Ideal Filters

Filters alter or remove unwanted frequencies. Depending on the frequency range that they either pass or attenuate, they can be classified into the following types:

The ideal frequency response of these filters is shown below.

You see that the lowpass filter passes all frequencies below fc, whereas the highpass filter passes all frequencies above fc. The bandpass filter passes all frequencies between fc1 and fc2, whereas the bandstop filter attenuates all frequencies between fc1 and fc2. The frequency points fc, fc1 and fc2 are known as the cut-off frequencies of the filter. When designing filters, you need to specify these cut-off frequencies.

The frequency range that is passed through the filter is known as the passband (PB) of the filter. An ideal filter has a gain of one (0 dB) in the passband so that the amplitude of the signal neither increases nor decreases. The stopband (SB) corresponds to that range of frequencies that do not pass through the filter at all and are rejected (attenuated). The passband and the stopband for the different types of filters are shown below.

Note that whereas the lowpass and highpass filters have one passband and one stopband, the bandpass filter has one passband and two stopbands, and the bandstop filter has two passbands and one stopband.