A band-pass filter is (usually) an electronic circuit that lets through frequencies between two other given frequencies. For example, an ideal bandpass filter would let through all signals above 30 Hz but below 100 Hz. All of the signal outside this range is attenuated or damped. See RLC circuit for basic theory regarding the frequencies passed.

It can be created by a combination of a low-pass filter and a high-pass filter. In practice, no bandpass filters are ideal and do not attenuate frequencies just outside the desired frequency range completely. There is generally a smooth and quick decrease in transmitted frequency outside the band. This is known as the roll-off, and is usually expressed in dB per octave.

In the atmospheric sciences, for example, it is common to band-pass filter the data with a period range of, say 3 to 10 days, so that only cyclones remain as fluctuations in the data fields.

Between the lower cutoff frequency f₁ and the upper cutoff frequency f₂ of a frequency band there is the center frequency f₀ or f_c.
It is only correctly calculated as the geometric mean:

Often a mistake is made in calculating the arithmetic mean as the passed band:

If, for instance, we are looking for the center frequency of the telphone audio band from 300 Hz to 3300 Hz, we get (3300 + 300) / 2 = "1800 Hz" for the false arithmetic mean calculation, but the root of 300 x 3300 = "995" Hz with the correct geometric mean formula.

The bandwidth of the filter is simply the difference between f₂ and f₁.

See also band-stop filter, passband.

External link

• Calculations and comparisons between the geometric mean and the arithmetic mean