well one of the neatest things about math is the confluence of different analogies, right?

for whatever reason it’s easy for me to visualize complex sinusoids geometrically, as spirals in the c-plane, with real sin/cos projections. euler’s identity and the derivative relationship of the projections becomes clear.

and of course i’m well used to thinking of filters in terms of response function (complex phasor multiplied by complex polynomial of phasors.) it’s a little less natural to always reach for the matrix / convolution representation of the whole signal and its IR. (but then, i’m not really a mathematician!)

maybe this is because my early experiences with these things were with analog circuits, where in fact you often have *nonlinear* (saturation) elements in the integrator, and good luck getting the impulse response directly. vadim has to deal with this when he starts considering saturation in the SVF and ladder structures. (iirc he does it by polynomial approximation.)

anyways, in this vein here are two of my favorite mind-blowing books:

https://books.google.com/books/about/Visual_Complex_Analysis.html?id=ogz5FjmiqlQC

https://books.google.com/books/about/The_Road_to_Reality.html?id=csaaQgAACAAJ