In system theory, filters are systems that amplify, attenuate, or reshape the frequency content of input signals. They’re used widely in communications systems, instrumentation, audio, biomedical systems, etc.
Passive filters are composed of only resistors, inductors, or capacitors, as they cannot amplify signals. Active filters use active components, like op amps. Oftentimes these filters will include RC elements but no inductors.
Several common types of filters are:
Filters can be designed using LTI systems by choosing an appropriate frequency response. Any filters used in real-time applications should be causal. Ideal filters are able to anticipate input changes (because it is not causal) and perfectly remove certain frequency components. Real filters react only after the input changes (because it is causal) and attenuates the desired frequency component but cannot remove it.