Filter Types and Descriptions

• Digital filter types are generally described in terms of their frequency magnitude response characteristic.

  Figure 2: Magnitude responses for several different filter types.

  

• Lowpass filters signficantly attenuate sinusoids above a certain “cutoff frequency” ($f_c$), ideally only passing frequency components below the cutoff.

• Highpass filters significantly attenuate sinusoids below a certain “cutoff frequency” and pass components higher than the cutoff.

• 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 $1/\sqrt{2} = 0.707$.

• Bandpass filters only pass sinusoids above and below a certain frequency region, while 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.