A filter selectively processes input signals in frequency- or time-domain.
In frequency domain, a filter can be allpass, lowpass, highpass, bandpass, bandstop, or multiband, the depictive namings depending on the range of frequencies it lets through. Filters can be implemented with analog parts, or if the signal has been digitized, with digital parts such as DSPs and FPGAs. Time domain deals with the linearity of the phase, of minimizing group delay.
Digital filters can be Finite Impulse Response (FIR), which are inherently stable, or Infinite Impulse Response (IIR), which have feedback and can be unstable.