electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

and

telecommunications Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...

, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower

cutoff frequencies In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather than ...

. It is usually defined as either the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the '' mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The co ...

or the

geometric mean In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...

of the lower cutoff frequency and the upper cutoff frequency of a band-pass system or a band-stop system. Typically, the geometric mean is used in systems based on certain transformations of lowpass filter designs, where the

frequency response In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of s ...

is constructed to be symmetric on a logarithmic frequency scale. The geometric center frequency corresponds to a mapping of the DC response of the prototype lowpass filter, which is a

resonant frequency Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...

sometimes equal to the peak frequency of such systems, for example as in a

Butterworth filter The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the ...

. The arithmetic definition is used in more general situations, such as in describing

passband A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...

telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...

systems, where filters are not necessarily symmetric but are treated on a linear frequency scale for applications such as

frequency-division multiplexing In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separat ...

References

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External links

Calculations and comparisons between the geometric mean and the arithmetic mean
Electrical engineering Telecommunication theory Frequency-domain analysis