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

and

telecommunications Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...

, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies. It is usually defined as either the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results fr ...

or the

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

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 (waves), phase of the output as a function of input frequency. The frequency response is widely used in the design and ...

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 is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

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 B ...

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

passband A passband is the range of frequency, frequencies or wavelengths that can pass through a Filter (signal processing), filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all t ...

telecommunication Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...

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 (signal processing), bandwidth available in a communication channel, communication medium is divided into a series of non-overlapping freque ...

References

{{reflist

External links

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