There are 2 kind of filters:
- FIR (Finite Impulse Response) filter, which only use the value of the input now and the value on the past.
- IIR (Infinite Impulse Response), which use the value of the input now and in the past, and also the value of the past outputs.
FIR filters are easy to design for many applications, but them response are limited for a low order filters. On the other hand, with IIR filters, we can achieve more aggressive responses, but they have the disadvantage that the filter can be unstable in certain cases.
https://www.controlpaths.com/2022/05/09/frequency-warping-using-the-bilinear-transform/