I'm currently studying sound design, however over the past couple of years i started creating audio effects/instruments. I have also been programming in C++ for quite some years. I noticed my shortcomings though; i can design compressors, envelopes and simple stuff like additive synthesis quite well along with basic signal knowledge (like samplerates, nyquist theorem), however i don't understand the theory behind some of the more dense mathematical subjects like filter designs, transfer functions, fourier transforms, complex numbers, time/frequency domain etc., or even the mathematical notation of such.

Without sounding too oblivious, what are the relevant fields for educating one in such topics? Also, if anyone has some book recommendations for easy introduction to required math/basic signal theory i would be most grateful :)


closed as primarily opinion-based by endolith, lennon310, Naresh, Phonon May 13 '14 at 4:03

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

The following blog has download-able IPython notebooks that you can run and tinker with.


Lots of concepts covered that you can compute yourself using the scientific Python toolchain.

Good luck!

  • Thanks, that seems interesting, will definitely check it out! About time i installed python again, anyway – Shaggi Apr 21 '14 at 20:06

I think you might like Introduction to Signal Processing by Orfanidis. It's very practically oriented and it's freely available. It contains all the necessary basics of the topics that you've mentioned.

  • Thanks a lot, seems to be exactly what i was looking for! – Shaggi Apr 21 '14 at 20:07
  • i reviewed Orfanidis's book for the Journal of the Audio Engineering Society back in the 90s. it's good. another might be Richard Lyons Understanding DSP. – robert bristow-johnson Apr 22 '14 at 6:16

The math required before getting too far into DSP theory might include some trigonometry, analytic geometry, arithmetic of complex numbers, linear algebra, and basic integral calculus. For music, a introduction to differential equations might help explain the relationship between the complex exponential equations and the (simplified) physics of the stuff that creates musical sound.

  • I have most of those covered at a basic level.. Except for complex numbers, no idea about those. – Shaggi Apr 23 '14 at 7:14

I think it would be best for you to get acquainted first with basics of digital signal processing. How is analog signal converted to digital signal. About sampling frequency. Then you can start looking into fourier series and fourier transform. Study about delta functions. Try to get understanding of impulse response of system. Get some introduction to z transform and look into creating various types of filter with it.

Digital Signal processing by SK Mitra is a good book to start. You can also get great study material at dspguide.com

Personally i prefer the video lectures : http://nptel.ac.in/courses/117102060/

  • Thanks for the link! Didn't consider video lectures, seems like a good idea. – Shaggi Apr 23 '14 at 7:12

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