Don Romano (alt)
1) Okay, so I now *think* I know how to use transfer functions, i.e. those previously so mysterious "H(s) = foo / bar" things you always find on Wikipedia instead of actual explanations when you're looking for information about audio equalisation filters.
I knew that s was the frequency, but not much else.
Solution:
s can be substituted with jω where j is the imaginary unit and ω is angular frequency.
The output format is a phasor, from which you can derive an amplitude and a phase.
Don Romano (alt)
2) More specifically, any constant or coefficient x in a transfer function H(s) that isn't imaginary is taken as a complex number x+0i. In other words, you turn everything into complex numbers. Any arithmetic is taken to be complex arithmetic.
ω is in radians per second, so ω = 2πf, where f is the frequency in hertz.
Output x + yi can be taken as a phasor/vector where sqrt(x² + y²) encodes amplitude and atan2(y, x) encodes the phase in radians.
Don Romano (alt)
3) Kind of annoys the hell out of me that math people can't boil stuff down to the essentials. Most documentation for developers is far better than the crap math students have to contend with. If math was a programming language, who the hell would use it? If you think your language has unreadable syntax and bad documentation, try math.
Don Romano (alt)
4) I mean, I basically had to spend half a day to figure out the math I needed to learn how to calculate a transfer function and make a Bode plot from it, and I'm a stubborn motherfucker.
I'm trying to use mathy variable names in my code but I'm very tempted to just use verbose names instead because my source code is damn near unreadable with all these one-letter variable names, much like the math it came from...
Don Romano (alt)
5) Mathematicians also like to use confusing words. Take "conjugate", which means to negate the imaginary part of a complex number — a programmer would probably call that an iFlip().
Also, I kind of agree with Randall Munroe about complex numbers: They're just vectors for people who are too cool for vectors.
Yes, yes, Euler and Fourier/Laplace transforms, but come ooon, you can write that stuff out as cos/sin and vectors...
Don Romano (alt)
5) Mathematicians also like to use confusing words. Take "conjugate", which means to negate the imaginary part of a complex number — a programmer would probably call that an iFlip().
Also, I kind of agree with Randall Munroe about complex numbers: If you're too cool for vectors, you use complex numbers.
Yes, yes, Euler and Fourier/Laplace transforms, but come ooon, you can write that stuff out as cos/sin and vectors...
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