Lowpass filters do not allow sinusoids above a certain “cutoff frequency” (fc) to pass through them.
Highpass filters only allow sinusoids above a certain “cutoff frequency” to pass through them.
The cutoff frequency of a filter is defined as the frequency at which the power transmitted is 1/2 the maximum power transmitted in the passband. This corresponds to a -3dB drop on a decibel scale. As the power of a signal is related to its amplitude squared, the cutoff frequency corresponds to an amplitude reduction of
Bandpass filters only allow sinusoids above and below a certain frequency region to pass through them.
Bandstop filters are designed to pass all sinusoids except those within a certain frequency region.
Resonance filters accentuate sinusoids within a certain frequency region. They may or may not pass sinusoidal frequencies outside that region.
Resonance filters are typically described in terms of their center frequency and quality factor (Q), which is given by the center frequency divided by the -3dB bandwidth. A higher Q indicates a “sharper” resonance.
Allpass filters do not affect the magnitude characteristics of a signal (their magnitude response is equal to 1 for all frequencies) but have frequency-dependent phase characteristics.