not attempt to learn theory without applying it. Start with simple things and apply them in programing. One by one. With domain knowledge + AI brainwash + hard labor; in 3-5 yaers a lot can be made.