Newbie here. I'm familiar with time and frequency domains from math. I think I understand what low and high pass filters do, sonically. But digging into an implementation of
tone in csounds, I think I'm missing something fundamental. Take this description:
A first-order recursive low-pass filter with variable frequency response.
tone is a 1 term IIR filter. Its formula is:
yn = c1 * xn + c2 * yn-1
b = 2 - cos(2 π hp/sr);
c2 = b - sqrt(b2 - 1.0)
c1 = 1 - c2
I see that there is a recurrence relation. But I'm reading about IIRs and filters in general I don't see any explanation of why it's there or what it does.
Would performing a single pass of this formula not be considered performing a "true" low or high pass filter?
Or is that it takes multiple passes (infinite, in theory) to completely "remove" the frequencies desiring to be removed, so it's a tradeoff between iterations versus computation?
I'm gravitating toward the latter, but I don't see where that is being said. Can someone point me to the essential statement of it on Wikipedia or somewhere?