I appreciate the mention and demonstration of Fourier Transforms. It makes a lot of previous sound codec discussions click a bit more now.
Sound
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Re: Sound
#52Bartosz' blog posts are in a league of their own.
They way he is able to explain complex subjects by starting from first principles, gently adding more and more layers, with beautiful, custom-made figures and animations is truly, literally, awesome.
I strongly recommend supporting the author via his Patreon if you enjoy his blog posts.
Re: Sound
#53+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…
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 b…
> "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.)
Re: Sound
#54+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…
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 b…
I posted this as a submission a while ago but you might find it helpful. While learning about signal processing my self I built a collection of educational tools for visualizing some concepts. [1]
Especially the fourier cube [2], the complex exponential [3], the digital filter designer [4] and the signal generator [5] might be helpful.
Additionally the matrix multiplier [6] has an option for complex numbers that highlights the perspective that complex numbers can be seen as just a subset of 2x2 matrices.
[1]: https://tools.laszlokorte.de/ [2]: https://static.laszlokorte.de/fourier/ [3]: https://static.laszlokorte.de/complex-exponential/ [4]: https://static.laszlokorte.de/signal-transform/ [5]: https://static.laszlokorte.de/signal-generator/ [6]: https://static.laszlokorte.de/matrix-multiplication/
Re: Sound
#55Earlier quoted context omitted.
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…
> 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?
In the same sense that a circle does not exist, because you can only approximate it with an arbitrary number of points/lines. But an infinite number of points the same distance from the origin is a good definition of a circle. In a similar way, an infinite set of sine waves approximating a square wave is a square wave, mathematically speaking.
Re: Sound
#56I love it when I'm halfway through something and take a second to pause and wonder why someone put so much effort into it, and them I appreciate that they did. This is amazing. One thing that surprised me the first time I learned it is how 'dense' air is under normal circumstances. The 'mean free path' is the mean distance that a particle travels before changing velocity (typ due to collision). The mean free path of…
I was able to reach 10^-7 mbar with a good vacuum system and I though I would have few thousand molecules, turns out there is a billion (10^9) molecules per cubic centimeter at that vacuum level.
Re: Sound
#57Earlier quoted context omitted.
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 b…
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...
Wow, thank you very much! Straight to the point and very helpful, especially the web audio stuff.
Re: Sound
#58+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…
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 b…
Your intuition is right, in that most of the heavy math is simply unnecessary or irrelevant at the practical level. Complex number notation doesn't fall into that category, though. The notion of frequency is intimately tied to the notion of vector rotation, and just as you can't represent Cartesian translation without negative numbers, you can't represent Cartesian rotation without complex ones.
The Smith book is definitely for you; also check out Rick Lyons's books. Bo Pirkle and Julius O. Smith are good for audio-specific theory and applications.
Re: Sound
#59Bartosz' blog posts are in a league of their own. They way he is able to explain complex subjects by starting from first principles, gently adding more and more layers, with beautiful, custom-made figures and animations is truly, literally, awesome. I strongly recommend supporting the author via his Patreon if you enjoy his blog posts.
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Re: Sound
#60I love it when I'm halfway through something and take a second to pause and wonder why someone put so much effort into it, and them I appreciate that they did. This is amazing. One thing that surprised me the first time I learned it is how 'dense' air is under normal circumstances. The 'mean free path' is the mean distance that a particle travels before changing velocity (typ due to collision). The mean free path of…
Whilst I imagine he'd produce content regardless of income, he does have a slightly successful Patreon. To encourage this effort, consider supporting him in some form, if you don't.
Nice callout. Done.