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+1 for the recommendation for "The Scientist and Engineer's Guide to Digital Signal Processing" by Steven W. Smith. I spoke to Steven many years ago about his p

+1 for the recommendation for "The Scientist and Engineer's Guide to Digital Signal Processing" by Steven W. Smith. I spoke to Steven many years ago about his putting all of the book PDFs online for free and since then have recommended at least 5 university libraries to buy it because the students could get free copies of a great book that can be referenced in the library. FWIW the The Scientist and Engineer's Guide doesn't actually cover a lot on sound. It starts in a particular DSP way with frequency domain definitions and convolution - and I actually think Steven's background is in medial imaging, though I could be mistaken.

belkarx 4y ago
The book is amazing: http://www.dspguide.com/ http://www.dspguide.com/ (link for the lazy)
- sporkl 4y ago
  pdfs are the chapters are available freely on that website, but if anyone wants to spare themselves the effort of combining them all into one for easier perusal, feel free to email me (in bio) and I can send the combined pdf. I'm currently around page 200, and it's been great as an introductory resource as someone with no other background in DSP.
- ahaferburg 4y ago
  Here [1] I found a link [2] to download all chapters in one .zip file. [1] https://www.analog.com/en/education/education-library/scientist_engineers_guide.html https://www.analog.com/en/education/education-library/scient... [2] https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_dspguide.zip https://www.analog.com/media/en/technical-documentation/dsp-...
WhitneyLand 4y ago
Wow. Such a profound insight could not get published for 15 years because others couldn’t grasp it. Including Lagrange! It’s an uncomfortable reminder of how essential reputation and credibility are in the machinery of science. ”The paper contained the controversial claim that any continuous periodic signal could be represented as the sum of properly chosen sinusoidal waves. Among the reviewers were two of history's most famous mathematicians, Joseph Louis Lagrange (1736-1813), and Pierre Simon de Laplace (1749-1827). While Laplace and the other reviewers voted to publish the paper, Lagrange adamantly protested. For nearly 50 years, Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. The Institut de France bowed to the prestige of Lagrange, and rejected Fourier's work. It was only after Lagrange died that the paper was finally published, some 15 years later.“ from chapter 8 http://www.dspguide.com/ch8/1.htm http://www.dspguide.com/ch8/1.htm
- comboy 4y ago
  > Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. Isn't that true though? You can only approximate it, right?
  - AceJohnny2 4y ago
    In practice, yes you can only approximate it, because in theory it requires an infinite series of sinusoidal waves. But since maths is all about the theory, Laplace's objections were silly. (though I admit I don't know what the state of acceptance of infinite series was at that time) Also, it's fine to cut off the infinite series of sinusoidal waves because all physical systems cut off around a given frequency, for example human hearing around ~20kHz.
    - armadsen 4y ago
      Also, in practice, there's no such thing as a truly sharp corner, which makes sense intuitively based on the math, I think. But real systems have inertia, friction, stray resistance/capacitance/inductance, etc. so you can't have a truly perfect square wave in a physical or electrical system in the real world.
    - tuatoru 4y ago
      * Lagrange's objections
      - AceJohnny2 4y ago
        whoops! thanks. Too late to edit.
    - andrepd 4y ago
      Not quite, that's not the problem. We're in the realm of maths here and therefore of pure abstraction, so that's not the point. Adding terms to the Fourier series of a square wave you have an overshoot that does not converge to zero as the number of terms goes to infinity. This is called the Gibbs phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon
rectang 4y ago
I have this conviction that I ought to be able to code up crude audio DSP processors before I understand the totality of the theory. For example, every DFT/FFT explanation seems to start with complex numbers. I wish there was a resource that was programming focused, starting with "Step 1: Process this artificially created periodic signal by multiplying it by sine waves of frequencies from from 1 to N. There are our bins! Step 2: OK, for real world signals we need phase, so now let's talk about complex numbers." I've been studying math for a while trying to build up the prerequisites for writing audio DSP code. I have this sneaking suspicion that at the end what I want to achieve won't be as hard as DSP resources imply. At least there will be parts that I could have done with hardly any theory at all. But because of the way these resources are written, I have to consume massive amounts of theory first. (For background, I've worked as a mastering engineer and have done a fair amount of audio production, so I know intimately what the tools ought to do.)
- skybrian 4y ago
  I've been writing notebooks about doing DSP and audio processing in JavaScript. It might be a good place to crib off of: https://observablehq.com/collection/@skybrian/digital-signal-processing https://observablehq.com/collection/@skybrian/digital-signal...
  - laszlokorte 4y ago
    Wow, thank you very much! Straight to the point and very helpful, especially the web audio stuff.
- cannam 4y ago
  > "Step 1: Process this artificially created periodic signal by multiplying it by sine waves of frequencies from from 1 to N. There are our bins! Step 2: OK, for real world signals we need phase, so now let's talk about complex numbers." Maybe the latter part could be prepped by resynthesising the time-domain signal by summing the sines, and seeing that it doesn't match the original. And it can't, not least because all of the sines start at 0. But if you have cosines as well, it can. Then refer to the geometrical relationship between sine/cosine and phase. A preliminary to the earlier part might be to multiply a single long sinusoid by another one, and see what happens when their frequencies do or don't match. (But there is a whole well here about what it means for frequencies to "match", which in the discrete world has to do with how long the relevant part of the signal is.)
SonOfLilit 4y ago
It's one of my favorite technical books. So simply explained, so full of engineering wisdom.
voidhorse 4y ago
I'm actually reading through it right now after trying out a few other DSP resources. It is by far the clearest and most approachable, without sacrificing much depth at all. It's a great book.
- anigbrowl 4y ago
  It's the best. I learned DSP from that ~20 years ago and still use those mental models whenever I need to think through a problem. A good book like that is a friend for life.

belkarx 4y ago

The book is amazing: http://www.dspguide.com/ http://www.dspguide.com/ (link for the lazy)

sporkl 4y ago
pdfs are the chapters are available freely on that website, but if anyone wants to spare themselves the effort of combining them all into one for easier perusal, feel free to email me (in bio) and I can send the combined pdf. I'm currently around page 200, and it's been great as an introductory resource as someone with no other background in DSP.
ahaferburg 4y ago
Here [1] I found a link [2] to download all chapters in one .zip file. [1] https://www.analog.com/en/education/education-library/scientist_engineers_guide.html https://www.analog.com/en/education/education-library/scient... [2] https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_dspguide.zip https://www.analog.com/media/en/technical-documentation/dsp-...

WhitneyLand 4y ago

Wow. Such a profound insight could not get published for 15 years because others couldn’t grasp it. Including Lagrange! It’s an uncomfortable reminder of how essential reputation and credibility are in the machinery of science. ”The paper contained the controversial claim that any continuous periodic signal could be represented as the sum of properly chosen sinusoidal waves. Among the reviewers were two of history's most famous mathematicians, Joseph Louis Lagrange (1736-1813), and Pierre Simon de Laplace (1749-1827). While Laplace and the other reviewers voted to publish the paper, Lagrange adamantly protested. For nearly 50 years, Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. The Institut de France bowed to the prestige of Lagrange, and rejected Fourier's work. It was only after Lagrange died that the paper was finally published, some 15 years later.“ from chapter 8 http://www.dspguide.com/ch8/1.htm http://www.dspguide.com/ch8/1.htm

comboy 4y ago
> Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. Isn't that true though? You can only approximate it, right?
- AceJohnny2 4y ago
  In practice, yes you can only approximate it, because in theory it requires an infinite series of sinusoidal waves. But since maths is all about the theory, Laplace's objections were silly. (though I admit I don't know what the state of acceptance of infinite series was at that time) Also, it's fine to cut off the infinite series of sinusoidal waves because all physical systems cut off around a given frequency, for example human hearing around ~20kHz.
  - armadsen 4y ago
    Also, in practice, there's no such thing as a truly sharp corner, which makes sense intuitively based on the math, I think. But real systems have inertia, friction, stray resistance/capacitance/inductance, etc. so you can't have a truly perfect square wave in a physical or electrical system in the real world.
  - tuatoru 4y ago
    * Lagrange's objections
    - AceJohnny2 4y ago
      whoops! thanks. Too late to edit.
  - andrepd 4y ago
    Not quite, that's not the problem. We're in the realm of maths here and therefore of pure abstraction, so that's not the point. Adding terms to the Fourier series of a square wave you have an overshoot that does not converge to zero as the number of terms goes to infinity. This is called the Gibbs phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon

rectang 4y ago

I have this conviction that I ought to be able to code up crude audio DSP processors before I understand the totality of the theory. For example, every DFT/FFT explanation seems to start with complex numbers. I wish there was a resource that was programming focused, starting with "Step 1: Process this artificially created periodic signal by multiplying it by sine waves of frequencies from from 1 to N. There are our bins! Step 2: OK, for real world signals we need phase, so now let's talk about complex numbers." I've been studying math for a while trying to build up the prerequisites for writing audio DSP code. I have this sneaking suspicion that at the end what I want to achieve won't be as hard as DSP resources imply. At least there will be parts that I could have done with hardly any theory at all. But because of the way these resources are written, I have to consume massive amounts of theory first. (For background, I've worked as a mastering engineer and have done a fair amount of audio production, so I know intimately what the tools ought to do.)

skybrian 4y ago
I've been writing notebooks about doing DSP and audio processing in JavaScript. It might be a good place to crib off of: https://observablehq.com/collection/@skybrian/digital-signal-processing https://observablehq.com/collection/@skybrian/digital-signal...
- laszlokorte 4y ago
  Wow, thank you very much! Straight to the point and very helpful, especially the web audio stuff.
cannam 4y ago
> "Step 1: Process this artificially created periodic signal by multiplying it by sine waves of frequencies from from 1 to N. There are our bins! Step 2: OK, for real world signals we need phase, so now let's talk about complex numbers." Maybe the latter part could be prepped by resynthesising the time-domain signal by summing the sines, and seeing that it doesn't match the original. And it can't, not least because all of the sines start at 0. But if you have cosines as well, it can. Then refer to the geometrical relationship between sine/cosine and phase. A preliminary to the earlier part might be to multiply a single long sinusoid by another one, and see what happens when their frequencies do or don't match. (But there is a whole well here about what it means for frequencies to "match", which in the discrete world has to do with how long the relevant part of the signal is.)

SonOfLilit 4y ago

It's one of my favorite technical books. So simply explained, so full of engineering wisdom.

voidhorse 4y ago

I'm actually reading through it right now after trying out a few other DSP resources. It is by far the clearest and most approachable, without sacrificing much depth at all. It's a great book.

anigbrowl 4y ago
It's the best. I learned DSP from that ~20 years ago and still use those mental models whenever I need to think through a problem. A good book like that is a friend for life.