Editing Center frequency (section)

{{Short description|Channel between upper and lower cutoff frequencies of a band system}}
[[File:Bandwidth 2.svg|300px|right|thumb|The frequency axis of this symbolic diagram may be linearly or logarithmically scaled. Except in special cases, the peak response will not align precisely with the center frequency.]]

In [[electrical engineering]] and [[telecommunications]], the '''center frequency''' of a filter or channel is a measure of a central frequency between the upper and lower [[cutoff frequency|cutoff frequencies]].  It is usually defined as either the [[arithmetic mean]] or the [[geometric mean]] of the lower cutoff frequency and the upper cutoff frequency of a [[band-pass filter|band-pass system]] or a [[band-stop filter|band-stop system]].

Typically, the geometric mean is used in systems based on certain transformations of [[lowpass filter]] designs, where the [[frequency response]] is constructed to be symmetric on a [[logarithmic scale|logarithmic]] frequency scale.<ref>{{cite book | title = CRC Handbook of Electrical Filters | author = John T. Taylor and Qiuting Huang | publisher = CRC Press | isbn = 0-8493-8951-8 | year =  1997| url =  https://books.google.com/books?id=HtyKSVF6zPsC&q=center+frequency+bandpass+%22geometric+mean%22&pg=PA57}}</ref> The geometric center frequency corresponds to a mapping of the DC response of the prototype lowpass filter, which is a [[resonant frequency]] sometimes equal to the peak frequency of such systems, for example as in a [[Butterworth filter]].

The arithmetic definition is used in more general situations, such as in describing [[passband]] [[telecommunication]] systems, where filters are not necessarily symmetric but are treated on a linear frequency scale for applications such as [[frequency-division multiplexing]].<ref>{{cite book | title = Fiber Optics Illustrated Dictionary | author = Julie K. Petersen | isbn = 0-8493-1349-X | year = 2003 | publisher = CRC Press | url = https://books.google.com/books?id=AcGFlqSqNEUC&q=center+frequency+bandpass+%22arithmetic+mean%22+fdm&pg=PA100}}</ref>