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Ideal filters allow a specified frequency range of interest to pass through while attenuating a specified unwanted frequency range. The following filter classifications are based on the frequency range a filter passes or blocks:

• Lowpass filters pass low frequencies and attenuate high frequencies.
• Highpass filters pass high frequencies and attenuate low frequencies.
• Bandpass filters pass a certain band of frequencies.
• Bandstop filters attenuate a certain band of frequencies.

The following figure shows the ideal frequency response of each of the preceding filter types.

In the previous figure, the filters exhibit the following behavior:

• The lowpass filter passes all frequencies below f _c.
• The highpass filter passes all frequencies above f _c.
• The bandpass filter passes all frequencies between f _{c 1} and f _{c 2}.
• The bandstop filter attenuates all frequencies between f _{c 1} and f _{c 2}.

The frequency points f _c, f _{c 1}, and f _{c 2} specify the cut-off frequencies for the different filters. When designing filters, you must specify the cut-off frequencies.

The passband of the filter is the frequency range that passes through the filter. An ideal filter has a gain of one (0 dB) in the passband so the amplitude of the signal neither increases nor decreases. The stopband of the filter is the range of frequencies that the filter attenuates. The following figure shows the passband (PB) and the stopband (SB) for each filter type.

The filters in the previous figure have the following passband and stopband characteristics:

• The lowpass and highpass filters have one passband and one stopband.
• The bandpass filter has one passband and two stopbands.
• The bandstop filter has two passbands and one stopband.

In practical applications, ideal filters are not realizable.