i'm in a similar boat, never bothered with filter design, costs money for books and good open source. however,
check with smashed transistors posts on complex oscillators
either the complex oscillator, or the quadrature oscillator - "same thing" but the gimpy efficient version i am fond of -
s0 -= f * s1;
s1 += f * s0;
(people say it's "not quite circular" but it outputs a perfect sine and circle if you take the half step)
...both of these can be turned into filters instead of oscillators if you modify them (see smashed transistors notes) by: adding an input, and adding some kind of gain coefficient.
because they have two states, they are resonant filters, but bandpass.
because they use w (2*pi*f/fs) or "angular frequency" they're easy for a beginner to wrap their head around.
not only is this perfect lovely bit of dsp ("ginsu dsp, it filters, it oscillates") a nice way to start thinking about filters, the difference between my efficient form and the slightly less efficient complex oscillator (same thing as 2d geometric matrix rotation) is an expression of zero delay filter versus non-zero delay filter
of course, when i say "ginsu dsp" around here, people act like i am rude and don't know anything. one day they'll apologise and be really sorry when i am dead and send a nice card i know it.
(Edit: Oh, and the audio output would be sin or tri)
